We have recently proposed and developed a multiobjective approach to training classification systems. In this approach, the objectives, i.e., the sensitivity and specificity, of a classifier are simultaneously optimized, resulting in a series of solutions that are equivalent in the absence of any a priori knowledge regarding the relative merits of the two objectives. These solutions form a receiver operating characteristic (ROC) curve that is, theoretically, the best possible ROC curve that can be obtained using the given classifier and given training dataset. We have applied this technique to the optimization of classifiers for the computerized detection of mass lesions in digitized mammograms. Comparisons will be made between the results obtained using the multiobjective approach and results obtained using more conventional approaches. We employed a database of 60 consecutive, non-palpable mass lesion cases. Features relating to the geometry, intensity, and gradients of the images were calculated for each visible lesion and for many false detections. Using a conventionally trained linear classifier we were able to achieve an A_z of 0.84 while the multiobjective approach to training a linear classifier yielded an A_z of 0.87 in the task of distinguishing between true lesions and false detections. Using a multiobjective approach to train a rule-based classifier with 5 thresholding rules resulted in an A_z of 0.88 in the task of distinguishing between true lesions and false detections.

A constraint satisfaction neural network (CSNN) has been developed for breast cancer diagnosis from mammographic and clinical findings. CSNN is a circuit network aiming to maximize the activation of its nodes given the constraints existing among them. The constraints are built into the network weights. An autoassociative backpropagation (auto-BP) learning scheme is initially used to determine the CSNN weights. During the training phase, the auto-BP learns to map any given pattern to itself. During the testing phase, the CSNN is applied to new cases. The CSNN weights remain fixed (as determined by auto-BP) but the activation levels of the nodes are modified iteratively to optimize a goodness function. The medical findings act as the external inputs to the corresponding nodes. For every test case, CSNN tries to reconstruct the diagnosis nodes given the network constraints and the external inputs to the network. The activation levels achieved by the target nodes are used as decision variables for further analysis. Our CSNN was successfully applied on 500 patients with biopsy confirmed diagnosis. The CSNN was also used as an associative memory simulating dynamic scenarios for prototype analysis in our database.

We propose a method for detection of masses in mammographic images that employs pyramidal or hierarchical decomposition and Gaussian filtering operations as pre-processing steps. A procedure is then developed to segment the mass portions by establishing gradual intensity links from the central portions of masses into the surrounding areas in the image. The proposed mass detection algorithm was tested with 39 cases (28 benign and 11 malignant) selected from the Mammographic Image Analysis Society database. The technique achieved a success rate of 91% in detecting the malignant tumors and 68% in detecting the benign masses in the test set. The segmented mass portions were evaluated in terms of their benign versus malignant discriminant capabilities by computing two gradient- based features and texture features based on gray-level co- occurrence matrices (GCMs). The features were computed using a ribbon of pixels across the mass boundaries. The GCM-based texture features in combination with the gradient-based features resulted in the best benign versus malignant classification of the mass regions segmented by the proposed algorithm, with an area of 0.84 under the receiver operating characteristics curve.

Mammography is recognized as an important means to reduce breast cancer mortality. However, its accuracy is limited, both in sensitivity (some cancers are missed) and specificity (many non-cancer cases are referred for invasive procedures). It has been shown that computer classification of expert radiologist's findings can improve the specificity of mammography. Our project is aimed at automatically extracting measurements by computer analysis of digital mammograms, so as to provide automatic inputs for a benign/malignant classifier. We tested classification of radiological findings and found an area under the ROC curve of 0.95, comparable to what has been reported in the literature. Image measurements were taken from manual segmentations of lesions as well as from two different automatic segmentations. We found that segmentation using a fuzzy clustering method with some post-processing gives results comparable to results on manual outlines with a positive predictive value of 73%. The fuzzy clustering strategy has the potential to provide fully automatic classifications comparable to those based on expert radiological findings. This approach may dramatically reduce the false alarm rate currently seen in screening mammography.

The General Regression Neural Network (GRNN) is well known to be an extremely effective prediction model in a wide variety of problems. It has been recently established that in many prediction problems, the results obtained by intelligently combining the outputs of several different prediction models are generally superior to the results obtained by using any one of the models. An overseer model that combines predictions from other independently trained prediction models is often called an oracle. This paper describes how the GRNN is modified to serve as a powerful oracle for combining decisions from four different breast cancer benign/malignant prediction models using mammogram data. Specifically, the GRNN oracle combines decisions from an evolutionary programming derived neural network, a probabilistic neural network, a fully- interconnected three-layer, feed-forward, error backpropagation network, and a linear discriminant analysis model. In all experiments conducted, the oracle consistently provided superior benign/malignant classification discrimination as measured by the receiver operator characteristic curve Az index values.

We are developing a computerized approach to characterize pulmonary nodules through quantitative analysis between sequential 3-D thoracic images. In this approach the registration procedure of sequential 3-D pulmonary images consisted of two transformation steps: the rigid transformation step between two sequential 3-D thoracic CT images and the affine transformation step between two sequential region-of-interest (ROI) images including the pulmonary nodule. In both transformation step, the normalized mutual information was used as a voxel-based similarity measure. After the registration procedure, the 3-D pulmonary nodule image was segmented from the ROI image by a deformable surface method. The curvatures of each voxel in the nodule were computed directly from the gray-level 3-D image. Through curvatures a local description of the lesion was obtained by using shape index, curvedness, and CT value. Based on this local description of the nodule, the evolution of geometrical parameters was tracked through the time interval. Additionally, to characterize globally the evolution of the local description, the shape and the curvedness spectra were introduced. The interval changes of the lesion were traced in the feature spaces. The application results of our method to the sequence of 3-D thoracic images demonstrated that the interval changes of pulmonary nodules could be made visible.

We have developed a novel method called local contralateral subtraction for reduction of false positives reported by a computer-aided diagnosis (CAD) scheme for detection of lung nodules in chest radiographs. Our method is based on the removal of normal structures in the regions of interest (ROIs), based on symmetry between the left and right lungs. In our method, two ROIs were extracted, one from the position where a candidate of a nodule is located, and the other from the anatomically corresponding location in the opposite lung, which contains similar normal structures. We employed a wavelet-based multiresolution image registration method to match the two ROIs, and subtraction was performed. A signal- to-noise ratio (SNR) between a central region and the adjacent background region was calculated for quantification of the remaining structures in the subtracted ROI. The SNR was then used for distinction between nodules and false positives. In an analysis of 550 ROIs consisting of 51 nodules and 499 false positives reported as detected nodules by our current CAD scheme, we were able to eliminate 44% of false positives with loss of only one nodule with this new method. This result indicates that our new method is effective in reducing false positives due to normal anatomic structures, and thus can improve the performance of our CAD scheme for detection of pulmonary nodules in chest radiographs.

We are developing an automated method to analyze the three- dimensional nature of structures within CT scans and identify those structures that represent lung nodules. The set of segmented lung regions from all sections of a CT scan forms a segmented lung volume within which multiple gray-level thresholds are applied. Contiguous three-dimensional structures are identified within each thresholded lung volume, and structures that satisfy a volume criterion constitute an initial set of nodule candidates. A feature vector is then computed for each nodule candidate. A rule-based scheme is applied to the initial candidate set to reduce the number of nodule candidates that correspond to normal anatomy. Feature vectors for the remaining candidates are merged through an automated classifier to further distinguish between candidates that correspond to nodules and candidates that correspond to normal structures. This automated method demonstrates promising performance in its ability to detect lung nodules in CT images. Such a technique may assist radiologists evaluate, for example, images from low-dose, screening thoracic CT examinations.

The development of computer assisted diagnosis systems for image-patterns is still in the early stages compared to the powerful image and object recognition capabilities of the human eye and visual cortex. Rules have to be defined and features have to be found manually in digital images to come to an automatic classification. The extraction of discriminating features is especially in medical applications a very time consuming process. The quality of the defined features influences directly the classification success. Artificial neural networks are in principle able to solve complex recognition and classification tasks, but their computational expenses restrict their use to small images. A new improved image object classification scheme consists of neural networks as feature extractors and common statistical discrimination algorithms. Applied to the recognition of different types of tumor nuclei images this system is able to find differences which are barely discernible by human eyes.

After Cataract surgery where a plastic implant lens is implanted into the eye to replace the natural lens, many patients suffer from cell growth across a membrane situated at the back of the lens which degrades their vision. The cell growth is known as Posterior Capsule Opacification (or PCO). It is important to be able to quantify PCO so that the effect of different implant lens types and surgical techniques may be evaluated. Initial results obtained using a neural network to detect PCO from implant lenses are compared to an established but less automated method of detection, which segments the images using texture segmentation in conjunction with co- occurrence matrices. Tests show that the established method performs well in clinical validation and repeatability trials. The requirement to use a neural network to analyze the implant lens images evolved from the analysis of over 1000 images using the established co-occurrence matrix segmentation method. The work shows that a method based on neural networks is a promising tool to automate the procedure of calculating PCO.

We evaluated the practical application of a Computer-Aided Diagnosis (CAD) system for viewing spiral computed tomography (CT) of the chest low-dose screening examinations which includes an automatic detection of pulmonary nodules. A UNIX- based CAD system was developed including a detection algorithm for pulmonary nodules and a user interface providing an original axial image, the same image with nodules highlighted, a thin-slab MIP, and a cine mode. As yet, 26 CT examinations with 1625 images were reviewed in a clinical setting and reported by an experienced radiologist using both the CAD system and hardcopies. The CT studies exhibited 19 nodules found on the hardcopies in consensus reporting of 2 experienced radiologists. Viewing with the CAD system was more time consuming than using hardcopies (4.16 vs. 2.92 min) due to analyzing MIP and cine mode. The algorithm detected 49% (18/37) pulmonary nodules larger than 5 mm and 30% (21/70) of all nodules. It produced an average of 6.3 false positive findings per CT study. Most of the missed nodules were adjacent to the pleura. However, the program detected 6 nodules missed by the radiologists. Automatic nodule detection increases the radiologists's awareness of pulmonary lesions. Simultaneous display of axial image and thin-slab MIP makes the radiologist more confident in diagnosis of smaller pulmonary nodules. The CAD system improves the detection of pulmonary nodules at spiral CT. Lack of sensitivity and specificity is still an issue to be addressed but does not prevent practical use.

As a strategic move toward improving the utility of computer- aided diagnosis (CAD) in breast cancer detection, this work aims to develop a computer-based decision support system, through a visual mapping of featured database, to explain the entire decision making process jointly by the computer-encoded knowledge and the user-interaction. The main purpose of the work is twofold: enhance the clinical utility of CAD and provide a mechanism for optimal system design. We adopt a mathematical feature extraction procedure to construct the featured database from the suspicious mass sites localized by the enhanced segmentation. The optimal mapping of the data points is then obtained by learning a hierarchical normal mixtures and associated decision boundaries. A visual explanation of the decision making is further invented through a multivariate data mining and knowledge discovery scheme. In particular, using multiple finite normal mixture models and hierarchical visualization spaces, new strategy is that the top-level model and projection should explain the entire data set, best revealing the presence of clusters and relationships, while lower-level models and projections should display internal structure within individual clusters, such as the presence of subclusters, which might not be apparent in the higher-level models and projections. We demonstrate the principle of the approach on several multimodal numerical data sets, and we then apply the method to the visual explanation in CAD for breast cancer detection from digital mammograms.

We previously developed a computerized method to classify mammographic masses as benign or malignant. In this method, mammographic features that are similar to the ones used by radiologists are automatically extracted to characterize a mass lesion. These features are then merged by an artificial neural network (ANN), which yields an estimated likelihood of malignancy for each mass. The performance of the method was evaluated on an independent database consisting of 110 cases (60 benign and 50 malignant cases). The method achieved an A_z of 0.91 from round-robin analysis in the task of differentiating between benign and malignant masses using the computer-extracted features only. As the most important clinical risk factor for breast cancer, age achieved a performance level (A_z equals 0.79) similar to that (A_z equals 0.77 and 0.80) of the computer-extracted spiculation features, which are the most important indicators for malignancy of a mass, in differentiating between the malignant and benign cases. In this study, age is included as an additional input feature to the ANN. The performance of the scheme (A_z equals 0.93) is improved when age is included. However, the improvement is not found to be statistically significant. Our results indicated that age may be a strong feature in predicting malignancy of a mass. For this database, however, the inclusion of age may not have a strong impact on the determination of the likelihood for a mammographic mass lesion when the major mammographic characteristics (e.g., spiculation) of a mass are accurately extracted and analyzed along with other features using an artificial neural network.

