This paper describes two statistical iterative reconstruction methods for X-ray CT. The first method assumes a mono-energetic model for X-ray attenuation. We approximate the transmission Poisson likelihood by a quadratic cost function and exploit its convexity to derive a separable quadratic surrogate function that is easily minimized using parallelizable algorithms. Ordered subsets are used to accelerate convergence. We apply this mono-energetic algorithm (with edge-preserving regularization) to simulated thorax X-ray CT scans. A few iterations produce reconstructed images with lower noise than conventional FBP images at equivalent resolutions. The second method generalizes the physical model and accounts for the poly-energetic X-ray source spectrum and the measurement nonlinearities caused by energy-dependent attenuation. We assume the object consists of a given number of non-overlapping tissue types. The attenuation coefficient of each tissue is the product of its unknown density and a known energy-dependent mass attenuation coefficient. We formulate a penalized-likelihood function for this poly-energetic model and develop an iterative algorithm for estimating the unknown densities in each voxel. Applying this method to simulated X-ray CT measurements of a phantom containing both bone and soft tissue yields images with significantly reduced beam hardening artifacts.

We propose a new noise-reduction method for tomographic reconstruction. The method incorporates a priori information on the source image for allowing the derivation of the energy spectrum of its ideal sinogram. In combination with the energy spectrum of the Poisson noise in the measured sinogram, we are able to derive a Wiener-like filter for effective suppression of the sinogram noise. The filtered backprojection (FBP) algorithm, with a ramp filter, is then applied to the filtered sinogram to produce tomographic images. The resulting filter has a closed-form expression in the frequency space and contains a single user-adjustable regularization parameter. The proposed method is hence simple to implement and easy to use. In contrast to the ad hoc apodizing windows, such as Hanning and Butterworth filters, that are commonly used in the conventional FBP reconstruction, the proposed filter is theoretically more rigorous as it is derived by basing upon an optimization criterion, subject to a known class of source image intensity distributions.

Electron Paramagnetic Resonance (EPR) allows for the non-invasive imaging of free radicals in biological systems. Although a number of physical factors have hindered the development of EPR as an imaging modality, EPR offers the potential for tissue oxymetry. EPR images are typically reconstructed using a traditional filtered back-projection technique. We are attempting to improve the quality of EPR images by using maximum-entropy based iterative image reconstruction algorithms. Our investigation has so far focused on two methods, the multiplicative algebraic reconstruction technique (MART), and an algorithm that is motivated by interior-point reconstruction. MART is a row-action method that maintains strict equality in the constraints while minimizing the entropy functional. The latter method, which we have named Least-Squares Barrier Entropy (LSBEnt), transforms the constrained problem into an unconstrained problem and maximizes entropy at a prescribed distance from the measured data. EPR studies are frequently characterized by low signal-to-noise ratios and wide line widths. The effect of the backprojection streaking artifact can be quite severe and can seriously compromise a study. We have compared the iterative results with filtered backprojection on two-dimensional (2-D) EPR acquisitions of various phantoms. Encouraging preliminary results have demonstrated that one of the clear advantages of the iterative methods is their lack of streaking artifacts that plague filtered backprojection.

We formulate the tomographic reconstruction problem in a variational setting. The object to be reconstructed is considered as a continuous density function, unlike in the pixel-based approaches. The measurements are modeled as linear operators (Radon transform), integrating the density function along the ray path. The criterion that we minimize consists of a data term and a regularization term. The data term represents the inconsistency between applying the measurement model to the density function and the real measurements. The regularization term corresponds to the smoothness of the density function. We show that this leads to a solution lying in a finite dimensional vector space which can be expressed as a linear combination of generating functions. The coefficients of this linear combination are determined from a linear equation set, solvable either directly, or by using an iterative approach. Our experiments show that our new variational method gives results comparable to the classical filtered back-projection for high number of measurements (projection angles and sensor resolution). The new method performs better for medium number of measurements. Furthermore, the variational approach gives usable results even with very few measurements when the filtered back-projection fails. Our method reproduces amplitudes more faithfully and can cope with high noise levels; it can be adapted to various characteristics of the acquisition device.

We developed an iterative reconstruction method for SPECT which uses list-mode data instead of binned data. It uses a more accurate model of the collimator structure. The purpose of the study was to evaluate the resolution recovery and to compare its performance to other iterative resolution recovery methods in the case of high noise levels The source distribution is projected onto an intermediate layer. Doing this we obtain the complete emission radiance distribution as an angular sinogram. This step is independent of the acquisition system. To incorporate the resolution of the system we project the individual list-mode events over the collimator wells to the intermediate layer. This projection onto the angular sinogram will define the probability a photon from the source distribution will reach this specific location on the surface of the crystal, thus being accepted by the collimator hole. We compared the SPECT list-mode reconstruction to MLEM, OSEM and RBI. We used Gaussian shaped point sources with different FWHM at different noise levels. For these distributions we calculated the reconstructed images at different number of iterations. The modeling of the resolution in this algorithm leads to a better resolution recovery compared to other methods, which tend to overcorrect.

In many cone beam reconstruction algorithms square geometry for the detector elements and cubic geometry for the reconstruction voxels are assumed. With such geometry the various operations in image reconstruction, notably projection and backprojection, can be carried out in the same manner at all angles, resulting in uniform image quality and ease of operation. However, in current multi-row cone beam CT systems the spacing between the detector rows is typically greater than the lateral spacing between the detector elements for the reconstruction of objects with slice thickness greater than the lateral resolutions. The asymmetric voxel dimensions and detector element dimensions introduce complications in the image reconstruction operations, and potentially non-uniform image quality. We have developed a procedure to preprocess the cone beam data detected on non-square detector elements for compatibility with cone beam reconstruction algorithms in which symmetric voxel dimensions and detector element dimensions are assumed. Complications and potential non-uniformity in image reconstruction operations are eliminated through simple scaling of the input cone beam projection data and decompression/elongation of the intermediate reconstructed image while retaining the symmetric geometry in the reconstruction algorithm. The procedure is a generic solution to cone beam image reconstruction applicable to all types of reconstruction algorithms.

The spatial resolution of echo planar image (EPI) data acquired for functional MRI (fMRI) studies is low. To facilitate their interpretation, conventional T1-weighted anatomical images are often acquired prior to the acquisition of the EP images. T1-weighted and EP images are then registered and activation patterns computed from the EP images are superimposed on the anatomic images. Registration between the anatomic and the EP images is required to compensate for patient motion between the acquisitions and for geometric distortions affecting EP images. Recently, methods have been proposed to register EP and anatomic images using non-rigid registration techniques. In these approaches, the transformation is parameterized using splines. Here, we propose an alternative solution to this problem based on optical flow with non-stationary stiffness constraint. The approach we propose also includes several preprocessing steps such as automatic skull removal and intensity remapping. Results obtained with eight studies on normal volunteers are presented.

A specially designed phantom consisting of a 3D array of 427 accurately manufactured spheres together with a point-based registration algorithm was used to detect distortion described by polynomial orders 1-4. More than thirty 3D gradient echo (FFE) and multi-slice spin echo (SE) phantom scans were acquired with a Philips 1.5T Gyroscan. Distortion was measured as a function of: readout gradient strength (0.72<= G_r <=1.7mT/m), TR/TE/flip angle, shim settings, and temporal distortion change for 11 weekly scans for the FFE sequence and TR/TE/slice gap for SE. Precision measurements for linear distortion were: scale <=0.03%, shear <=0.04 degrees. Linear distortion in the readout dependent directions increased with decreased readout strength (r>0.93). There was a significantly higher (p<0.01) sagittal shear for 5 SE scans compared with 5 FFE ones with the same G_r - possibly because of slice selection. Different shim settings produced only linear distortion change: up to 2% scale and 1 degree shear. There was negligible distortion change over time: scale < 0.1%, shear <= 0.05 degrees. There was a decrease in distortion as a function of polynomial order (r>0.9, n=33), 75% of the distortion was either first or second order.

In interventional procedures, computed tomography (CT) has demonstrated its effectiveness in guiding operators through otherwise difficult tasks. By providing near real time feedback, CT fluoroscopy (CTF) enables the operator to dynamically adjust the location and orientation of the biopsy instrument. The most important performance parameter of CTF is the system temporal response. In this paper, we present a mathematical framework that accurately characterizes the system response of a needle type instrument. Based on the model, a modified halfscan reconstruction algorithm is presented. The algorithm makes use of the redundant nature of CTF data processing and enables efficient generation of CT images. The effectiveness of the algorithm is demonstrated by theoretical analysis and phantom experiments.

An algorithm for the reconstructions of ISO-resolution volumetric MR data sets from two standard orthogonal MR scans having anisotropic resolution has been developed. The reconstruction algorithm starts by registering a pair of orthogonal volumetric MR data sets. The registration is done by maximizing the correlation between the gradient magnitude using a simple translation-rotation model in a multi-resolution approach. Then algorithm assumes that the individual voxels on the MR data are an average of the magnetic resonance properties of an elongated imaging volume. Then, the process is modeled as the projection of MR properties into a single sensor. This model allows the derivation of a set of linear equations that can be used to recover the MR properties of every single voxel in the SO-resolution volume given only two orthogonal MR scans. Projections on convex sets (POCS) was used to solve the set of linear equations. Experimental results show the advantage of having a ISO-resolution reconstructions for the visualization and analysis of small and thin muscular structures.

Three-dimensional angiographic reconstrcution has emerged as an alternative to the traditional depiction of aneurysm angioarchitecture provided by 2-D perspective projections acquired by digital subtraction angiography (DSA) and fluoroscopy. One clinical application of research involving 3-D angiographic reconstruction is intraoperative localization and visualization during aneurysm embolization procedures. For this procedure, reconstruction quality is important for the 3-D reconstruction of anatomy as well as for the reconstrucution of intraaneurysm coils imaged endovascularly and subsequently rendered within an existing 3-D anatomic representation. Rotational angiography involves the acquisition of a series of 2-D, cone-beam projections of intracranial anatomy by a rotating x-ray gantry following a single injection of contrast media. Our investigation focuses on the practicality of using methods that employ algebraic reconstruction techniques (ART) to reconstruct 3-D data from 2-D cone-beam projections acquired using rotational angiography during embolization procedures. Important to our investigation are issues that arise within the implementation of the projection, correction and backprojection steps of the reconstruction algorithm that affect reconstruction quality. Several methods are discussed to perform accurate voxel grid projection and backprojection. Various parameters of the reconstruction algorithm implementation are also investigated. Preliminary results indicating that quality 3-D reconstructions from 2-D projections of synthetic volumes are presented. Further modifications to our implementation hold the promise of achieving accurate reconstruction results with a lower computation cost than the algorithm implemention used for this study. We have concluded that methods to extend the traditional ART algorithm for cone-beam projection acquisition produce quality 3-D reconstructions.

Multi-slice CT (MCT) is one of the most recent technical advancements in computed tomography. MCT offers high volume coverage, faster scan speed, and reduced x-ray tube loading. When combined with the helical scan mode, MCT provides even higher volume coverage as a result of the elimination of the inter-scan delays. Similar to the single slice CT, the projection data collected in MCT is inherently inconsistent. To combat projection inconsistency, many image reconstruction algorithms were investigated and developed. Recent studies have shown, however, that the image quality of MCT can be significantly degraded when the data is collected in a tilted helical mode. The degradation can be so severe that it is unacceptable for routine clinical usage. In this paper, we present a detailed investigation to show that the root cause of the image quality degradation is the deviation of the reconstruction iso-center from the gantry iso-center. An analytical model is derived to establish a quantitative relationship between the iso0center shift and other system parameters. The model serves as the mathematical basis for the derivation of a frequency-domain correction algorithm. Detailed performance evaluation is provided in terms of spatial resolution, noise, computational efficiency, and image artifacts.

We present a novel approximate image reconstruction technique for helical cone-beam CT, called the Advanced Multiple Plane Reconstruction (AMPR). The method is an extension of the ASSR algorithm presented in Medical Physics vol. 27, no. 4, 2000 by Kachelriess et al. In the ASSR, the pitch is fixed to a certain value and dose usage is not optimum. These limitations have been overcome in the AMPR algorithm by reconstructing several image planes from any given half scan range of projection angles. The image planes are tilted in two orientations so as to optimally use the data available on the detector. After reconstruction of several sets of tilted images, a subsequent interpolation step reformats the oblique image planes to a set of voxels sampled on a cartesian grid. Using our novel approach on a scanner with 16 slices, we can achieve image quality superior to what is currently a standard for four-slice scanners. Dose usage in the order of 95% for all pitch values can be achieved. We present simulations of semi-antropomorphic phantoms using a standard CT scanner geometry and a 16 slice design.

Computer-aided surgery requires the accurate registration of tomographic pre-operative images with intra-operative surface points acquired with 3D spatial localizers. Surface-based registration of these tomographic images with the surface points does, in turn, require a precise and accurate surface representation of the structures to be registered. This paper presents a level set technique for the automatic segmentation of the liver in abdominal CT scans. The main difficulty with level set methods is the design of appropriate speed functions for particular applications. Here we propose a novel speed function that is designed to (1) stop the propagating front at organ boundaries with weak edges, and (2) incorporate a-priori information on the relative position of the liver and other structures. We show that the new speed function we have designed to stop the front a weak edges is superior to other approaches proposed in the literature both on simulated images and on CT images. Results obtained with our approach for the segmentation of the liver in several CT scans are compared to contours obtained manually.

The multiscale approach derives a segmentation from the evolution of appropriate signal-descriptive features in scale-space. Features that are stable for a wide range of scales are assumed to belong to visually sensible regions. To compensate the well-known drawbacks of linear scale- spaces, the shape-preserving properties of morphological scale-space filtering are utilized. The limiting duality of morphological filters is overcome by a selfdual morphological approach considering both light and dark structures in either the opening or the closing branch of the scale-space. Reconstructive opening/closing-filters enable the scale=analysis of 2D signals, since they are causal with respect to regional maxima/minima. This allows to identify important regions in scale=space via their extrema. Each extremum is assigned a region by a gradient watershed of the corresponding scale. Due to morphological filtering, the scale behavior of the regions is representable by a tree structure describing the spatial inter- and intra-scale relations among regions. The significance of a watershed region is automatically derived from its scale behavior by considering various attributes describing scale-dependent, morphological, and statistical properties of the region. The most significant regions from the segmentation of the image. The algorithm was verified for various medical image domains, such as cytological micrographs, bone x-rays, and cranial NMR slices.