An evolutionary programming (EP) technique was investigated to reduce the complexity of artificial neural network (ANN) models that predict the outcome of mammography-induced breast biopsy. By combining input variables consisting of mammography lesion descriptors and patient history data, the ANN predicted whether the lesion was benign or malignant, which may aide in reducing the number of unnecessary benign biopsies and thus the cost of mammography screening of breast cancer. The EP has the ability to optimize the ANN both structurally and parametrically. An EP was partially optimized using a data set of 882 biopsy-proven cases from Duke University Medical Center. Although many different architectures were evolved, the best were often perceptrons with no hidden nodes. A rank ordering of the inputs was performed using twenty independent EP runs. This confirmed the predictive value of the mass margin and patient age variables, and revealed the unexpected usefulness of the history of previous breast cancer. Further work is required to improve the performance of the EP over all cases in general and calcification cases in particular.

Design of a generalized technique for medical image segmentation is a challenging task. Currently a number of approaches are being investigated for 2-D and 3-D medical image segmentation for diagnostic and research applications. The methodology used in this work is aimed at obtaining a generalized solution of non-convex optimization problems by including a structural constraint of mass or density and the concept of additivity properties of entropy to a recently developed statistical approach to clustering and classification. The original computationally intensive procedure is made more efficient both in processing time and accuracy by employing a new similarity parameter for generating the initial clusters that are updated by minimizing an energy function relating the image entropy and expected distortion. The application of the computationally intensive yet generalized solution to nonconvex optimization to a limited set of medical images has resulted in excellent segmentation when compared to other clustering based segmentation approaches. The addition of the parametric approach to determine the initial number of clusters allows significant reduction in processing time and better design of automated segmentation procedure. This research work generalizes a deterministic annealing i.e. a specific statistical approach to solve nonconvex optimization problems by developing a more efficient technique applicable to nonconvex optimization problems (getting trapped in local minima). However, the DA approach is extremely computationally intensive for applications such as image segmentation. The new integrated approach developed in this work allows this optimization technique to be used for medical image segmentation.

The National Library of Medicine has archived a collection of 17,000 digitized x-rays of the cervical and lumbar spines. Extensive health information has been collected on the subjects of these x-rays, but no information has been derived from the image contents themselves. We are researching algorithms to segment anatomy in these images and to derive from the segmented data measurements useful for indexing this image set for characteristics important to researchers in rheumatology, bone morphometry, and related areas. Active Shape Modeling is currently being investigated for use in location and boundary definition for the vertebrae in these images.

Thresholding is a popular image segmentation method that converts a gray level image into a binary image. The selection of optimum thresholds has remained a challenge over decades. Besides being a segmentation tool on its own, often it is also a step in many advanced image segmentation techniques in spaces other than the image space. Most of the thresholding methods reported to date are based on histogram analysis using information-theoretic approaches. These methods have not harnessed the information buried in image morphology. Here, we introduce a novel thresholding method that accounts for both intensity-based class uncertainty -- a histogram-based property -- and region homogeneity -- an image morphology- based property. The idea here is to select the optimum threshold at which pixels with high class uncertainty accumulate mostly around object boundaries. To achieve this, a new threshold energy criterion is formulated using class- uncertainty and region homogeneity such that, at any image location, a high energy is created when both class uncertainty and region homogeneity are high or both are low. Finally, the method selects that threshold which corresponds to the minimum overall energy. Qualitative experiments based on both phantoms and clinical images show significant improvements using the proposed method over a recently-published maximum segmented image information (MSII) method. Quantitative analysis on phantoms generated under a range of conditions of blurring, noise, and background variation confirm the superiority of the new method.

Many medical imaging modalities produce spatial or temporal stacks of image data. Segmentation of such image stacks has many applications ranging from quantitative measurements to surgical and radiation treatment planning. The key idea presented in this paper is that of propagating information serially from one slice to the next within an interactive framework. Since information on adjacent slices is very similar, segmentation on one slice can be propagated with slight modification to adjacent slices. The segmentation algorithms that we have developed within this framework are all based on energy minimization principles with an additional constraint that the segmentation on a given image slice is similar to the segmentation predicted from the previous image slice. An optical flow approach is used to predict segmentation from one slice to the next. Three types of algorithms have been developed within the above paradigm for different applications --(1) A Mumford and Shah energy- minimizing algorithm combining edge and region information in a region-growing framework, (2) an active contour model-based tracking method, and (3) an algorithm based on pixel classification and Markov random fields. We recognize the fact that interactivity is very important in medical image segmentation. Therefore, our segmentation tools are available in a Java-based graphical user interface (GUI), allowing users to initialize various segmentation algorithms or to edit the results of automatic segmentation, if desired.

The purpose of this work was to develop an automated method for segmenting pediatric kidneys in contrast-enhanced helical CT images and measuring the volume of the renal parenchyma. An automated system was developed to segment the abdomen, spine, aorta and kidneys. The expected size, shape, topology an X-ray attenuation of anatomical structures are stored as features in an anatomical model. These features guide 3-D threshold-based segmentation and then matching of extracted image regions to anatomical structures in the model. Following segmentation, the kidney volumes are calculated by summing included voxels. To validate the system, the kidney volumes of 4 swine were calculated using our approach and compared to the 'true' volumes measured after harvesting the kidneys. Automated volume calculations were also performed retrospectively in a cohort of 10 children. The mean difference between the calculated and measured values in the swine kidneys was 1.38 (S.D. plus or minus 0.44) cc. For the pediatric cases, calculated volumes ranged from 41.7 - 252.1 cc/kidney, and the mean ratio of right to left kidney volume was 0.96 (S.D. plus or minus 0.07). These results demonstrate the accuracy of the volumetric technique that may in the future provide an objective assessment of renal damage.

Image segmentation techniques using fuzzy connectedness principles have shown their effectiveness in segmenting a variety of objects in several large applications in recent years. However, one problem with these algorithms has been their excessive computational requirements. In an attempt to substantially speed them up, in the present paper, we study systematically a host of 18 algorithms under two categories -- label correcting and label setting. Extensive testing of these algorithms on a variety of 3D medical images taken from large ongoing applications demonstrates that a 20 - 360 fold improvement over current speeds is achievable with a combination of algorithms and fast modern PCs. The reliable recognition (assisted by human operators) and the accurate, efficient, and sophisticated delineation (automatically performed by the computer) can be effectively incorporated into a single interactive process. If images having intensities with tissue specific meaning (such as CT or standardized MR images) are utilized, all parameters for the segmentation method can be fixed once for all, all intermediate data can be computed before the user interaction is needed, and the user can be provided with more information at the time of interaction.

Active Appearance Models (AAM), which have been recently introduced by Cootes et al., describe the shape of objects and gray level appearance from a set of example images. An AAM is created from user-placed contours defining the shape of objects of interest in each training image. The information about shape changes observed in the training set is used to model the shape variation. Principle component analysis (PCA) is utilized to model gray level variation observed in the training set. The resulting model describes objects as a linear combination of eigen vectors both in shape and gray levels applied to the mean image. The main purpose of this work is to investigate the clinical potential of AAMs for segmentation of cardiovascular MR images acquired in routine clinical practice. An AAM was constructed using 102 end- diastolic short-axis cardiac MR images at the papillary muscle level from normals and patients with varying pathologies. The resulting AAM is a compact representation consisting of a mean image and a limited number of coefficients of eigen vectors, representing 97% of shape and gray level variation observed in the training set. The segmentation performance is tested in 60 end-diastolic short-axis cardiac MR images from different patients.

The 3-D regions obtained as a result of a volume image segmentation often need to be geometrically modeled and rendered. In this paper, use of rational Gaussian (RaG) surfaces in modeling and rendering 3-D regions is described. A new parametrization technique is introduced that morphs a sphere in a coarse-to-fine fashion to a 3-D region. Knowing parameters of points on the sphere, parameters of voxels on the region are determined. Having the parameters of the voxels, a RaG surface is then fitted to the voxels to obtain a smooth representation for the region. Examples of the proposed representation on various 3-D regions are presented.

To facilitate hepatic surgical planning, we have developed a new system for the automatic 3D delineation of anatomical and pathological hepatic structures from a spiral CT scan. This system also extracts functional information useful for surgery planning, such as portal vein labeling and anatomical segment delineation following the conventional Couinaud definition. From a 2 mm thick enhanced spiral CT scan, a first stage automatically delineates the skin, bones, lungs and kidneys, by combining the use of thresholding, mathematical morphological methods and distance maps. Next, a reference 3D model is immerged in the image and automatically deformed to the liver contour. Then an automatic Gaussians fitting on the imaging histogram allows to threshold the intensities of parenchyma, vessels and lesions. The next stage improves this first classification by an original topological and geometrical analysis, providing an automatic and precise delineation of lesions and veins. Finally, a topological and geometrical analysis based on medical knowledge provides the hepatic functional information invisible in medical imaging: portal vein labeling and hepatic anatomical segments. Clinical validation performed on more than 30 patients shows that this method allows a delineation of anatomical structures, often more sensitive and more specific than manual delineation by a radiologist.

Identification of anatomical structure boundaries in radiographs is a necessary step for detecting abnormalities. The aim of this study is to develop a knowledge-based approach to automatically segment the interested structure boundaries in X-ray images. Our method contains four main steps. First, the original gray-level radiograph is segmented into a binary image. Second, the region of interest (ROI) is detected by matching the features extracted from the binary image with a pre-defined anatomical model, and the location of ROI will serve as the landmark for the following search. Third, an anatomical model will be hierarchically applied to the original image. Correlation values and anatomical constraints will be applied to choose the closer match edge candidates. According to the shape of the global model, the best match edge candidates will be selected and connected to generate the boundaries of the interested structure. Finally, active contour model is used to refine the boundaries. The results show the effectiveness and the efficiency of this proposed method.

Medical images provide experienced physicians with meaningful visual stimuli but their features are frequently hard to decipher. The development of a computational model to mimic physicians' expertise is a demanding task, especially if a significant and sophisticated preprocessing of images is required. Learning from well-expertised images may be a more convenient approach, inasmuch a large and representative bunch of samples is available. A four-stage approach has been designed, which combines image sub-sampling with unsupervised image coding, supervised classification and image reconstruction in order to directly extract medical expertise from raw images. The system has been applied (1) to the detection of some features related to the diagnosis of black tumors of skin (a classification issue) and (2) to the detection of virus-infected and healthy areas in retina angiography in order to locate precisely the border between them and characterize the evolution of infection. For reasonably balanced training sets, we are able to obtained about 90% correct classification of features (black tumors). Boundaries generated by our system mimic reproducibility of hand-outlines drawn by experts (segmentation of virus-infected area).

We propose a segmentation method different from active contours, which can cope with incomplete edges. The algorithm has been developed to segment heart cavities, but may be extended to more complex object shapes. Due to the almost convex geometry of heart cavities we are using a polar coordinate system with its origin near the cavity's center. The image is scanned from the origin for potential edge points. In order to assess the likelihood of an edge point to belong to the myocardial wall, region based information, such as visibility and local wall thickness, is included. The local information (edge points) progressively is expanded by first grouping the edge points to line segments and then selecting a subgroup of segments to obtain the final closed contour. This is done by means of minimizing a cost function. The plausibility of the result is checked and, if needed, the contour is corrected and/or refined by searching for additional potential edge points. For multidimensional images the algorithm is applied slice-by-slice without the need of further user interaction. The new segmentation method has been applied to clinical ultrasound images, the result being that the myocardial wall correctly was detected in the vast majority of cases.