The textural-feature-based segmentation methods were widely applied to the segmentation problems of ultrasonic images. However the manual selection of textural features in the previous approaches not only makes these segmentation methods inadaptable but could lead to the results with bias. Herein we propose an auto-feature-selection algorithm to solve the problems. This algorithm includes three steps: The feature library composed of 32 textural features was established at first. The genetic algorithm was then used to auto-select the features and give each of them different weight according to their importance. The fitness of each gene was evaluated by five factors including region dissimilarity, number of edge points, edge fragmentation, edge thickness, and curvature. Finally, K-means process classified the image into 3 different tissues using the selected features with different weights. The segmentation outcomes of various ultrasonic images by this auto-feature selection algorithm have shown better correspondence with human comprehension in comparison with the results of previous works. In addition, it provides a more adaptive way to adjust the weight of the features used for clustering process and therefore to avoid takeover by the big-value features. This problem has been paid little attention in the traditional K-means process in which all the features have the same weight.

A new fully automatic algorithm for the segmentation of the brain and cerebro-spinal fluid (CSF) from T1-weighted volume MRI scans of the head was specifically developed in the context of serial intra-cranial volumetry. The method is an extension of a previously published brain extraction algorithm. The brain mask is used as a basis for CSF segmentation based on morphological operations, automatic histogram analysis and thresholding. Brain segmentation is then obtained by iterative tracking of the brain-CSF interface. Grey matter (GM), white matter (WM) and CSF volumes are calculated based on a model of intensity probability distribution that includes partial volume effects. Accuracy was assessed using a digital phantom scan. Reproducibility was assessed by segmenting pairs of scans from 20 normal subjects scanned 8 months apart and 11 patients with epilepsy scanned 3.5 years apart. Segmentation accuracy as measured by overlap was 98% for the brain and 96% for the intra-cranial tissues. The volume errors were: total brain (TBV): -1.0%, intra-cranial (ICV):0.1%, CSF: +4.8%. For repeated scans, matching resulted in improved reproducibility. In the controls, the coefficient of reliability (CR) was 1.5% for the TVB and 1.0% for the ICV. In the patients, the Cr for the ICV was 1.2%.

A vessel extraction approach is presented that permits visualization of the cerebral vasculature in 3D from anatomical proton density (PD) weighted magnetic resonance imaging (MRI) volumes. The approach presented utilizes general knowledge about the shape and size of the cerebral vasculature and is divided into multi-scale vessel enhancement filtering, centre-line extraction, and surface modeling. To improve the discrimination between blood vessels and other tissue a multi-scale filtering method that enhances tubular structures is used as a pre-processing step. Centre-line extraction is applied to roughly estimate the centre-line of the vasculature involving both segmentation and skeletonization. The centre-line is used to initialize an active contour modeling process where cylinders are used to model the 3D surface of the blood vessels. The accuracy and robustness of the vessel extraction approach have been demonstrated on both simulated and real data (1mm³ voxels). On simulated data, the mean error of the estimated radii was found to be less than 0.4mm. On real data, the vasculature was successfully extracted from 20 MRI data sets using the same input parameters. An expert found the extracted vessel surfaces to coincide with the vessel walls in the data. Results from CTA data indicate that the approach will work successfully with other imaging modalities as well.

This paper presents an automatic segmentation procedure for MRI neuroimages that overcomes part of the problems involved in multidimensional clustering techniques like partial volume effects (PVE), processing speed and difficulty of incorporating a priori knowledge. The method is a three-stage procedure: 1) Exclusion of background and skull voxels using threshold-based region growing techniques with fully automated seed selection. 2) Expectation Maximization algorithms are used to estimate the probability density function (PDF) of the remaining pixels, which are assumed to be mixtures of gaussians. These pixels can then be classified into cerebrospinal fluid (CSF), white matter and grey matter. Using this procedure, our method takes advantage of using the full covariance matrix (instead of the diagonal) for the joint PDF estimation. On the other hand, logistic discrimination techniques are more robust against violation of multi-gaussian assumptions. 3) A priori knowledge is added using Markov Random Field techniques. The algorithm has been tested with a dataset of 30 brain MRI studies (co-registered T1 and T2 MRI). Our method was compared with clustering techniques and with template-based statistical segmentation, using manual segmentation as a gold-standard. Our results were more robust and closer to the gold-standard.

Segmentation and representation of the human cerebral cortex from magnetic resonance images is an important goal in neuroscience and medicine. Accurate cortical segmentation requires preprocessing of the image data to separate certain subcortical structures from the cortex in order to generate a good initial white-matter/gray-matter interface. This step is typically manual or semi-automatic. In this paper, we propose an automatic procedure that is based on a careful analysis of the brain anatomy. Following a fuzzy segmentation of the brain image, the method first extracts the ventricles using a geometric deformable surface model. A region force, derived from the cerebrospinal membership function, is used to deform the surface towards the boundary of the ventricles, while a curvature force controls the smoothness of the surface and prevents it from growing into the outer pial surface. Next, region-growing identifies and fills the subcortical regions in each cortical slice using the detected ventricles as seeds and the white matter and several automatically determined sealing lines as boundaries. To make the method robust to segmentation artifacts, a putamen mask drawn in the Talairach coordinate system is also used to help the region growing process. Visual inspection and initial results on 15 subjects show the success of the proposed method.

The notion of fuzzy connectedness captures the idea of hanging-togetherness of image elements in an object by assigning a strength of connectedness to every possible path between every possible pair of image elements. This concept leads to powerful image segmentation algorithms based on dynamic programming whose effectiveness has been demonstrated on 1000s of images in a variety of applications. In a previous framework, we introduced the notion of relative fuzzy connectedness for separating a foreground object from a background object. In this framework, an image element c is considered to belong to that among these two objects with respect to whose reference image element c has the higher strength of connectedness. In fuzzy connectedness, a local fuzzy reflation called affinity is used on the image domain. This relation was required for theoretical reasons to be of fixed form in the previous framework. In the present paper, we generalize relative connectedness to multiple objects, allowing all objects (of importance) to compete among themselves to grab membership of image elements based on their relative strength of connectedness to reference elements. We also allow affinity to be tailored to the individual objects. We present a theoretical and algorithmic framework and demonstrate that the objects defined are independent of the reference elements chosen as long as they are not in the fuzzy boundary between objects. Examples from medical imaging are presented to illustrate visually the effectiveness of multiple object relative fuzzy connectedness. A quantitative evaluation based on 160 mathematical phantom images demonstrates objectively the effectiveness of relative fuzzy connectedness with object- tailored affinity relation.

Segmentation is fundamental for automated analysis of medical images. However, a unified approach for evaluation does not yet exist. Gold standards are often unapplicable because they require invasive preparations or tissue extraction. Empirical evaluations only reflect the conformity of segmentation with the subjective visual expectance of users, which is underlying inter- as well as intra-observer variabilities. This paper presents a consistent approach to create synthetic but realistic images with a-priori known object boundaries (silver standards), which are suitable for optimization nd evaluation of various segmentation algorithms. Rectangular example patches are collected for each tissue (interior, exterior, and a contour zone). Fourier amplitude and phase images are stored together with the mean gray value. For silver standard generation, a reference contour is either manually given or automatically extracted form real data applying the algorithm under evaluation. For each class of tissue, the amplitude of one patch is randomly combined with the perturbed phase of another. A randomly chosen mean from the same class is superimposed to the inverse Fourier transform. Numerous silver standards are obtained form only a few texture patches of each tissue. Based on microscopy, CT, and functional MRI data, the applicability of silver standards is proven in two, three, and four dimensions. They are analyzed with respect to systematic deviations. Minor deviations occur for two dimensional images while those for three or four dimensions are larger but still acceptable.