In this paper an image-based method founded on mathematical morphology is presented in order to facilitate the segmentation of cerebral structures on 3D magnetic resonance images (MRIs). The segmentation is described as an immersion simulation, applied to the modified gradient image, modeled by a generated 3D region adjacency graph (RAG). The segmentation relies on two main processes: homotopy modification and contour decision. The first one is achieved by a marker extraction stage where homogeneous 3D regions are identified in order to attribute an influence zone only to relevant minima of the image. This stage uses contrasted regions from morphological reconstruction and labeled flat regions constrained by the RAG. The goal of the decision stage is to precisely locate the contours of regions detected by the marker extraction. This decision is performed by a 3D extension of the watershed transform. Upon completion of the segmentation, the outcome of the preceding process is presented to the user for manual selection of the structures of interest (SOI). Results of this approach are described and illustrated with examples of segmented 3D MRIs of the human head.

Derived from a model based segmentation algorithm for hand radiographs proposed in our former work we now present a method to determine skeletal maturity by an automated analysis of regions of interest (ROI). These ROIs including the epiphyseal and carpal bones, which are most important for skeletal maturity determination, can be extracted out of the radiograph by knowledge based algorithms.

The purpose of individual 3D region-of-interest atlas extraction is to automatically define anatomically meaningful regions in 3D MRI images for quantification of functional parameters (PET, SPECT: rMRGlu, rCBF). The first step of atlas extraction is to automatically classify brain tissue types into gray matter (GM), white matter (WM), cerebrospinal fluid (CSF), scalp/bone (SB) and background (BG). A feed-forward neural network with back-propagation training algorithm is used and compared to other numerical classifiers. It can be trained by a sample from the individual patient data set in question. Classification is done by a 'winner takes all' decision. Automatic extraction of a user-specified number of training points is done in a cross-sectional slice. Background separation is done by simple region growing. The most homogeneous voxels define the region for WM training point extraction (TPE). Non-white-matter and nonbackground regions are analyzed for GM and CSF training points. For SB TPE, the distance from the BG region is one feature. For each class, spatially uniformly distributed training points are extracted by a random generator from these regions. Simulated and real 3D MRI images are analyzed and error rates for TPE and classification calculated. The resulting class images can be analyzed for extraction of anatomical ROIs.

After neural network-based classification of tissue types, the second step of atlas extraction is knowledge-based class image analysis to get anatomically meaningful objects. Basic algorithms are region growing, mathematical morphology operations, and template matching. A special algorithm was designed for each object. The class label of each voxel and the knowledge about the relative position of anatomical objects to each other and to the sagittal midplane of the brain can be utilized for object extraction. User interaction is only necessary to define starting, mid- and end planes for most object extractions and to determine the number of iterations for erosion and dilation operations. Extraction can be done for the following anatomical brain regions: cerebrum; cerebral hemispheres; cerebellum; brain stem; white matter (e.g., centrum semiovale); gray matter [cortex, frontal, parietal, occipital, temporal lobes, cingulum, insula, basal ganglia (nuclei caudati, putamen, thalami)]. For atlas- based quantification of functional data, anatomical objects can be convoluted with the point spread function of functional data to take into account the different resolutions of morphological and functional modalities. This method allows individual atlas extraction from MRI image data of a patient without the need of warping individual data to an anatomical or statistical MRI brain atlas.

To allow a more objective interpretation of 3D carotid bifurcation images, we have implemented and evaluated on patient data, automated volume registration of 3D magnetic resonance angiography (MRA), 3D power Doppler (PD) ultrasound, and 3D B-mode ultrasound. Our algorithm maximizes the mutual information between the thresholded intensities of the MRA and PD images. The B-mode images, acquired simultaneously in the same orientation as PD, are registered to the MRA using the transformation obtained from the MRA-PD registration. To test the algorithm we misaligned clinical ultrasound images and simulated mismatches between the datasets due to different appearances of diseased vessels by removing 3D sections of voxels from each of the paired scans. All registrations were assessed visually using integrated 3D volume, surface, and 2D slice display. 97% of images misaligned within a range of 40 degrees and 40 pixels were correctly registered. The deviation from the mean registration parameters due to the simulated defects was 1.6 +/- 2.5 degrees, 1.5 +/- 1.6 pixels in X, Y and 0.7 +/- 0.7 pixels in Z direction. The algorithm can be used to register carotid images with misalignment range of 40 pixels in X, Y directions, 10 pixels in Z direction and 40 degree rotations, even in the case of different image appearances due to vessel stenoses.

In this paper we propose a novel method to register at least two vide images to a 3D surface model. The potential applications of such a registration method could be in image guided surgery, high precision radiotherapy, robotics or computer vision. Registration is performed by optimizing a similarity measure with respect to the pose parameters. The similarity measure is based on 'photo-consistency' and computes for each surface point, how consistent the corresponding video image information in each view is with a lighting model. We took four video views of a volunteer's face, and used an independent method to reconstruct a surface that was intrinsically registered to the four views. In addition, we extracted a skin surface from the volunteer's MR scan. The surfaces were misregistered from a gold standard pose and our algorithm was used to register both types of surfaces to the video images. For the reconstructed surface, the mean 3D error was 1.53 mm. For the MR surface, the standard deviation of the pose parameters after registration ranged from 0.12 to 0.70 mm and degrees. The performance of the algorithm is accurate, precise and robust.

This paper presents the first comparison between theoretical estimates and clinically observed values for registration accuracy in point-based rigid-body registration. Rigid-body registration is appropriate for applications in which relatively rigid parts of the body are involved. In some such applications rigid-body registration is accomplished by aligning two sets of discrete points. In neurosurgical guidance, for example, the points are found by localizing the centroids of fiducial markers. We have previously provided two fundamental theoretical results on the relationship between localization error and registration error in rigid-body, point-based registration and have justified these results by showing them to be close to those given by numerical simulations. Rigid-body, point-based registration is accomplished by finding a rigid-body transformation that aligns pairs of homologous 'fiducial' points. The imprecision in locating a fiducial point is known as the 'fiducial localization error' (FLE). Fiducial points may be centroids of attached markers, which tend to have small, equal FLEs, or salient points in segmented anatomic features, whose FLEs tend to be larger and more varied. Alignment is achieved by minimizing the 'fiducial registration error' (FRE), which is the root mean square distance between homologous fiducials after registration. Closed form solutions for the rigid transformation that minimizes FRE have been known since 1966. A more critical and direct measure of registration error is the 'target registration error' (TRE), which is the distance between homologous points other than the centroids of fiducials. This error measure has been investigated by numerical simulation for many years, and we presented at this meeting in 1998 the first derivation of theoretical estimates of TRE. In that paper we showed that these estimates agree well with our simulations and those of others. We made the simplifying assumption in both the derivations and the simulations that the FLE is isotropic, i.e. that it has the same distribution in each coordinate direction. In the present work, we extend the validation beyond simulated data sets to clinically acquired head images from a set of 86 patients. We use the actual localizations of skull-implanted, visible fiducial markers in the images to compare the observed TRE values with those estimated by theory. This approach provides a clinically relevant estimate of the usefulness of the theoretical predictions. We also make a comparison between the observed TRE values and those given by numerical simulation: this allows us to determine whether the assumptions we use for the derivation of our results are good ones in practice. Although the distributions of observed and theoretical values appear different, ROC analysis shows that the theoretical values are good predictors of the observed ones. This gives some validity to the assumptions we make governing the point- based registration process (e.g., that the FLE is isotropic, and that it is independent and identically distributed at each fiducial point), and shows that our theory has practical use in a clinical setting.

In this paper, we present an automated multi-modality registration algorithm based on hierarchical feature extraction. The approach, which has not been used previously, can be divided into two distinct stages: feature extraction (edge detection, surface extraction), and geometric matching. Two kinds of corresponding features -- edge and surface -- are extracted hierarchically from various image modalities. The registration then is performed using least-squares matching of the automatically extracted features. Both the robustness and accuracy of feature extraction and geometric matching steps are evaluated using simulated and patient images. The preliminary results show the error is on the average of one voxel. We have shown the proposed 3D registration algorithm provides a simple and fast method for automatic registering of MR-to-CT and MR-to-PET image modalities. Our results are comparable to other techniques and require no user interaction.

We present an operator-independent software technique for segmentation, realignment and analysis of brain perfusion images, with both voxel-wise and regional quantitation methods. Inter-subject registration with normalized mutual information was tested with simulated defects. Brain perfusion images (HMPAO-SPECT) from 56 subjects (21 AD; 35 controls) were retrospectively analyzed. Templates were created from the 3-D registration of the controls. Automatic segmentation was developed to remove extraneous activity that disrupts registration. Two new registration methods, robust least squares (RLS) and normalized mutual information (NMI) were implemented and compared with sum of absolute differences (CD). The automatic segmentation method caused a registration displacement of 0.4 +/- 0.3 pixels compared with manual segmentation. NMI registration proved to be less adversely effected by simulated defects than RLS or CD. The error in quantitating the patient-template parietal ratio due to mis- registration was 2.0% and 0.5% for 70% and 85% hypoperfusion defects, respectively. The registration processing time was 1.6 min (233 MHz Pentium). The most accurate discriminant utilized a logistic equation parameterized by mean counts of the parietal and temporal regions of the map, (91 +/- 8% Se, 97 +/- 5% Sp). BRASS is a fast, objective software package for single-step analysis of brain SPECT, suitable to aid diagnosis of AD.

This paper presents work towards a system for intra-operative registration of 3D CT data to 2D X-ray radiographs. The registration procedure involves iterative comparison of Digitally Reconstructed Radiographs (DRRs) with X-ray images acquired during surgery. A new data structure called a Transgraph permits rapid generation of DRRS, and greatly speeds up the registration process. The underlying data structures are described, and the registration algorithm is evaluated for application to an existing image guided radiosurgery system.

This work introduces an enhancement to currently existing methods of intra-operative vertebral registration by allowing the portion of the spinal column surface that correctly matches a set of physical vertebral points to be automatically selected from several possible choices. Automatic selection is made possible by the shape variations that exist among lumbar vertebrae. In our experiments, we register vertebral points representing physical space to spinal column surfaces extracted from computed tomography images. The vertebral points are taken from the posterior elements of a single vertebra to represent the region of surgical interest. The surface is extracted using an improved version of the fully automatic marching cubes algorithm, which results in a triangulated surface that contains multiple vertebrae. We find the correct portion of the surface by registering the set of physical points to multiple surface areas, including all vertebral surfaces that potentially match the physical point set. We then compute the standard deviation of the surface error for the set of points registered to each vertebral surface that is a possible match, and the registration that corresponds to the lowest standard deviation designates the correct match. We have performed our current experiments on two plastic spine phantoms and one patient.

Body motion and heart upward creep are among the most frequent sources of artifacts in the single-photon emission computed tomography (SPECT) of nuclear medicine. This paper provides a new method for automatic correction of such motions. Under the formulation of a variable length correlation, abrupt body motions, gradual body motions, and heart upward creep are corrected in sequential passes. An affine transformation is used to compensate for changes in heart appearance caused by varying view angles in image acquisition. Additionally, a method is proposed for automatic exclusion of non-cardiac organs. The effectiveness of the method has been demonstrated with experimental results.

We investigated the use of MI to register images of the pelvis and thorax regions which is a complex problem compared to the head since changes occur in soft tissue while the bony anatomy stays stable. We focused on the bony anatomy eliminating the soft tissue data by applying the MI for bone intensities. Instead of linear binning the whole spectrum of CT intensities, we bin the intensities chosen by the user as corresponding to the bone. We truncated the data spatially by choosing a region, because some bony anatomy might move from scan to scan relative to the stable parts i.e. ribs in the lung region might move with breathing or legs in the pelvis. We compare the effects of using our intensity-dependent- regional MI to the original MI for 9 pairs of CT-CT pelvis, 3 pairs of CT-CT lung and 5 pairs of CT-PET patient studies. With the original algorithm, the root-mean-square registration error can be as high 2 cm for CT-CT. The registration error with the intensity-dependent-regional algorithm, however, was on the average 2 mm for CT-CT pelvic and 4 mm for CT-CT lung studies. Using just the bone intensities and a specific region, we have a smaller sample size, which decreased our calculation time up to 8 times to less than 15 seconds. For CT-PET studies the average registration error is reduced from 3.2 cm to 0.5 cm.