Purpose - To reduce partial volume contamination, we present a linear interpolation combining quantitative T1 information with segmented base images. In addition, manual segmentation was completed for comparison to both of the techniques. Methods - To quantitatively assess T1, a precise and accurate inversion recovery (PAIR) sequence was acquired. The Kohonen SOM segmentation algorithm used the four base images as inputs and had nine output neurons. The segmented regions were manually classified by an expert for training a multi-layered backpropagation neural network to automate this process. A linear interpolation based on mean T1 relaxivity for each segmented class (regional method) and a pixel by pixel basis (pixel method) was performed. Manual segmentation was performed directly on base images by three observers. Differences between the techniques are reported as percent errors of the mean difference divided by the mean estimates of the manual segmentation. Results and Discussion -Within observer variances for the manual segmentation were less than 5.6% while between observer variances were 11.7% and 7.2% for white and gray matter respectively. The regional method had variances of 4.1% and 1.0% while the pixel method produced variances of 5.8% and 1.5% for white and gray matter, respectively, compared to the manual segmentation.

Statistical models of shape and appearance are powerful tools for interpreting medical images. We assume a training set of images in which corresponding landmark points have been marked on every image. From this data we can compute a statistical model of the shape variation, a model of the texture variation and a model of the correlations between shape and texture. With enough training examples such models should be able to synthesize any image of normal anatomy. By finding the parameters which optimize the match between a synthesized model image and a target image we can locate all the structures represented by the model. Two approaches to the matching will be described. The Active Shape Model essentially matches a model to boundaries in an image. The Active Appearance Model finds model parameters which synthesize a complete image which is as similar as possible to the target image. By using a difference decomposition approach the current difference between target image and synthesized model image can be used to update the model parameters, leading to rapid matching of complex models. We will demonstrate the application of such models to a variety of different problems.

Active Appearance Models (AAMs) are useful for segmentation of static cardiac MR images since they exploit prior knowledge about the cardiac shape and image appearance. However, applying 2D AAMs to full cardiac cycle segmentation would require multiple models for different phases of the cardiac cycle because traditional AAMs account only for the variations within image classes and not temporal classes. This paper presents a novel 2D+time Active Appearance Motion Model (AAMM) that represents the dynamics of the cardiac cycle in combination with shape and image appearance of the heart, ensuring a time-continuous segmentation of a complete cardiac MR sequence. In AAMM, single-beat sequences are phase-normalized into sets of 2D images and the shape points and gray intensities between frames are concatenated into a shape vector and intensity vector. Appearance variations over time are captured using Principal Component Analysis on both vectors in the training set. Time-continuous segmentation is achieved by minimizing the model appearance-to-target differences by adjusting the model eigen-coefficients using gradient descent approach. In matching tests, the model shows to be robust in initial position and approximates the true segmentation very well. Large-scale clinical validation in patients is ongoing.

Active Appearance Models (AAM) are suitable for segmenting 2D images, but for image sequences time-continuous results are desired. Active Appearance-Motion Models (AAMM) model shape and appearance of the heart over the full cardiac cycle. Single-beat sequences are phase-normalized into stacks of 16 2D images. In a training set, corresponding shape points on the endocard are defined for each image based on expert drawn contours. Shape (2D) and intensity vectors are derived similar to AAM. Intensities are normalized non-linearly to handle ultrasound-specific problems. For all time frames, shape vectors are simply concatenated, as well as and intensity vectors. Principal Component Analysis extracts appearance eigenvariations over the cycle, capturing typical motion patterns. AAMMs perform segmentation on complete sequences by minimizing model-to-target differences, adjusting AAMM eigenvariation coefficients using gradient descent minimization. This results in time-continuous segmentation. The method was trained and tested on echocardiographic 4-chamber sequences of 129 unselected patients split randomly into a training set (n=65) and a test set (n=64). In all sequences, an independent expert manually drew endocardial contours. On the test set, fully automated AAMM performed well in 97% of cases (average distance 3.3 mm, 9.3 pixels, comparable to human inter- and intraobserver variabilities).

For the purpose of building a statistical shape model of a 3D object, a landmarked training set must be obtained. The purpose of this work is to develop a streamlined, slice-by-slice, volumetric landmarking scheme that requires no prior segmentation of the object and directly produces a set of corresponding landmark points for each 3D object in the training set. To achieve inter-object correspondence, the procedure's main feature is the establishment of an object-based coordinate system. Minimal user interaction is employed to locate an origin and axes on each volume by presenting the user with appropriate image slices and annotation tools, as dictated by the data under study. The volumes can then be aligned so that locating a physical point, relative to the established coordinate system, is repeatable from one instance of the object to another. For the purpose of verifying and demonstrating the proposed procedure, a set of test data consisting of image volumes of ten mangoes was obtained. Results of the landmarking scheme for this data, as well as for medical image data, demonstrate good object segmentation and landmark point correspondence.

In this work, we present a method for exploring the relationship among morphometric variables and the possible anatomic significance of these relationships. The analysis is based on the Jacobian determinant field resulting from the registration of a template to a set of subjects, which is represented as a factorial analytic model. In addition to morphometric variables, information about medical diagnosis is considered in the analytic model and corroborates to exploratory investigation of the relationship between regions of interest and pathologies. The definition of the number of factors to be considered is based on a robust analysis of the statistical fit of the factor model, instead of using as hoc criteria. The advantages of the proposed methodology are demonstrated in a study of shape differences between the corpora callosa of schizophrenic patients and normal controls. We show that the regions where these differences can occur can be determined by unsupervised analysis, indicating the method's potential for exploratory studies.

Understanding the function of the human brain cortex is a primary goal in human brain mapping. Methods to unfold and flatten the cortical surface for visualization and measurement have been described in previous literature; but comparison across multiple subjects is still difficult because of the lack of a standard mapping technique. We describe a new approach that maps each hemisphere of the cortex to a portion of a sphere in a standard way, making comparison of anatomy and function across different subjects possible. Starting with a three-dimensional magnetic resonance image of the brain, the cortex is segmented and represented as a triangle mesh. Defining a cut around the corpus collosum identifies the left and right hemispheres. Together, the two hemispheres are mapped to the complex plane using a conformal mapping technique. A Mobius transformation, which is conformal, is used to transform the points on the complex plane so that a projective transformation maps each brain hemisphere onto a spherical segment comprising a sphere with a cap removed. We determined the best size of the spherical cap by minimizing the relative area distortion between hemispherical maps and original cortical surfaces. The relative area distortion between the hemispherical maps and the original cortical surfaces for fifteen human brains is analyzed.

This paper presents and compares two image processing methods for differentiating benign from malignant microcalcifications in mammograms. The gold standard method for differentiating benign from malignant microcalcifications is biopsy, which is invasive. The goal of the proposed methods is to reduce rate of biopsies with negative results. In the first method, we extract 17 shape features from each mammogram. These features are related to shapes of individual microcalcifications or to their clusters. In the second method, we extract 44 texture features from each mammogram using co-occurrence method of Haralick. Next, we select best features from each set using a genetic algorithm, to maximize area under ROC curve. This curve is created using a k-nearest neighbor (kNN) classifier and a malignancy criterion. Finally, we evaluate the methods by comparing ROC's with greatest areas obtained using each method. We applied the proposed methods, with different values of k in kNN classifier, to 74 malignant and 29 benign microcalcification clusters. Truth for each mammogram was established based on the biopsy results. We found greatest area under ROC curve for each set of features used in each method. For shape features this area was 0.82 (k = 7) and for Haralick features it was 0.72(k=9).

We describe a novel method to build 3D statistical shape models for anatomic objects in tomographic images, and demonstrate the use of the model to guide image segmentation. Our method consists of two main steps. In the first step, a statistical shape model is built for a collection of training images. Boundary similarities between adjacent transverse slices are matched to guide inter-slice interpolation. Slice-by-slice correspondences are established between images in the training sets by matching mean boundary curvatures. A statistical shep model is then obtained by principal components analysis. During the second step, the model is used to guide image segmentation. Segmentation is initialized by placing the mean shape into the image under analysis. The model deforms iteratively by updating its shape and pose parameters using the principles of the active shape model. Following the active shape model, an active contour model (snake) is used to refine the object boundary. The proposed methods have been tested using ten volumetric chest HRCT images. The results show that the new method is able to automatically generate 3D object shape models without the need for manual landmark identification. The combination of the active shape model with the active contour model yields a fast, accurate object segmentation.

A novel one-pass 3D thinning algorithm is proposed in this paper. 3D thinning can be regarded as an essential step in many image-processing tasks such as image quantification, image compression, motion tracking, path generation, and object navigation. The proposed algorithm generates both connected and non-connected skeletons. It is faster and more accurate than currently available techniques in the literature. In addition, it adaptively removes spurious branches of the skeleton, and hence, generates a smooth and refined skeleton, representing the essential structure of 3D elongated objects such as vessels, airways, and other similar organic shapes.

The efficient representation of shape and shape variability is a key issue in computerized 3D image processing. One of the common goals is the ability to express as much shape variability as necessary with as few parameters as possible. In this paper we focus on the capture of shape variability on the basis of free surface vibration modes. We do not model the interior of an elastic object, but rather its triangulated surface. As in the case of 3D statistical point-distribution models (PDM) we assume that the shape of an anatomical object can efficiently be approximated by a weighted sum of a mean shape and a number of variation modes. The variation modes are in our case Eigenvectors of a stiffness-matrix. Based on a given surface triangulation we define a physical model by placing mass points at the vertices and coil- and leaf-spring elements at the edge positions of the triangulation. Ordered by wavelength, the resulting free vibration modes can be used to efficiently approximate shape variability in a coarse to fine manner, similar to a Fourier decomposition. As real-object examples from the medical image-processing domain, we applied the method to triangulated surfaces of segmented lumbar vertebra and femor-head from CT data sets. A comparison to corresponding statistical shape models shows, that natural variability of anatomical shape can efficiently be approximated by free surface vibration modes.

This paper proposes an approach integrating multiple segmentation methods in a systematic way, which can improve overall accuracy without deteriorating accuracy of highly confident segments of a boundary. A segmentation method produces boundary segments, which are then evaluated with an evaluation function considering pros/cons of the current and next methods to apply. Boundary segments with low confidence are replaced by next method while the other segments are kept. These steps are repeated until all segmentation methods are applied. Coarser and more robust method is applied earlier than the others. The proposed approach is implemented for the segmentation of muscles in the Visible Human color images. A balloon method, a minimum cost path finding method, and a Seeded Region Growing method are integrated. The final segmentation results showed improvements in both overall evaluation and segment-based evaluation.

In this paper, we present different solutions for improving spline-based snakes. First, we demonstrate their minimum curvature interpolation property, and use it as an argument to get rid of the explicit smoothness constraint. We also propose a new external energy obtained by integrating a non-linearly pre-processed image in the closed region bounded by the curve. We show that this energy, besides being efficiently computable, is sufficiently general to include the widely used gradient-based schemes, Bayesian schemes, their combinations and discriminant-based approaches. We also introduce two initialization modes and the appropriate constraint energies. We use these ideas to develop a general snake algorithm to track boundaries of closed objects, with a user-friendly interface.

We have developed a knowledge-based deformable surface for segmentation of medical images. This work has been done in the context of segmentation of hippocampus from brain MRI, due to its challenge and clinical importance. The model has a polyhedral discrete structure and is initialized automatically by analyzing brain MRI sliced by slice, and finding few landmark features at each slice using an expert system. The expert system decides on the presence of the hippocampus and its general location in each slice. The landmarks found are connected together by a triangulation method, to generate a closed initial surface. The surface deforms under defined internal and external force terms thereafter, to generate an accurate and reproducible boundary for the hippocampus. The anterior and posterior (AP) limits of the hippocampus is estimated by automatic analysis of the location of brain stem, and some of the features extracted in the initialization process. These data are combined together with a priori knowledge using Bayes method to estimate a probability density function (pdf) for the length of the structure in sagittal direction. The hippocampus AP limits are found by optimizing this pdf. The model is tested on real clinical data and the results show very good model performance.

The Geometric Deformable Model (GDM) is a useful segmentation method that combines the energy minimization concepts of physically deformable models and the flexible topology of implicit deformable models in a mathematically well-defined framework. The key aspect of the method is the measurement of length and area using a conformal metric derived from the image. This conformal metric, usually a monotonicly decreasing function of the gradient, defines a Riemannian space in which the surface evolves. The success of the GDM for 3D segmentation in medical applications is directly related to the definition of the conformal metric. Like all deformable models, the GDM is susceptible to poor initialization, varying contrast, partial volume, and noise. This paper addresses these difficulties via the definition of the conformal metric and describes a new method for computing the metric in 3D. This method, referred to as a confidence-based mapping, incorporates a new 3D scale selection mechanism and an a-priori image model. A comparison of the confidence-based approach and previous formulations of the conformal metric is presented using computer phantoms. A preliminary application in two clinical examples is given.

Radiologists are always looking for more reliable and robust methods to help them assess, describe and classify bone structures in x-ray images. Although, in the recent years, computer-assisted techniques have proven to be useful in this regard, they still face difficult challenges such as inter-subject variability in shape and a lack of contrast in the digitized images of radiographs. These challenges have focused the attention of the computer vision research community on techniques that employ deformable models. One such technique, i.e., Active Shape Models (ASM), has received significant attention due to its ability to capture the shape variability and to deal with the poor quality of the images in a straightforward manner. However, as is often the case with iterative optimization techniques, success of the ASM search step is highly dependent on the initial positioning of the mean shape on the target image. Within the specific framework of automatic, cervical vertebra segmentation, we have developed and tested an up-front preprocessing algorithm that estimates the orientation and position of the cervical vertebrae in x-ray images and leads to a more accurate, initial placement of the mean shape. The algorithm estimates the orientation of the spine by calculating parallel-beam line integrals of the x-ray images. The position of the spine is estimated by considering the density of edges perpendicular to the line integral that gives the estimate of the orientation. The output of the algorithm is a bounding box surrounding the cervical spine area. Morphometric points placed by expert radiologists on a set of 40, digitized radiographs were used to quantify the efficacy of the estimation. This test yielded acceptable results in estimating the orientation and the locating of the cervical spine.