We present an algorithm for registering, segmenting and quantifying multiple scanned electrophoresis images. (2D gel) Electrophoresis is a technique for separating proteins or other macromolecules in organic material according to net charge and molecular mass and results in scanned grayscale images with dark spots against a light background marking the presence of such macromolecules. The algorithm begins by registering each of the images using a non-rigid registration algorithm. The registered images are then jointly segmented using a Markov random field approach to obtain a single segmentation. By using multiple images, the effect of noise is greatly reduced. We demonstrate the algorithm on several sets of real data.

Non-rigid registration of multi-modality images is an important tool for assessing temporal and structural changesbetween images. For rigid registration, voxel similarity measures like mutual information have been shown to alignimages from different modalities accurately and robustly. For non-rigid registration, mutual information can besensitive to local variations of intensity which in MR images may be caused by RF inhomogeneity. The reasonfor the sensitivity of mutual information towards intensity variations stems from the fact that mutual informationignores any spatial information. In this paper we propose an extension of the mutual information framework whichincorporates spatial information about higher-order image structure into the registration process and has the potentialto improve the accuracy and robustness of non-rigid registration in the presence of intensity variations. We haveapplied the non-rigid registration algorithm to a number of simulated MR brain images of a digital phantom whichhave been degraded by a simulated intensity shading and a known deformation. In addition, we have applied thealgorithm for the non-rigid registration of eight pre- and post-operative brain MR images which were acquired withan interventional MR scanner and therefore have substantial intensity shading due to RF field inhomogeneities. Inall cases the second-order estimate of mutual information leads to robust and accurate registration.

In previous work we have introduced an approach to improving the registration of EPI fMRI data with anatomical MRI by accounting for differences in magnetic field induced geometric distortion in the two types of MRI acquisition. In particular we began to explore the use of imaging physics based constraints in a non-rigid multi-modality registration algorithm. In this paper we present phantom based experimental work examining the behavior of different non-rigid registration constraints compared to a field map acquisition of the MRI distortion. This acquisition provides a pixel by pixel 'ground truth' estimate of the displacement field within the EPI data. In our registration based approach we employ a B-spline based estimate of the relative geometric distortion with a multi-grid optimization scheme. We maximize the normalized mutual information between the two types of MRI scans to estimate the B-Spline parameters. Using the field map estimates as a gold standard, registration estimates using no additional geometric constraints are compared to those using the spin echo based signal conservation. We also examine the use of logarithmic EPI values in the criteria to provide additional sensitivity in areas of low signal. Results indicate that registration of EPI to conventional MRI incorporating a spin echo distortion model can provide comparable estimates of geometric distortion to those from field mapping data without the need for significant additional acquisitions during each fMRI sequence.

This paper presents a fast hierarchical method to perform dense deformable inter-subject matching of 3D MR Images of the brain. To recover the complex morphological variations in neuroanatomy, a hierarchy of 3D deformations fields is estimated, by minimizing a global energy function over a sequence of nested subspaces. The nested subspaces, generated from a single scaling function, consist of deformation fields constrained at different scales. The highly non linear energy function, describing the interactions between the target and the source images, is minimized using a coarse-to-fine continuation strategy over this hierarchy. The resulting deformable matching method shows low sensitivity to local minima and is able to track large non-linear deformations, with moderate computational load. The performances of the approach are assessed both on simulated 3D transformations and on a real data base of 3D brain MR Images from different individuals. The method has shown efficient in putting into correspondence the principle anatomical structures of the brain. An application to atlas-based MRI segmentation, by transporting a labeled segmentation map on patient data, is also presented.

In this pair, we describe experiments designed to validate some techniques used for spatial normalization of diffusion tensor (DT) images. In particular, we have previously described the problems involved in applying transformations to these images and proposed several techniques for addressing this problem. DTs contain orientational information, which must be handled appropriately when a DT image is transformed. In this paper, we review the previously proposed techniques for estimating the appropriate reorientation of each DT that should accompany a given transformation of the image. We describe the design of some synthetic data sets and some experiments, which use this data to test the effectiveness of the techniques under affine transformations of DT images. Results confirm that one particular technique, which takes into account the more complex reorientational effects of shearing and stretching transformations, is the most effective.

Soft-tissue deformation can be a problem if a pre-operative modality is used to help guide a surgical or an interventional procedure. We present a method which can warp a pre-operative CT image to represent the intra-operative scene shown by an interventional fluoroscopy image. The method is a novel combination of a 2D-3D image registration algorithm and a deformation algorithm which allows rigid bodies to be incorporated into a non-linear deformation based on a radial basis function. The 2D-3D registration algorithm is used to obtain information on relative vertebral movements between pre-operative and intra-operative images. The deformation algorithm uses this information to warp the pre-operative image to represent the intra-operative scene more accurately. Images from an aortic stenting procedure were used. The observed deformation was 5 degree flexion and 5 mm lengthening of the lumbar spine. The vertebral positions in the warped CT volume represent the intra-operative scene more accurately than in the pre-operative CT volume. Although we had no gold- standard with which to assess the registration accuracy of soft-tissue structures, the position of soft-tissue structures within the warped CT volume appeared visually realistic.

The advanced single-slice rebinning algorithm (ASSR) is a highly accurate and efficient approximative algorithm for cone-beam spiral CT that (1) yields high image quality even at large cone angles, (2) makes use of available 2D backprojection algorithms/hardware and (3) allows for sequential data processing. It uses virtual R-planes (reconstruction planes) that are tilted to optimally fit 180 degree spiral segments. Along these R-planes data of a virtual 2D parallel scanner are synthesized via rebinning from the measured spiral cone-beam data. Reconstruction with 2D filtered backprojection yields the object cross-section in world coordinates [x, y, z(x, y)] which is resampled to carthesian coordinates (x, y, z) by z-filtering. Geometrical misalignments as well as any arbitrary detector geometry can be easily incorporated in the ASSR algorithm. ASSR, unlike other approximate algorithms, does not show severe cone-beam artifacts when going to larger cone angles. Even for scanners with a high number of detector rows, e.g. 64 rows, a high and isotropic z-resolution is achieved. In-plane resolution is determined by the 2D reconstruction filters which can be chosen as in 2D CT. Even in the case of only M equals 4 or M equals 8 simultaneously measured slices, ASSR may outperform standard z-interpolation algorithms such as 180 degree MFI. Due to its high efficiency and high image quality ASSR has the potential to be used for medical cone-beam CT.

A recently published local region-of-interest (ROI) technique makes it possible to image a ROI in a long object in cone beam spiral scans without blurring from the overlaying materials; the local ROIs refer to the portions of the object bounded by the parallel projections of the spiral scan path on the (phi) planes in the Radon space. First, the Radon derivative data for the local ROIs are computed from the cone beam data; second, the local ROIs are reconstructed; and finally the ROI is reconstructed from the local ROIs. For any cone beam image detected near the top and the bottom of the spiral path, the integration line segments are limited in different manners depending on whether the local ROI projects onto the corresponding (phi) plane on the uppermost/lowermost complete stage of the projected spiral or not. In this first part in a series of two papers reformulating the local ROI method into a filtered backprojection (FBP)-based algorithm, the theoretical derivation of the FBP-based local ROI method is presented, and the demanding numerical implementation together with the simulation results are reported in the second paper. We have developed a simple procedure to group line segments for the filtering operation according to the manner they are limited. Furthermore, it is found that the filtering operation on the cone beam images is equivalent to a number of 1D Hilbert transforms followed by 1D differentiation in the projected scan path direction.

In the long object problem it is intended to reconstruct exactly a region-of-interest (ROI) of an object from spiral cone beam data which covers the ROI and its nearest vicinity only. In the first paper in a series of two the theory of the local ROI method is derived using the filtered-backprojection approach. In the present second paper the demanding numerical implementation is described. The straightforward 4-step algorithm is applied. It mainly consists of explicit calculations of the derivatives of partial plane integrals of the object from line segments in the projection images. In the local ROI method grouping of line segments to particular (phi) -planes in 3-D Radon space is important. A rigorous grouping causes artifacts which can be avoided by a fuzzy correspondence of line segments to (phi) -planes. In the ROI the same image quality is achieved for a partial scan as for a full scan. However, the method suffers from high computational requirements. The filtering step can be speeded up by replacing the 4-step algorithm by convolution with spatially variant 1-D Hilbert transforms. An in-depth analysis of the empirical PSF of detector pixels filtered by the 4-step algorithm confirmed the theoretical results. Modifications for practical implementation are outlined which are subject to further investigations.

Cone beam reconstruction has been the focus of many studies. One of the most widely referenced and used algorithms for circular trajectory is the Feldkamp algorithm. The advantage of the algorithm is its simplicity of implementation, efficiency in computation, and close resemblance to the well- known filtered backprojection algorithm for fan beam and parallel beam reconstruction. The algorithm is effective in terms of combating some of the cone beam artifacts. However, when objects with high density and non-uniform distribution are placed off the center plane (the fan beam plane), severe shading artifact will result. In the paper, we propose a two- pass cone beam reconstruction scheme. The algorithm is based on the observation that the high-density object reconstructed with the Feldkamp algorithm is accurate to a first order. The shading and streaking artifacts near the high-density objects are caused mainly by the incomplete sample of the circular trajectory. As a result, we can use the reconstructed ages with Feldkamp algorithm as the basis for error estimation. By segmenting these objects, we could recreate the cone beam artifacts by synthesizing the projection and reconstruction processing. The final images are produced by removing error images from the first-pass images.

A multitude of approximate cone-beam algorithms have been proposed suited for reconstruction of small cone angle CT data. The goal of this study is to identify a practical and efficient approximate cone-beam method, and to investigate its performance at medium cone angles associated to area detectors. Three different approximate algorithms for spiral cone-beam CT will be compared: the (pi) -method, the Multirow- Fourier-Reconstruction and the Advanced Single-Slice Rebinning method. These algorithms are different in the way how the two- dimensional detector images are filtered. In each view x-ray samples are identified which describe an approximation to a virtual reconstruction plane. The image quality of the respective reconstruction will be assessed with respect to image artifacts, the slice sensitivity profile, and the in- plane modulation transfer function. It turns out that the performance of approximate reconstruction improves as the virtual reconstruction plane better fits the spiral focus path. The Advanced Single-Slice Rebinning method using tilted reconstruction planes is a practical algorithm, providing image quality comparable to that of a single-row scanning system even with a 46 row detector at a table feed of 64 mm per rotation of the gantry.

A nonlinear inversion scheme formulated on small subzones of the total region of interest (ROI) is developed. The algorithm reconstructs the distribution of a linear elastic stiffness term and a Maxwellian damping parameter over the entire ROI through a least squares optimization. The subzones are generated in a hierarchical manner based on progressive error minimization and processed in an automated, sweeping fashion until certain performance criterion are met. Simulation results show that the algorithm works well to minimize global error and is capable of simultaneously reconstructing both property parameter distributions even in the presence of random noise, although initial experience suggests that the elastic property image is superior to its attenuation coefficient counterpart.

The Bayes Inference Engine (BIE) has been used to perform a 4D reconstruction of a first-pass radiotracer bolus distribution inside a CardioWest Total Artificial Heart, imaged with the University of Arizona's FastSPECT system. The BIE estimates parameter values that define the 3D model of the radiotracer distribution at each of 41 times spanning about two seconds. The 3D models have two components: a closed surface, composed of bi-quadratic Bezier triangular surface patches, that defines the interface between the part of the blood pool that contains radiotracer and the part that contains no radiotracer, and smooth voxel-to-voxel variations in intensity within the closed surface. Ideally, the surface estimates the ventricular wall location where the bolus is infused throughout the part of the blood pool contained by the right ventricle. The voxel-to-voxel variations are needed to model an inhomogeneously-mixed bolus. Maximum a posterior (MAP) estimates of the Bezier control points and voxel values are obtained for each time frame. We show new reconstructions using the Bezier surface models, and discuss estimates of ventricular volume as a function of time, ejection fraction, and wall motion. The computation time for our reconstruction process, which directly estimates complex 3D model parameters from the raw data, is performed in a time that is competitive with more traditional voxel-based methods (ML-EM, e.g.).