In this paper we propose a technique for 3-D segmentation of abdominal aortic aneurysm (AAA) from computed tomography angiography (CTA) images. Output data (3-D model) form the proposed method can be used for measurement of aortic shape and dimensions. Knowledge of aortic shape and size is very important in planning of minimally invasive procedure that is for selection of appropriate stent graft device for treatment of AAA. The technique is based on a 3-D deformable model and utilizes the level-set algorithm for implementation of the method. The method performs 3-D segmentation of CTA images and extracts a 3-D model of aortic wall. Once the 3-D model of aortic wall is available it is easy to perform all required measurements for appropriate stent graft selection. The method proposed in this paper uses the level-set algorithm for deformable models, instead of the classical snake algorithm. The main advantage of the level set algorithm is that it enables easy segmentation of complex structures, surpassing most of the drawbacks of the classical approach. We have extended the deformable model to incorporate the a priori knowledge about the shape of the AAA. This helps direct the evolution of the deformable model to correctly segment the aorta. The algorithm has been implemented in IDL and C languages. Experiments have been performed using real patient CTA images and have shown good results.

A semi-automatic method for localisation and segmentation of bifurcated aortic endografts in CTA images is presented. The graft position is established through detection of radiopaque markers sewn on the outside of the graft. The user indicates the first and the last marker, whereupon the rest of the markers are detected automatically by second order scaled derivative analysis combined with prior knowledge of graft shape and marker configuration. The marker centres obtained approximate the graft sides and central axis. The graft boundary is determined, either in the original CT slices or in reformatted slices orthogonal to the local graft axis, by maximizing the local gradient in the radial direction along a deformable contour passing through both sides. The method has been applied to ten CTA images. In all cases, an adequate segmentation is obtained. Compared to manual segmentations an average similarity (i.e. relative volume of overlap) of 0.93 +/- 0.02 for the graft body and 0.84 +/- 0.05 for the limbs is found.

Within 3D image, edge surfaces usually correspond to structural boundaries. Therefore, their recognition and modeling are of basic importance in 3D image analysis. Several approaches have been proposed to find or visualize them, such as 3D edge detection and volume rendering algorithms. But edge detectors mainly seek discrete 3D edge-like points in a 3D image, and volume rendering is mainly used for display. Neither extracts a continuous edge surface model, which is usually needed for further analysis, understanding and interpretation of structures within a 3D image. We present two ways, simple and easy to implement, to extract surface models of step-like edge surfaces directly from a 3D image.

This work is a contribution to the problem of localizing key cerebral structures in 3D MRIs and its quantitative evaluation. In pursuing it, the cooperation between an image-based segmentation method and a hierarchical deformable registration approach has been considered. 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 of an image, I(s), from the data set are identified. These regions, M(I), are obtained combining information from deformable atlas, achieved by the warping of eight previous labeled maps on I(s). Then, the goal of the decision stage is to precisely locate the contours of the 3D regions set by the markers. This contour decision is performed by a 3D extension of the watershed transform. The anatomical structures taken into consideration and embedded into the atlas are brain, ventricles, corpus callosum, cerebellum, right and left hippocampus, medulla and midbrain. The hybrid method operates fully automatically and in 3D, successfully providing segmented brain structures. The quality of the segmentation has been studied in terms of the detected volume ratio by using kappa statistic and ROC analysis. Results of the method are shown and validated on a 3D MRI phantom. This study forms part of an on-going long term research aiming at the creation of a 3D probabilistic multi-purpose anatomical brain atlas.

Many of the existing computer-aided diagnosis (CAD) schemes for detection of nodules in chest radiographs suffer from a large number of false positives. Previously, we reported a local contralateral subtraction method that removes false positives due to the presence of normal structures effectively. In this approach, registration of the left and right lung regions is performed for extraction of lung nodules while the normal anatomic structures are removed. In this study, we developed a novel method for simultaneous registration and segmentation which registers two similar images while a region with significant difference is adaptively segmented, and incorporated it into the local contralateral subtraction method. In this method, a non- linear functional that models the statistical properties of the subtraction of the two images is formulated, and the function is minimized by a coarse-to-fine approach to yield a mapping that yields the registration and a boundary that yields the segmentation. A preliminary result shows that the new method is effective in segmenting the abnormal structures and removing normal structures. The local contralateral subtraction based on the new segmentation and registration method was shown to be effective in reducing the number of false detections reported by our computer- aided diagnosis scheme for detection of lung nodules in chest radiographs.

In osteoarthritis, articular cartilage loses integrity and becomes thinned. This usually occurs at sites which bear weight during normal use. Measurement of such loss from MRI scans, requires precise and reproducible techniques, which can overcome the difficulties of patient repositioning within the scanner. In this study, we combine a previously described technique for segmentation of cartilage from MRI of the knee, with a technique for 3D image registration that matches localized regions of interest at followup and baseline. Two patients, who had recently undergone meniscal surgery, and developed lesions during the 12 month followup period were examined. Image registration matched regions of interest (ROI) between baseline and followup, and changes within the cartilage lesions were estimate to be about a 16% reduction in cartilage volume within each ROI. This was more than 5 times the reproducibility of the measurement, but only represented a change of between 1 and 2% in total femoral cartilage volume. Changes in total cartilage volume may be insensitive for quantifying changes in cartilage morphology. A combined used of automated image segmentation, with 3D image registration could be a useful tool for the precise and sensitive measurement of localized changes in cartilage from MRI of the knee.

We discuss the design of feature-extraction methods based on the strategy of the ideal observer. We restrict our discussion to a binary hypothesis-testing task where the observer has to decide whether a signal is added onto a nonuniform background.

We describe a new nonlinear discriminant analysis method for feature extraction. This method applies a nonsingular transform to the data such that the transformed data have a Gaussian distribution. Then a Bayes likelihood ratio is calculated for the transformed data. The nonsingular transform makes use of wavelet transforms and histogram matching techniques. Wavelet transforms are an effective tool in analyzing data structures. Histogram matching is applied to the wavelet coefficients and the ordinary image pixel values in order to create a transformed image that has the desired Gaussian statistics.

The Markov Chain Monte Carlo technique provides a means for drawing random samples from a target probability density function (pdf). MCMC allows one to assess the uncertainties in a Bayesian analysis described by a numerically calculated posterior distribution. This paper describes the Hamiltonian MCMC technique in which a momentum variable is introduced for each parameter of the target pdf. In analogy to a physical system, a Hamiltonian H is defined as a kinetic energy involving the momenta plus a potential energy (phi) , where (phi) is minus the logarithm of the target pdf. Hamiltonian dynamics allows one to move along trajectories of constant H, taking large jumps in the parameter space with relatively few evaluations of (phi) and its gradient. The Hamiltonian algorithm alternates between picking a new momentum vector and following such trajectories. I show that the efficiency of the Hamiltonian method for multidimensional isotropic Gaussian pdfs remains constant at around 7% for up to several hundred dimensions. The Hamiltonian method handles correlations among the variables much better than the standard Metropolis algorithm. A new test, based on the gradient of (phi) , is proposed to measure the convergence of the MCMC sequence.

The Image Foresting Transform (IFT) reduces optimal image partition problems from seed pixels into a shortest-path forest problem in a graph, whose solution can be obtained in linear time. It has allowed a unified and efficient approach to edge tracking, region growing, watershed transforms, multiscale skeletonization, and Euclidean distance transform. In this paper, we extend the IFT to introduce two connected operators: cutting-off-domes and filling-up-basins. The former simplifies grayscale images by reducing the height of its domes, while the latter reduces the depth of its basins. By automatically or interactively specifying seed pixels in the image and computing a shortest-path forest, whose trees are rooted at these seeds, the IFT creates a simplified image where the brightness of each pixel is associated with the length of the corresponding shortest-path. A label assigned to each seed is propagated, resulting a labeled image that corresponds to the watershed partitioning from markers. The proposed operators may also be used to provide regional image filtering and labeling of connected components. We combine the cutting-off-domes and filling-up-basins to implement regional minima/maxima, h-domes/basins, opening/closing by reconstruction, leveling, area opening/closing, closing of holes, and removal of pikes. Their applications are illustrated with respect to medical image segmentation.

The quality of ultrasound images is limited due to granular speckle noise. The presented despeckle algorithm compensates the depth-dependent shape of granular speckles in sector scans by an initial coordinate transform. This yields a horizontally oriented speckle pattern of constant resolution and hence allows the use of constant filter templates. The signal-dependent nature of multiplicative speckle noise is considered by a ratio pyramid containing noise-normalized, subsampled scales corrupted by signal- independent noise. Since speckles can be identified as positive and negative impulses on the subsampled scales, they are removed by selfdual nonlinear multistage filters (NMF). The templates are adapted to the granular appearance of the speckles and the degree of filtering is individually controlled by the local noise power in each scale. We propose a new selfdual morphological pyramid with the common erosion/dilation as analysis operators and the reconstructive dilation/erosion as synthesis operators. The resulting closing-by-reconstruction and opening-by- reconstruction branches consider local intensity amplifications and attenuations, respectively. They are generated separately and combined only for scale-selective restoration by NMFs. Besides morphological decomposition, a ratio Laplacian pyramid is evaluated and its performance is compared with the proposed morphological decomposition, a ratio Laplacian pyramid is evaluated and its performance is compared with the proposed morphological decomposition. Both methods lead to significant noise reduction, where the morphological method introduces less signal degenerations.

Two new approaches to hair removal from skin images using auto-regressive (AR) model signal and band-limited (BL) signal interpolation have been compared to conventional linear interpolation and found to lead to smaller interpolation errors. Experimental results illustrate that the proposed approaches are able to reduce the disruption of hair removal on the skin line pattern.

Blood vessels in retinal images are often spread wildly across the image surface. By using this feature, this paper presents a novel approach for illumination normalization of retinal images. With the assumption that the reflectance of the vessels (including both major and small vessels) is a constant, it was found in our study that the illumination distribution of a retinal image can be estimated based on the locations of the vessel pixels and their intensity values. The procedures for estimating the illumination consists of two steps: (1) obtain the vessel map of the retinal image, and (2) estimate the illumination function (IF) of the image by interpolating the intensity values (luminance) of non-vessel pixels using a bicubic model function based on the locations of the vessel pixels and their intensity values. The illumination-normalized image can then be obtained by subtracting the original image from the estimated IF.20 non-uniformly illuminated sample retinal images that were tested using the proposed method. The results showed that the over-all standard deviation of the illumination for the image background reduced by 56.8% from 19.82 to 8.56, and the signal-to-noise ratio of the normalized images was greatly improved in the application of the global thresholding for image/region segmentation. Furthermore, when measured by the local luminosity histograms, the contrast of regions with low illumination containing features that are normally difficult to detect (such as small lesions and vessels) was also enhanced significantly. Therefore, it is concluded that the proposed method can be used to produce a desirable illumination- normalized image, from which region segmentation can be made easier and more accurate.

Mutual information has been demonstrated to be an accurate and reliable criterion function to perform registration of medical data. Due to speckle noise, ultrasound volumes do not provide a smooth mutual information function. Consequently the optimization technique used must be robust enough to avoid local maxima and converge on the desired global maximum eventually. While the well-known downhill simplex optimization uses a single criterion function, our extension to multi-function optimization uses three criterion functions, namely mutual information computed at three levels of intensity quantization and hence three degrees of noise suppression. Registration was performed with rigid as well as simple non-rigid transformation modes for real-time 3D ultrasound datasets of the left ventricle. Pairs of frames corresponding to the most stationary end- diastolic cardiac phase were chosen, and an initial misalignment was artificially introduced between them. The multi-function simplex optimization reduced the failure rate by a factor of two in comparison to the standard simplex optimization, while the average accuracy for the successful cases was unchanged. A more robust registration resulted form the parallel use of criterion functions. The additional computational cost was negligible, as each of the three implementations of the mutual information used the same joint histogram and required no extra spatial transformation.

Applying edge detection prior to performing image registration yields several advantages over raw intensity- based registration. Advantages include the ability to register multicontrast or multimodality images, immunity to intensity variations, and the potential for computationally efficient algorithms. In this work, a common framework for edge-based image registration is formulated as an adaptation of snakes used in boundary detection. Called active edge maps, the new formulation finds a one-to-one transformation T(x) that maps points in a source image to corresponding locations in a target image using an energy minimization approach. The energy consists of an image component that is small when edge features are well matched in the two images, and an internal term that restricts T(x) to allowable configurations. The active edge map formulation is illustrated here with a specific example developed for affine registration of carotid artery magnetic resonance images. In this example, edges are identified using a magnitude of gradient operator, image energy is determined using a Gaussian weighted distance function, and the internal energy includes separate, adjustable components that control volume preservation and rigidity.

Establishing the average shape and spatial variability for a set of similar anatomical objects is important for detecting and discriminating morphological differences between populations. This may be done using deformable templates to synthesize a 3D CT/MRI image of the average anatomy from a set of CT/MRI images collected from a population of similar anatomical objects. This paper investigates the error associated with the choice of template selected from the population used to synthesize the average population shape. Population averages were synthesized for a population of five infant skulls with sagittal synostosis and a population of six normal adult brains using a consistent linear-elastic image registration algorithm. Each data set from the populations was used as the template to synthesize a population average. This resulted in five different population averages for the skull population and six different population averages for the brain population. The displacement variance distance from a skull within the population to the other skulls in the population ranged from 5.5 to 9.9 mm² while the displacement variance distance from the synthesized average skulls to the population ranged from 2.2 to 2.7 mm². The displacement variance distance from a brain within the population to the other brains in the population ranged from 9.3 to 14.2 mm² while the displacement variance distance from the synthesized average brains to the population ranged from 3.2 to 3.6 mm². These results suggest that there was no significant difference between the choice of template with respect to the shape of the synthesized average data set for these two populations.