In optical tomography (OT) one attempts to reconstruct cross- sectional images of various body parts given data from near- infrared transmission measurements. The cross-sectional images display the spatial distribution of optical properties, such as the absorption coefficient (mu) _a, the reduced scattering coefficient (mu) _s^', or a combination thereof. One of the major problems of the novel imaging technology is that many different spatial distributions of optical properties inside the medium can lead to the same detector readings on the surface of the medium. Therefore, the reconstruction problem in optical tomography is ill posed. The choice of an appropriate method to overcome this problem is of crucial importance for any successful optical tomographic image reconstruction algorithm. In this work we approach the problem within a gradient-based image iterative reconstruction (GIIR) scheme. The image reconstruction is considered as a minimization of an appropriately defined objective function. The objective function can be separated into a least-square- error term, which compares predicted and actual detector readings, and additional penalty terms that may contain a priori information about the system. We present the underlying concepts in our approach to overcome ill-posedness in optical tomography and show how different penalty terms affects the performance of the image reconstruction.

We present an algorithm which is able to reconstruct dynamic emission computed tomography (ECT) image series directly from inconsistent projection data that have been obtained using a rotating camera. By finding a reduced dimension time-activity curve (TAC) basis with which all physiologically feasible TAC's in an image may be accurately approximated, we are able to recast this large non-linear problem as one of constrained linear least squares (CLLSQ) and to reduce parameter vector dimension by a factor of 20. Implicit is the assumption that each pixel may be modeled using a single compartment model, as is typical in ^99mTc teboroxime wash-in wash-out studies; and that the blood input function is known. A disadvantage of the change of basis is that TAC non-negativity is no longer ensured. As a consequence, non-negativity constraints must appear in the CLLSQ formulation. A warm-start multiresolution approach is proposed, whereby the problem is initially solved at a resolution below that finally desired. At the next iteration, the number of reconstructed pixels is increased and the solution of the lower resolution problem is then used to warm-start the estimation of the higher resolution kinetic parameters. We demonstrate the algorithm by applying it to dynamic myocardial slice phantom projection data at resolutions of 16 X 16 and 32 X 32 pixels. We find that the warm-start method employed leads to computational savings of between 2 and 4 times when compared to cold start execution times. A 20% RMS error in the reconstructed TAC's is achieved for a total number of detected sinogram counts of 1 X 10⁵ for the 16 X 16 problem and at 1 X 10⁶ counts for the 32 X 32 grid. These errors are 1.5 - 2 times greater than those obtained in conventional (consistent projection) SPECT imaging at similar count levels.

Truncated Projection Computer Tomography (TPCT) is similar to conventional Computer Tomography (CT) in that it acquires projection information. The difference is that it weights and/or truncates the projections along their integration paths. The problem is succinctly stated as an integral equation termed the incomplete Radon transform. TPCT image reconstruction is equivalent to inversion of the incomplete Radon transform. We presented an inversion formula for this transform at SPIE Medical Imaging 1999. The solution involves the application of an integral transform that is equivalent to a combination of a square-root geometrical distortion and a Fourier transform. Subsequent to the 1999 presentation, we recast part of the inversion derivation in terms of Lagrange multipliers. Doing so led us to the realization that the incomplete Radon transform is a member of a much larger class of integral equations that lend themselves to the TPCT inversion techniques. In the present work we touch briefly on several topics. We will exhibit the larger class of integral equations in the form of Hilbert-space scalar products. They define generalized spatial filtering operations anchored simultaneously in direct space and any one of a multitude of transform spaces. In the examples relating to the TPCT reconstruction algorithm's stability, we perform computer simulations using off-axis Gaussian distributions as objects.

The Temple University Medical School has a sequence of over 400 serial sections of adult normal ventricular human heart tissue, cut at 25 micrometer thickness. We used a Zeiss Ultraphot with a 4x planapo objective and a Pixera digital camera to make a series of 45 sequential montages to use in the 3D reconstruction of a fascicle (muscle bundle). We wrote custom software to merge 4 smaller image fields from each section into one composite image. We used SurfDriver software, developed by Scott Lozanoff of the University of Hawaii and David Moody of the University of Alberta, for registration, object boundary identification, and 3D surface reconstruction. We used an Epson Stylus Color 900 printer to get photo-quality prints. We describe the challenge and our solution to the following problems: image acquisition and digitization, image merge, alignment and registration, boundary identification, 3D surface reconstruction, 3D visualization and orientation, snapshot, and photo-quality prints.

In continuous X-ray fluoroscopy images are sometimes blurred uniformly due to motion of the operating table. Additionally, low-dose fluoroscopy images are degraded by relatively strong quantum noise, which is not affected by the blur. We quantify the degradation due to motion blur by assessing the blur's effect on the Detective Quantum Efficiency (DQE), which captures the signal- and noise transfer properties of an imaging system. The estimation of the motion blur parameters, viz. direction and extent, is carried out one after the other. The central idea for direction detection is to apply an inertia-like matrix to the global spectrum of the degraded image, which assesses the anisotropy caused by the blur. Once the blur direction is obtained by this tensor approach, its extent is identified from an estimated power spectrum or bispectrum slice along this direction. The decision for either method is based on the eigenvalues of the inertia matrix. The blur parameters are used as input for a nonlinear Maximum-a- posteriori restoration technique based on a Generalized Gauss- Markov Random field for which several efficient optimization strategies are presented. This approach includes a thresholdless edge model. The DQE is generalized as a quality measure to assess the signal- and noise transfer properties of the restoration method.

We present a new method of enhancing cerebral vessels in subtraction angiography that defines shape attributes in terms of pixel features. Vessel knowledge comprises information on the imaging process, e.g., distribution of contrast media, noise characteristics, and morphological information on the vessels. The latter is computed as a fuzzy measure because pixels have not yet been classified into vessel and background pixels. We model our image as result of a process of projecting discrete contrast media voxels on the image plane. The projection is assumed to be distorted by noise. The shape feature is derived from the Karhunen-Loeve transformation (KLT) that is computed at each pixel from the covariance of the contrast distribution in a given neighborhood. Vessel likelihood is computed from local elongatedness. The latter is derived from the variances along the two principal axes and from the first central moment of the contrast distribution. The directional information from the KLT is used for anisotropic diffusion for noise reduction. Results of the enhancement step on angiographic data showed a significant improvement of the contrast while not blurring the image. Closely neighboring vessels could be differentiated if they were one pixel apart and if the SNR were better than 2:1.

Treatment planning in brachytherapy depends heavily on the accurate localization of markers in a catheter implant. We are developing an interactive system to combine the image information of biplane X-ray images to reconstruct the 3D marker positions. Current systems ask the user to identify all corresponding markers in both images manually. Especially in cases where multiple, eventually crossing catheters are present this is very time consuming and difficult as markers that are visible in one image may be hidden in the other image. To improve the procedure of marker detection we apply image-processing techniques. We investigate two approaches. One is based on 3D snakes. This is a model-based technique that is not sensitive to noise or ambiguities in the image. After the user has given a number of corresponding points per catheter, the system automatically detects the complete catheter and determines all 3D-marker positions. The second approach uses edge detection in a small region of interest (ROI). In both cases, knowledge about the catheter is used to guide the marker detection algorithm. The user has to examine the result visually. In case of erroneous marker detection the user can move, add or delete single maker points. To be able to judge the accuracy of the reconstruction it is necessary to locate possible error sources. For an accurate reconstruction of the catheter positions it is important to know the exact geometry of the imaging system. With a mathematical model the influence of uncertainties in parameters on the reconstruction result is studied.

This paper presents a sub-voxel analysis method for multi- parameter volumetric images such as MRI to provide partial volume estimation. The proposed method finds a continuous function for a neighboring structure of each voxel. The estimation function and neighboring structure are chosen from the quadratic/cubic polynomials and a set of 2D/3D symmetric neighborhood architectures, respectively. Then, a new form of the eigenimage method, based on Gram-Schmidt orthogonalization, is derived for each choice of estimation function and neighboring structure. Finally, the above estimators are applied to a simulation model consisting of materials similar to CSF, WM, and GM of the human brain in T1- , T2-, and PD-weighted MRI. In the presence of noise, the examined continuous estimators show a smaller standard deviation (up to 40%) than the standard eigenimage method. Also the chosen estimators have analytical solution for their Gram-Schmidt filters, so their execution times are comparable with that of the standard eigenimage method. In addition, the proposed approach can determine the 3D distribution of each material and extract the connecting surfaces of the materials within each voxel.

In order to improve the accuracy of image-guided neurosurgery, different biomechanical models have been developed to correct preoperative images w.r.t. intraoperative changes like brain shift or tumor resection. All existing biomechanical models simulate different anatomical structures by using either appropriate boundary conditions or by spatially varying material parameter values, while assuming the same physical model for all anatomical structures. In general, this leads to physically implausible results, especially in the case of adjacent elastic and fluid structures. Therefore, we propose a new approach which allows to couple different physical models. In our case, we simulate rigid, elastic, and fluid regions by using the appropriate physical description for each material, namely either the Navier equation or the Stokes equation. To solve the resulting differential equations, we derive a linear matrix system for each region by applying the finite element method (FEM). Thereafter, the linear matrix systems are linked together, ending up with one overall linear matrix system. Our approach has been tested using synthetic as well as tomographic images. It turns out from experiments, that the integrated treatment of rigid, elastic, and fluid regions significantly improves the prediction results in comparison to a pure linear elastic model.

One of the important clinical features to differentiate benign melanocytic nevi from malignant melanomas is the irregularity of the lesion border. A careful examination of a lesion border reveals two types of irregularity: texture irregularity and structure irregularity. Texture irregularities are the small variations along the border, while structure irregularities are the global indentations and protrusions, which may suggest excess of cell growth or regression of a melanoma. Therefore, measuring border irregularity by structural indentations and protrusions may detect the malignancy of the lesion. The common shape descriptors such as compactness index and fractal dimension are more sensitive to texture irregularities than structure irregularities. They do not provide an accurate estimation for the structure irregularity. Therefore, we have designed a new measurement for border irregularity. The proposed method first locates all indentations and protrusions along the lesion border. Then a new area-based index, called irregularity index, is computed for each indentation and protrusion. The overall border irregularity is estimated by the sum of all individual indices. In addition, the new method offers an extra feature: localization of the significant indentations and protrusions. As the result, the new measure is sensitive to structure irregularities and may be useful for diagnosing melanomas.

Variation in the diameter of vessels is a key information for treatment of stenosis. This information is usually obtained from standard 2-D projective acquisitions. We propose an automatic method for the quantification of vessels cross- sections in 3D vascular reconstructions from x-ray images. First, a closed continuous surface is extracted. This surface represents the vessels contours selected with a given centerline. Then, the area of the cross-sections along the central axis is obtained by intersection of the contour and the plane of each cross-section. A model of the vessels allows to correct the first estimation. Tests on phantom images give a precision of the vessels radius below 0.5 voxel. Results are also presented on real vessels containing stenosis.

Registration of anatomical images is useful for many applications including image segmentation, characterization of normal and abnormal shape, and creating deformable anatomical shape atlases. The usefulness of the information derived from image registration depends on the degree of anatomically meaningful correspondence between the images. We assume that an ideal image registration algorithm can determine an unique correspondence mapping between any two image volumes imaged from a homogeneous population of anatomies; and that these transformations have the properties of invertibility and transitivity. Unfortunately, current image registration algorithms are far from ideal. In this paper we test the invertibility and transitivity of transformations computed from a 'traditional' and a consistent linear-elastic registration algorithm. Invertibility of the transformations was evaluated by comparing the composition of transformations from image A-to-B and B-to-A to the identity mapping. Transitivity of the transformations was evaluated by measuring the difference between the identity mapping and the composition the transformations from image A-to-B, B-to-C, and C-to-A. Transformations were generated by matching computer generated phantoms, CT data of infant heads, and MRI data of adult brains. The consistent algorithm out performed the 'traditional' algorithm by 8 to 16 times for the invertibility test and 2 to 5 times for the transitivity test.

We describe a method for creating semi-isometric flat maps of sections of the human cortical surface. These maps can be used for a wide range of applications including visualization of the distribution of functional activation over the unfolded brain surface and generating parametric models for the cortical surface that are appropriate for performing geometrical transformations and surface based inter-subject registration. In particular, their application in creating multi-resolution representations of arbitrarily shaped complex surfaces is presented in this paper. Using the property that every simultaneous conformal and equiareal mapping is isometric, we have formulated the calculation of an isometric mapping between surfaces as a constrained optimization problem. We have designed an energy function whose minima occur when the surface points are positioned in an unfolded configuration. Constraint functions imposing the requirements of preservation of angles and areas guarantee that the surface will deform to produce conformal and equiareal mappings. The constraints are imposed using penalty functions in an unconstrained conjugate gradient algorithm. The surface unfolds gradually, deforming to a near-flat form that corresponds to a minimum of the weighted sum of the energy and penalty function terms.

An essential part of the IRMA-project (Image Retrieval in Medical Applications) is the categorization of digitized images into predefined classes using a combination of different independent features. To obtain an automated and content-based categorization, the following features are extracted from the image data: Fourier coefficients of normalized projections are computed to supply a scale- and translation-invariant description. Furthermore, histogram information and Co-occurrence matrices are calculated to supply information about the gray value distribution and textural information. But the key part of the feature extraction is the shape information of the objects represented by an Active Shape Model. The Active Shape Model supports various form variations given by a representative training set; we use one particular Active Shape Model for each image class. These different Active Shape Models are matched on preprocessed image data with a simulated annealing optimization. The different extracted features were chosen with regard to the different characteristics of the image content. They give a comprehensive description of image content using only few different features. Using this combination of different features for categorization results in a robust classification of image data, which is a basic step towards medical archives that allow retrieval results for queries of diagnostic relevance.

This paper presents a factor analytic approach to morphometry in which strong intercorrelations among a high-dimensional set of shape-related variables are sought. The correlated variables potentially correspond to substructures of anatomy and thus have a natural interpretation. The analysis is based on information about the pointwise size differences between the anatomy depicted in a template image and the anatomy in a subject image, obtained by registering the template to the subject and then calculating the Jacobian determinant of the registration transformation over the image volume. The method is demonstrated in a preliminary study of shape differences between the corpora callosa of schizophrenic patients and normal controls. We show that the regions where these differences occur can be determined by unsupervised analysis, indicating the method's potential for exploratory studies.

One of the most important tasks for virtual endoscopy is path planning for viewing the lumen of hollow organs. For geometry complex objects, for example the lungs, it remains an unsolved problem. While alternative visualization modes have been proposed, for example, cutting and flattening the hollow wall, a skeleton of the lumen is still necessary as a reference for the cutting. A general-purpose skeletonization algorithm often generates redundant skeletons because of the local shape variation. In this study, a multistage skeletonization method for tree-like volumes, such as airway system, blood vessels, and colon, was presented. By appropriately defining the distance between voxels, the distance to the root from each voxel in the volume can be effectively determined with means of region growing techniques. The end points of all branches and the shortest path from each end point to the root can be extracted based on this distance map. A post-processing algorithm is applied to the shortest paths to remove redundant ones and to centralize the remained ones. The skeleton generated is one-voxel wide, along which every branch of the 'tree' can be viewed. For effectively processing volume of large size, a modified multiresolution analysis was also developed to scale down the binary segmented volume. Tests on airway, vessel, and colon dataset were promising.

Image acquisition techniques often suffer from low signal-to- noise ratio (SNR) and/or contrast-to-noise ratio (CNR). Although many acquisition techniques are available to minimize these, post acquisition filtering is a major off-line image processing technique commonly used to improve the SNR and CNR. A major drawback of filtering is that it often diffuses/blurs important structures along with noise. In this paper, we introduce two novel scale-based filtering methods that use local structure size or 'object scale' information to arrest smoothing around fine structures and across even low-gradient boundaries. The first of these methods uses a weighted average over a scale-dependent neighborhood while the other employs scale-dependent diffusion conductance to perform filtering. Both methods adaptively modify the degree of filtering at any image location depending on local object scale. Qualitative experiments based on both phantoms and patient MR images show significant improvements using the scale-based methods over the extant anisotropic diffusive filtering method in preserving fine details and sharpness of object boundaries. Quantitative analysis on phantoms generated under a range of conditions of blurring, noise, and background variation confirm the superiority of the new scale-based approaches.

We present a semi-automated method for constraining the topology of inner cerebral cortex volumes generated from T1- weighted magnetic resonance images (MRI). An initial tissue classification is generated based on a measurement model that accounts for partial volume effects and the presence of image inhomogeneities due to field non-uniformities. This classification is used to generate an interior cerebral white matter brain volume. This volume is processed by our algorithm to ensure that the topology of the cortical surface, that of a two-dimensional sheet, is represented in tessellations of the volume. We extend our previous work on topological constraints, which introduced an automated correction procedure that creates graph representations of volumetric objects in order to identify topological defects in their segmentation. We improve this method by performing an iterative correction process that limits the severity of changes made to the initial segmentation. The previous method also requires the duplication of slices of data wherever a change is required, which significantly increases the size of the volume. In the new method we identify a set of corrections that can be made without slice duplication. The key benefits to the improvements in our method are improved localization and correction of topological defects resulting in increased accuracy of the resulting cortical surface representation and a decrease in the size of the resulting volume.

A fully automated 3D version of the so-called white matter method for correcting intensity non-uniformity in MR T1- weighted neuro images is presented. The algorithm is an extension of the original work published previously. The major part of the extension was the development of a fully automated method for the generation of the reference points. In the design of this method, a number of measures were introduced to minimize the effects of possible inclusion of non-white matter voxels in the selection process. The correction process has been made iterative. A drawback of this approach is an increased cost in computational time. The algorithm has been tested on T1-weighted MR images acquired from a longitudinal study involving elderly subjects and people with probable Alzheimer's disease. More quantitative measures were used for the evaluation of the algorithm's performance. Highly satisfactory correction results have been obtained for images with extensive intensity non-uniformity either present in raw data or added artificially. With intensity correction, improved accuracy in the measurement of the rate of brain atrophy in Alzheimer's patients as well as in elderly people due to normal aging has been achieved.

The design of a database containing head Computed Tomography (CT) studies is presented, along with a justification for the database's composition. The database will be used to validate software algorithms that screen normal head CT studies from studies that contain pathology. The database is designed to have the following major properties: (1) a size sufficient for statistical viability, (2) inclusion of both normal (no pathology) and abnormal scans, (3) inclusion of scans due to equipment malfunction, technologist error, and uncooperative patients, (4) inclusion of data sets from multiple scanner manufacturers, (5) inclusion of data sets from different gender and age groups, and (6) three independent diagnosis of each data set. Designed correctly, the database will provide a partial basis for FDA (United States Food and Drug Administration) approval of image processing algorithms for clinical use. Our goal for the database is the proof of viability of screening head CT's for normal anatomy using computer algorithms. To put this work into context, a classification scheme for 'computer aided diagnosis' systems is proposed.

Recent developments in digital detectors have led to investigating the importance of grids in mammography. We propose to examine the use Bayesian Image Estimation (BIE) as a software means of removing scatter post acquisition and to compare this technique to a grid. BIE is an iterative, non- linear statistical estimation technique that reduces scatter content while improving CNR. Images of the ACR breast phantom were acquired both with and without a grid on a calibrated digital mammography system. A BIE algorithm was developed and was used to process the images acquired without the grid. Scatter fractions (SF) were compared for the image acquired with the grid, the image acquired without the grid, and the image acquired without the grid and processed by BIE. Images acquired without the anti-scatter grid had an initial SF of 0.46. Application of the Bayesian image estimation technique reduced this to 0.03. In comparison, the use of the grid reduced the SF to 0.19. The use of Bayesian image estimation in digital mammography is beneficial in reducing scatter fractions. This technique is very useful as it can reduce scatter content effectively without introducing any adverse effects such as aliasing caused by gridlines.

This paper presents development and application of an optimal linear filter for delineation of activated areas of the brain from functional MRI (fMRI) time series data. The steps of the work accomplished are as follows. (1) Delineation of activated areas is formulated as an optimal linear filtering problem. In this formulation, a linear filter (image combination method) is looked for, which maximizes the signal-to-noise ratio (SNR) of the activated areas subject to the constraint of removing inactivated areas from the image. (2) An analytical solution for the problem is found. (3) Image pixel vectors and expected time series pattern (signature) for inactivated pixels are used to calculate the weighting vectors numerically. (4) The segmented image by the proposed method is compared to those generated by the conventional methods (correlation, t- statistic, and z-statistic). Visual qualities of the images as well as their SNR's are compared. The optimal linear filter outperforms the conventional methods of fMRI analysis based on improved SNR and contrast-to-noise ratio (CNR) of the images generated by the proposed method compared to those generated by the other methods. In addition, this method does not require a priori knowledge of the fMRI response to the paradigm for its application. The method is linear and most of the work is done analytically, thereby numerical implementation and execution of the method are faster than the conventional methods.

Recognizing that conspicuous multiple sclerosis (MS) lesions have high intensities in both dual-echo T2 and PD-weighted MR brain images, we show that it is possible to automatically determine a thresholding mechanism to locate conspicuous lesion pixels and also to identify pixels that suffer from reduced intensity due to partial volume effects. To do so, we first transform a T2-PD feature space via a log(T2)- log(T2+PD) remapping. In the feature space, we note that each MR slice, and in fact the whole brain, is approximately transformed into a line structure. Pixels high in both T2 and PD, corresponding to candidate conspicuous lesion pixels, also fall near this line. Therefore we first preprocess images to achieve RF-correction, isolation of the brain, and rescaling of image pixels into the range 0 - 255. Then, following remapping to log space, we find the main linear structure in feature space using a robust estimator that discounts outliers. We first extract the larger conspicuous lesions which do not show partial volume effects by performing a second robust regression for 1D distances along the line. The robust estimator concomitantly produces a threshold for outliers, which we identify with conspicuous lesion pixels in the high region. Finally, we perform a third regression on the conspicuous lesion pixels alone, producing a 2D conspicuous lesion line and confidence interval band. This band can be projected back into the adjacent, non-conspicuous, region to identify tissue pixels which have been subjected to the partial volume effect.

Melanoma diagnosis greatly relies on the observation of some characteristic features on skin tumors. Similarly, a computer- based diagnostic system has been designed to detect these features. However, specificity and sensitivity of features often rely on their location within the tumor. Locating the border of lesions is therefore of utmost importance. Segmentation of tumors is not easy because of high variability of coloration from one tumor to another and because of numerous 'artifacts' such as hairs, or skin lines. An adaptive and supervised approach was consequently chosen to segment lesions. Dermatologists were asked to hand-outline borders of lesions and, after an automatic selection of a point inside the tumor, radial intensity profiles were generated. The location of border was associated with each of them. A neural network was taught to predict border from these labeled profiles. Our approach has been found efficient and robust in such a way that human correction of automatic segmentation are most of the time insignificant. Features such as asymmetry of texture and inhomogeneity of colors can subsequently be observed and their clinical significance evaluated.

An image segmentation algorithm based on back-propagation neural network with robust supervised training, is presented. Using this algorithm it is possible to do brain MRI segmentation with good resolution between white and gray matter and recognition of some structures. Initial weight parameter evaluation takes fair amount of computational time resulting in a fast slice segmentation once the network has been trained. The training step consists of choosing a set of optimal weights for interchanging network nodes such that when the values of gray level patterns are presented to the network, it classifies them for different tissue types.

An automatic method for the delineation of posterior ribs in frontal chest radiographs is presented. We develop a statistical shape model for the complete rib cage. Contrary to previous work, we fit the global rib cage directly to a radiograph, instead of detecting rib border candidates locally and applying rules to infer the rib cage from these candidates. Each posterior rib is modeled by two parallel parabolas. The full rib cage, from rib 2 up and including rib 10, therefore contains 72 parameters. This number is reduced with principal component analysis: It is demonstrated that 10 parameters explain over 98% of the variability in a training set of 35 chest radiographs. The rib cage is fitted with Powell's direction set method for optimizing the model parameters, with a fit measure that gives high output when rib borders are located on edge pixels in the image. The method is robust and fairly accurate: On the 35 test images with a resolution of 512 by 512 pixels, rib borders are located with an accuracy of 3 pixels on average.

This paper describes the application of a statistical-based deformable model algorithm to the segmentation of kidneys in x-ray computed tomography (CT) images of laboratory mice. This segmentation algorithm has been developed as the crucial first step in a process to automatically screen mice for genetically-induced polycystic kidney disease (PKD). The algorithm is based on active shape models (ASMs) initially developed by Cootes, et al. Once the segmentation is complete, texture measurements are applied within kidney boundaries to detect the presence of PKD. The challenges associated with the segmentation of mouse kidneys (non-rigid organs) are presented, and the motivation for using ASMs in this application is discussed. Also, improvements were made to published ASM methods that may be generally helpful in other segmentation applications. In 15 of the 18 cases tested, the mouse kidneys and spine were detected with only minor errors in boundary position. In the remaining three cases, small parts of the kidneys were missed and/or some extra abdominal tissue was inadvertently included by the boundary. In all 18 cases, however, the kidneys were successfully detected at a level where PKD could be automatically screened for using mean-of-local-variance (MOLV) texture measurements.

The aim of this study is to evaluate the use of a local affine transformation for computer-aided interval change analysis in mammography. A multistage regional registration technique was developed for identifying masses on temporal pairs of mammograms. In the first stage, the breast images from the current and prior mammograms were globally aligned. An initial fan-shape search region was defined on the prior mammogram. In the second stage, the location of the fan-shape region was refined by warping, based on an affine transformation and simplex optimization. A new refined search region was defined on the prior mammogram. In the third stage a search for the best match between the lesion template from the current mammogram and a structure on the prior mammogram was carried out within the search region. This technique was evaluated on 124 temporal pairs of mammograms containing biopsy-proven masses. Eighty-six percent of the estimated lesion locations resulted in an area overlap of at least 50% with the true lesion locations. The average distance between the estimated and the true centroid of the lesions on the prior mammogram was 4.4 +/- 5.9 mm. The registration accuracy was improved in comparison with our previous study that used a data set of 74 temporal pairs of mammograms. This improvement gain is mainly from the local affine transformation.

This paper presents an automated method for segmenting CT images of the fractured foot. Segmentation boundary is determined by fuzzy inference with two types of knowledge acquired from orthopedic surgeons. Knowledge of joint is used to determine the boundary of adjacent normal bones. It gives higher degree to the articular cartilage according to local structure (parallelity) and intensity distribution around a joint part. Knowledge of fragment is used to find a contact place of fragments. It evaluates Euclidian distance map (EDM) of the contact place and gives higher degree to the narrow part. Each of the knowledge is represented by fuzzy if-then rules, which can provide degrees for segmentation boundary. By evaluating the degrees in region growing process, a whole foot bone is decomposed into each of anatomically meaningful bones and fragments. An experiment was done on CT images of the subjects who have depressed fractures on their calcanei. The method could effectively give higher degrees on the essential boundary, suppressing generation of useless boundary caused by the internal cavities in the bone. Each of the normal bones and fragments were correctly segmented.

We are developing computerized feature extraction and classification methods to analyze malignant and benign pulmonary nodules in three-dimensional (3-D) thoracic images. This paper focuses on an approach for characterizing the internal texture which is one of important clues for differentiating between malignant and benign nodules. In this approach, each voxel was described in terms of shape index derived from curvatures on the voxel. The voxels inside the nodule were aggregated via shape histogram to quantify how much shape category was present in the nodule. Topological features were introduced to characterize the morphology of the cluster constructed from a set of voxels with the same shape category. The properties such as curvedness and CT density were also built into the representation. We evaluated the effectiveness of the topological and histogram features extracted from 3-D pulmonary nodules for classification of malignant and benign internal structures. We also compared the performance of the computerized classification with the experienced physicians. The classification performance based on the combined feature space reached the performance of the experienced physicians. Our results demonstrate the feasibility of using topological and histogram features for analyzing internal texture to assist physicians in making diagnostic decisions.

The aim of this work was to determine a methodology to selection of the best features subset and artificial neural network (ANN) topology to classify masses lesions. The backpropagation training algorithm was used to adjust the weights of ANN. A total of 118 regions of interest images were chosen (68 benign and 50 malignant lesions). In a first step, images were submitted to a combined process of thresholding, mathematical morphology, and region growing techniques. After, fourteen texture features (Haralick descriptors) and fourteen shape features (circularity, compactness, Gupta descriptors, Shen descriptors, Hu descriptors, Fourier descriptor and Wee descriptors) were extracted. The Jeffries-Matusita method was used to select the best features. Three shape features sets and three texture features sets were selected. The Receiver Operating Characteristic (ROC) analyses were conducted to evaluated the classifier performance. The best result for shape feature set was accurate classification rate of 98.21%, specificity of 98.37%, sensitivity of 98.00% and the area under ROC curve of 0.99, for a ANN with 5 hidden units. The best result for texture feature set was accurate classification rate of 97.08%, specificity of 98.53%, sensitivity of 95.11% and the area under ROC curve of 0.98, for an ANN with 4 hidden units.

In this paper, we propose an efficient semi-automatic algorithm to segment a 3-D object by using a given segmentation result in a single slice. In the proposed algorithm, the segmentation is performed slice-by-slice using z correlation as well as xy correlation based on the assumption that the region to be segmented is homogeneous and has discernable boundaries. We first estimate a parametric motion model of the organ from the previous slice to the current slice, and find an estimated boundary of the organ by projecting the previous result. Then, we extract 3 kinds of seeds in the current slice by using the projected boundaries and the pixel luminance values. All extracted seeds are grown to produce the precise boundary of the organ. And wrong boundary portions due to region growing at low gradient areas are corrected by the post-processing based on a Fourier descriptor. Finally, to catch up on newly appearing areas, a two-way tracking method is applied. The proposed algorithm provides satisfactory results in segmenting kidneys from an X- ray CT body image set of 82 slices.

This paper presents a fuzzy rule-based region growing method for segmenting two-dimensional (2-D) and three-dimensional (3- D) magnetic resonance (MR) images. The method is an extension of the conventional region growing method. The proposed method evaluates the growing criteria by using fuzzy inference techniques. The use of the fuzzy if-then rules is appropriate for describing the knowledge of the legions on the MR images. To evaluate the performance of the proposed method, it was applied to artificially generated images. In comparison with the conventional method, the proposed method shows high robustness for noisy images. The method then applied for segmenting the dynamic MR images of the liver. The dynamic MR imaging has been used for diagnosis of hepatocellular carcinoma (HCC), portal hypertension, and so on. Segmenting the liver, portal vein (PV), and inferior vena cava (IVC) can give useful description for the diagnosis, and is a basis work of a pres-surgery planning system and a virtual endoscope. To apply the proposed method, fuzzy if-then rules are derived from the time-density curve of ROIs. In the experimental results, the 2-D reconstructed and 3-D rendered images of the segmented liver, PV, and IVC are shown. The evaluation by a physician shows that the generated images are comparable to the hepatic anatomy, and they would be useful to understanding, diagnosis, and pre-surgery planning.

A novel approach is presented for fully automated boundary extraction and rectification of bony tissue from planar CT data. The approach extracts and rectifies feature boundary in a hierarchical fashion. It consists of a fuzzy multilevel thresholding operation, followed by a small void cleanup procedure. Then a binary morphological boundary detector is applied to extract the boundary. However, defective boundaries and undesirable artifacts may still be present. Thus two innovative anatomical knowledge based algorithms are used to remove the undesired structures and refine the erroneous boundary. Results of applying the approach on lumbar CT images are presented, with a discussion of the potential for clinical application of the approach.

In this paper, we propose a method to automate the segmentation of airway tree structures in lung from a stack of gray-scale computed tomography (CT) images. A three- dimensional seeded region growing is performed on images without any preprocessing operation to obtain the segmented bronchus area. We first apply genetic algorithm (GA) to retrieve the seed point and it is based on the geometric features (shape, location and size) of the airway tree. By the feature of the size of the lung and airway tree, an optimal threshold value is obtained. The final extracted bronchus area with the optimal threshold value is reconstructed and visualized by 3D texture mapping method.

In this paper a method for three-dimensional (3-D) semi- automatic segmentation of volumes of medical images is described. The method is semi-automatic in the sense that, in the initial phase, the user assistance is required for manual segmentation of a certain number of slices (cross-sections) of the volume. In the second phase, the algorithm for automatic segmentation is started. The segmentation algorithm is based on the active contour approach. A semi 3-D active contour algorithm is used in the sense that additional inter-slice forces are introduced in order to constrain the obtained solution. The energy function which is minimized is modified to exploit information provided by the manual segmentation of some of the slices performed by the user. The experiments have been performed using computed tomography (CT) scans of the abdominal region of the human body. In particular, CT images of abdominal aortic aneurysms have been segmented to determine the location of aorta. The experiments have shown the feasibility of the approach.

A technique for segmentation of articular cartilage from 3D MRI scans of the knee has been developed. It overcomes the limitations of the conventionally used region growing techniques, which are prone to inter- and intra-observer variability, and which can require much manual intervention. We describe a hybrid segmentation method combining expert knowledge with directionally oriented Canny filters, cost functions and cubic splines. After manual initialization, the technique utilized 3 cost functions which aided automated detection of cartilage and its boundaries. Using the sign of the edge strength, and the local direction of the boundary, this technique is more reliable than conventional 'snakes,' and the user had little control over smoothness of boundaries. This means that the automatically detected boundary can conform to the true shape of the real boundary, also allowing reliable detection of subtle local lesions on the normally smooth cartilage surface. Manual corrections, with possible re-optimization were sometimes needed. When compared to the conventionally used region growing techniques, this newly described technique measured local cartilage volume with 3 times better reproducibility, and involved two thirds less human interaction. Combined with the use of 3D image registration, the new technique should also permit unbiased segmentation of followup scans by automated initialization from a baseline segmentation of an earlier scan of the same patient.

Heart image analysis is a challenging and important process used for a range of purposes such as image based measurement, visualization, etc. The most important step in medical image analysis is segmentation. In this work we present an algorithm for CT heart image segmentation. The segmentation is based on two basic pieces of information, pixels brightness and motion. The motion information is gathered as the optical flow information. Such information is later used for definition of an energy function for image labeling. This energy function represents a Markov random field (MRF) posterior distribution function. The MAP estimation of the segmented image has been determined using the simulated annealing (SA) algorithm.

In this study, a computerized method for detection of pulmonary embolism in spiral CT angiography was developed. The method is based on segmentation of pulmonary vessels to limit the search space for thrombi. Several three-dimensional image features such as local contrast, second derivatives, and distance to the vessel wall were employed for detection of thrombi and for elimination of false positives. Volume rendering was applied for display of detection results. Preliminary results based on several clinical data show the potential of our method.

We present further improvements to the methods of interpretation of the Posterior Capsular Opacification (PCO) images. These retro-illumination images of the back surface of the implanted lens are used to monitor the state of patient's vision after cataract operation. A common post-surgical complication is opacification of the posterior eye capsule caused by the growth of epithelial cells across the back surface of the capsule. Interpretation of the PCO images is based on their segmentation into transparent image areas and opaque areas, which are affected by the growth of epithelial cells and can be characterized by the increase in the image local variance. This assumption is valid in majority of cases. However, for different materials used for the implanted lenses it sometimes happens that the epithelial cells grow in a way characterized by low variance. In such a case segmentation gives a relatively big error. We describe an application of an anisotropic diffusion equation in a non-linear pre-processing of PCO images. The algorithm preserves the high-variance areas of PCO images and performs a low-pass filtering of small low- variance features. The algorithm maintains a mean value of the variance and guarantees existence of a stable solution and improves segmentation of the PCO images.

Fractal dimension (fd) of lesion borders has been proposed as a feature to discriminate between malignant and benign masses on MR breast images. The fd value is computed using a sample space of fractal models, an approach that reduces sensitivity to signal noise and image variability. The user specifies a rectangular region of interest (ROI) around the mass and the algorithm generates a segmentation zone from the ROI. Fractal models are constructed on multiple threshold intensity contours within the segmentation zone. Preliminary results show that the combination of statistical fd feature and expert-observer interpretations improves separation of benign from malignant breast masses when compared to expert-observer interpretations alone. The statistical fd feature has been incorporated into a prototype computer-aided-diagnosis (CAD) system that outputs the following to assist the diagnostician in determining clinical action: (1) A likelihood-of-cancer measure computed from fd and reader interpretations, (2) A binary categorical value indicating whether a test case is fd- highly suspicious or fd-inconclusive, (3) The ROI with portions of the mass border with the most cancer-like fractal characteristics highlighted.

We have developed a computer algorithm to detect breast masses on digitized mammograms. In this study, we analyze the performance of the trained algorithm with independent, clinical mammograms to assess its potential as an aid to the radiologist in mammographic interpretation. A digitized mammogram is processed with an adaptive enhancement filter followed by region growing to detect significant breast structures. Morphological and texture features are then extracted from each of the detected structures and used to identify potential breast masses. In the current study, we evaluated the performance of the algorithm with independent sets of 92 prior mammograms (films acquired 1 to 4 years prior to biopsy) and 260 preoperative mammograms from 123 patients. The computer algorithm had a 'by-film' mass detection sensitivity of 51% with 2.3 FPs/image when applied to the prior mammograms including the detection of 57% of the malignant masses. When applied to the set of preoperative mammograms, the algorithm identified 73% of the masses with 2.2 FPs/image and had a malignant mass detection sensitivity of 83%. The 'by-case' sensitivity was 67% (74% for malignant masses) and 85% (92% for malignant masses) for the prior and preoperative mammograms, respectively. This study indicates that the computer algorithm may be useful as a second reader in the clinical interpretation of mammograms because it has the ability to detect masses in both preoperative and prior mammograms.

Liver cancer is one of the leading cancerous diseases that can disappoint a physician before reaching the final diagnosis. Thus far, all cancer diagnoses should and usually do have tissue diagnose. A physician gets a little piece of tissue from the abnormal area and a pathologist determines if it is cancer or not. Therefore, the biopsy is the definitive test for liver cancer. In this paper, we present an unsupervised approach using Hopfield Neural Network (HNN) to segment color images of liver tissues prepared by standard staining method. The segmentation problem is formulated as the minimization of an energy function synonymous to that of HNN for optimization. We modify the HNN to reach a status close to the global minimum in a prespecified time of convergence. Furthermore, the nuclei and their corresponding cytoplasm regions are automatically extracted based on the features of color image histogram. The nuclei and cytoplasm regions are then used to formulate the diagnostic rules. In the analysis, we show a tables of the ratio of (nuclei/cytoplasm) image areas inside different subwindow sizes of the image. Each liver color image is represented in the RGB, HSV and HLS color spaces to investigate the effect of color system choice on the results. The automation of the extraction process in the liver pathological image can be easily implemented in the clinic in order to provide more accurate quantitative information that can help for a better liver cancer diagnosis.

We present development, application, and performance evaluation of three different texture feature extraction methods for classification of benign and malignant microcalcifications in mammograms. The steps of the work accomplished are as follows. (1) A total of 103 regions containing microcalcifications were selected from a mammographic database. (2) For each region, texture features were extracted using three approaches: co-occurrence based method of Haralick; wavelet transformations; and multi-wavelet transformations. (3) For each set of texture features, most discriminating features and their optimal weights were found using a real-valued genetic algorithm (GA) and a training set. For each set of features and weights, a KNN classifier and a malignancy criterion were used to generate the corresponding ROC curve. The malignancy of a given sample was defined as the number of malignant neighbors among its K nearest neighbors. The GA found a population with the largest area under the ROC curve. (4) The best results obtained using each set of features were compared. The best set of features generated areas under the ROC curve ranging from 0.82 to 0.91. The multi-wavelet method outperformed the other two methods, and the wavelet features were superior to the Haralick features. Among the multi-wavelet methods, redundant initialization generated superior results compared to non-redundant initialization. For the best method, a true positive fraction larger than 0.85 and a false positive fraction smaller than 0.1 were obtained.

We formulate a model for probability distributions on image spaces. We show that any distribution of images can be factored exactly into conditional distributions of feature vectors at one resolution (pyramid level) conditioned on the image information at lower resolutions. We would like to factor this over positions in the pyramid levels to make it tractable, but such factoring may miss long-range dependencies. To fix this, we introduce hidden class labels at each pixel in the pyramid. The result is a hierarchical mixture of conditional probabilities, similar to a hidden Markov model on a tree. The model parameters can be found with maximum likelihood estimation using the EM algorithm. We have obtained encouraging preliminary results on the problems of detecting masses in mammograms.

In this paper, we propose a method of recognition of lung nodules using 3D nodule and blood vessel models considering uncertainty of recognition. Region of interest (ROI) areas are extracted by our quoit filter which is a kind of Mathematical Morphology filter. We represent nodules as sphere models, blood vessels as cylinder models and the branches of the blood vessels as the connections of the cylinder models, respectively. All of the possible models for nodules and blood vessels are generated which can occur in the ROI areas. The probabilities of the hypotheses of the ROI areas coming from the sphere models are calculated and the probabilities for the cylinder models are also calculated. The most possible sphere models and cylinder models which maximize the probabilities are searched considering uncertainty of recognition. If the maximum probability for the nodule model is higher, the shadow candidate is determined to be abnormal. By applying this new method to actual CT images (37 patient images), good results have been acquired.

This paper describes a prototype computer aided diagnosis system to assist in the interpretation of mammograms. The distinctive feature of our work is the combination of image processing and decision support. We wish, in our system, to relate the data in a digital image to a decision contained in a clinical guideline describing a patient's management. Our system is designed to present a user with sets of arguments for each of the possible interpretations of a feature detected on the image and for each of the possible management options that might be followed in handling the patient's care. We have carried out an extensive knowledge elicitation exercise, involving the analysis of 'think out loud' protocols obtained from expert radiologists interpreting mammograms form a carefully selected test set. The results of this analysis reveal which terms capture the most salient characteristics of calcifications. These terms will be used to construct the arguments used in the decision support provided by CADMIUM II. The final element of CADMIUM II is a library of image processing algorithms. A set of different approaches to the detection and characterization of calcifications has been implemented. The image processing is used to provide a quantitative estimate of the evidence that an image contains in support of an argument.

Multiple Sclerosis (MS) is an acquired disease of the central nervous system. Subjective cognitive and ambulatory test scores on a scale called EDSS are currently utilized to assess the disease severity. Various MRI protocols are being investigated to study the disease based on how it manifests itself in the images. In an attempt to eventually replace EDSS by an objective measure to assess the natural course of the disease and its response to therapy, we have developed image segmentation methods based on fuzzy connectedness to quantify various objects in multiprotocol MRI. These include the macroscopic objects such as lesions, the gray matter (GM), white matter (WM), cerebrospinal fluid (CSF), and brain parenchyma as well as the microscopic aspects of the diseased WM. Over 1000 studies have been processed to date. By far the strongest correlations with the clinical measures were demonstrated by the Magnetization Transfer Ratio (MTR) histogram parameters obtained for the various segmented tissue regions emphasizing the importance of considering the microscopic/diffused nature of the disease in the individual tissue regions. Brain parenchymal volume also demonstrated a strong correlation with the clinical measures indicating that brain atrophy is an important indicator of the disease. Fuzzy connectedness is a viable segmentation method for studying MS.

In this paper, we present a computer-aided diagnosis (CAD) system for lung cancer to detect nodule candidates at an early stage from the present and the early helical CT screening of the thorax. We developed an algorithm that can compare automatically the slice images of present and early CT scans for the assistance of comparative reading in retrospect. The algorithm consists of the ROI detection and shape analysis based on comparison of each slice image in the present and the early CT scans. The slice images of present and early CT scans are both displayed in parallel and analyzed quantitatively in order to detect the changes in size and intensity affection. We validated the efficiency of this algorithm by application to image data for mass screening of 50 subjects (total: 150 CT scans). The algorithm could compare the slice images correctly in most combinations with respect to physician's point of view. We validated the efficiency of the algorithm which automatically detect lung nodule candidates using CAD system. The system was applied to the helical CT images of 450 subjects. Currently, we are carrying out the clinical field test program using the CAD system. The results of our CAD system have indicated good performance when compared with physician's diagnosis. The experimental results of the algorithm indicate that our CAD system is useful to increase the efficiency of the mass screening process. CT screening of thorax will be performed by using the CAD system as a counterpart to the double reading technique actually used in herical CT screening program, not by using the film display.

Chest radiographs represent a difficult class of images concerning automatic analysis with image processing methods. In our former work we presented a model based method to detect the rib borders and implemented a compensation algorithm of the rib structures. Recently we developed an improved method for rib border detection and algorithms to find the objects like chest border, vertebral spine, heart and intravascular catheter within a model driven approach. The determined borders of these objects allow further analysis and image enhancement for diagnose assistance.

Any segmentation approach assumes certain knowledge concerning data modalities, relevant organs and their imaging characteristics. These assumptions are necessary for developing criteria by which to separate the organ in question from the surrounding tissue. Typical assumptions are that the organs have homogeneous gray-value characteristics (region growing, region merging, etc.), specific gray-value patterns (classification methods), continuous edges (edge-based approaches), smooth and strong edges (snake approaches), or any combination of these. In most cases, such assumptions are invalid, at least locally. Consequently, these approaches prove to be time consuming either in their parameterization or execution. Further, the low result quality makes post- processing necessary. Our aim was to develop a segmentation approach for large 3D data sets (e.g., CT and MRI) that requires a short interaction time and that can easily be adapted to different organs and data materials. This has been achieved by exploiting available knowledge about data material and organ topology using anatomical models that have been constructed from previously segmented data sets. In the first step, the user manually specifies the general context of the data material and specifies anatomical landmarks. Then this information is used to automatically select a corresponding reference model, which is geometrically adjusted to the current data set. In the third step, a model-based snake approach is applied to determine the correct segmentation of the organ in question. Analogously, this approach can be used for model-based interpolation and registration.

Segmentation of brain hemispheres is necessary to study left- right differences in structure and function. For extraction of a 3D individual region-of-interest atlas of the human brain, detection of the midplane is the sine qua non as it provides the reference plane for determining other anatomical objects. Extraction of the sagittal midplane is done in two main steps. First, a 2D filter is used to give a first approximation of the midplane position. To model symmetry properties of the midplane neighborhood, the different filter columns contain class-dependent weights for cerebrospinal fluid, gray and white matter. The filter can be rotated in a range of angles. In a user-defined range of planes, the global maximum of the filter response is searched for and the resulting position is utilized to restrict the search in the remaining planes. In a second step, midplane extraction is refined by searching for the optimal path of the midplane within the filter mask at optimum position. Symmetry properties are modeled analogous to the first step with class-dependent weights of the filter columns. The extraction of the midplane gives accurate and reliable results in simulated data sets and patient studies even if asymmetric artifacts are simulated.

To model the true shape of MRI brain images, automatically classified T1-weighted 3D MRI images (gray matter, white matter, cerebrospinal fluid, scalp/bone and background) are utilized for simulation of grayscale data and imaging artifacts. For each class, Gaussian distribution of grayscale values is assumed, and mean and variance are computed from grayscale images. A random generator fills up the class images with Gauss-distributed grayscale values. Since grayscale values of neighboring voxels are not correlated, a Gaussian low-pass filtering is done, preserving class region borders. To simulate anatomical variability, a Gaussian distribution in space with user-defined mean and variance can be added at any user-defined position. Several imaging artifacts can be added: (1) to simulate partial volume effects, every voxel is averaged with neighboring voxels if they have a different class label; (2) a linear or quadratic bias field can be added with user-defined strength and orientation; (3) additional background noise can be added; and (4) artifacts left over after spoiling can be simulated by adding a band with increasing/decreasing grayscale values. With this method, realistic-looking simulated MRI images can be produced to test classification and segmentation algorithms regarding accuracy and robustness even in the presence of artifacts.