A novel method for the automated extraction of important geometrical parameters of the pelvis and hips from APR images is presented. The shape and intensity variations in APR images are encompassed by the statistical shape and appearance models built from a set of training images for each of the three anatomies, i.e., pelvis, right and left hip, separately. The identification of the pelvis and hips is defined as a flexible object recognition problem, which is solved by generating anatomically plausible object instances and matching them to the APR image. The criterion function minimizes the resulting match error and considers the object topology. The obtained flexible object defines the positions of anatomical landmarks, which are further used to calculate the hip joint contact stress. A leave-one-out test was used to evaluate the performance of the proposed method on a set of 26 APR images. The results show the method is able to properly treat image variations and can reliably and accurately identify anatomies in the image and extract the anatomical landmarks needed in the hip joint contact stress calculation.

The purpose of the proposed template propagation method is to support the comparative analysis of image pairs even when large deformations (e.g. from movement) are present. Starting from a position where valid starting estimates are known, small sub-volumes (templates) are registered rigidly. Propagating registration results to neighboring templates, the algorithm proceeds layer by layer until corresponding points for the whole volume are available. Template classification is important for defining the templates to be registered, for propagating registration results and for selecting successfully registered templates which finally represent the motion vector field. This contribution discusses a template selection and classification strategy based on the analysis of the similarity measure in the vicinity of the optimum. For testing the template propagation and classification methods, deformation fields of four volume pairs exhibiting considerable deformations have been estimated and the results have been compared to corresponding points picked by an expert. In all four cases, the proposed classification scheme was successful. Based on homologous points resulting from template propagation, an elastic transformation was performed.

In this work we consider the process of aligning a set of anatomical MRI scans, from a group of subjects, to a single reference MRI scan as accurately as possible. A key requirement of this anatomical normalization is the ability to bring into alignment brain images with different ages and disease states with equal accuracy and precision, enabling the unbiased comparison of different groups. Typical images of such anatomy may vary in terms of both tissue shape, location and contrast. To address this we have developed, a highly localized free-form inter-subject registration algorithm driven by normalized mutual information. This employs an efficient multi-image resolution and multi-deformation resolution registration procedure. In this paper we examine the behavior of this algorithm when applied to aligning high-resolution MRI of groups of younger, older and atrophied brain anatomy to different target anatomies. To gain an insight into the quality of the spatial normalization, we have examined two properties of the transformations: The residual intensity differences between spatially normalized MRI values and the spatial discrepancies in transformation estimates between group and reference, derived from transformations between 168 different image pairs. These are examined with respect to the coarseness of the deformation model employed.

Non-rigid multimodal registration requires similarity measure with two important properties: locality and multi- modality. Unfortunately all commonly used multimodal similarity measures are inherently global and cannot be directly used to estimate local image properties. We have derived a local similarity measure based on joint entropy, which can operate on extremely small image regions, e.g. individual voxels. Using such small image regions reflects in higher sensitivity to noise and partial volume voxels, consequently reducing registration speed and accuracy. To cope with these problems we enhance the similarity measure with image segmentation. Image registration and image segmentation are related tasks, as segmentation can be performed by registering an image to a pre-segmented reference image, while on the other hand registration yields better results when the images are pre-segmented. Because of these interdependences it was anticipated that simultaneous application of registration and segmentation should improve registration as well as segmentation results. Several experiments based on synthetic images were performed to test this assumption. The results obtained show that our method can improve the registration accuracy and reduce the required number of registration steps.

A much-used measure for registration of three-dimensional medical images is mutual information, which originates from information theory. However, information theory offers many more measures that may be suitable for image registration. Such measures denote the divergence of the joint grey value distribution of two images from the joint distribution for complete independence of the images. This paper compares the performance of mutual information as a registration measure with that of other information measures. The measures are applied to rigid registration of clinical PET/MR and MR/CT images, for 35 and 41 image pairs respectively. An accurate gold standard transformation is available for the images, based on implanted markers. Both registration performance and accuracy of the measures are studied. The results indicate that some information measures perform very poorly for the chosen registration problems, yielding many misregistrations, even when using a good starting estimate. Other measures, however, were shown to produce significantly more accurate results than mutual information.

The constrained, localized warping (CLW) algorithm was developed to minimize the registration errors caused by hypoperfusion lesions. SPECT brain perfusion images from 21 Alzheimer patients and 35 controls were analyzed. CLW automatically determines homologous landmarks on patient and template images. CLW was constrained by anatomy and where lesions were probable. CLW was compared with 3rd-degree, polynomial warping (AIR 3.0). Accuracy was assessed by correlation, overlap, and variance. 16 lesion types were simulated, repeated with 5 images. The errors in defect volume and intensity after registration were estimated by comparing the images resulting from warping transforms calculated when the defects were or were not present. Registration accuracy of normal studies was very similar between CLW and polynomial warping methods, and showed marked improvement over linear registration. The lesions had minimal effect on the CLW algorithm accuracy, with small errors in volume (> -4%) and intensity (< +2%). The accuracy improvement compared with not warping was nearly constant regardless of defect: +1.5% overlap and +0.001 correlation. Polynomial warping caused larger errors in defect volume (< -10%) and intensity (> +2.5%) for most defects. CLW is recommended because it caused small errors in defect estimation and improved the registration accuracy in all cases.

The aim of this paper is to introduce a structural dissimilarity measure which allows to detect outliers in automatically extracted landmark pairs in two images. In previous work, to extract landmarks automatically, candidate points have been defined using invariance criteria coming from differential geometry such as maximum curvature; or they are statistical entities such as gravity centers of confiners, where the confiners are defined as the connected components of the level sets. After a first estimation of the semi-rigid transformation (representing translation, rotation, and scaling) relating the candidate point sets, outliers are detected applying the euclidian distance between corresponding points. However, this approach does not allow to distinguish between real deformations and outliers coming from noise or additional features in one of the images. In this paper, we define a structural dissimilarity measure which we use to decide if two associated candidate points come from two corresponding confiners. We select landmarks pairs with a dissimilarity value smaller than a given threshold and we calculate the affine transformation relating best all selected landmark pairs. We evaluated our technique on successive slices of a MRI image of the human brain and show that we obtain a significantly sharper error diminution using the new dissimilarity measure instead of the euclidian distance for outlier rejection.

This paper investigates the problem of point-based registration under a similarity transformation. This is a transformation that consists of rotation, translation, and isotropic scaling. There are many applications for registration under a similarity transform. First, the medical applications that usually use rigid-body registration may in some cases be improved by using a scale factor to account for particular types of distortion (for example, drift in gradient strength in MR image volumes). Second, similarity transforms are often used in biometrics to analyze and compare different sets of data. It was shown by Gower in 1971 that the choice of scale factor is independent from the choice of rotation and translation. We use a well-known solution for the rotation and translation parts of the transformation, and concentrate on the problem of choosing the scale factor. We examine three different methods of scaling, one of which is a novel maximum likelihood approach. We derive the target registration error and show the bias for each method. We introduce two different models of fiducial localization error, and we show that for one error model, Gower's method of scaling to minimize the sum of squared distances between corresponding points is also the maximum likelihood solution. Under the other error model, however, maximum likelihood leads to a new method of scaling.

An automated algorithm for frameless registration of intra-cranial 3D X-ray angiograms (3DXA) to Magnetic Resonance (MR) images is described and evaluated. The registration procedure starts with the manual designation of a pre-defined anatomical point in both modalities. Then, the registration is performed through an iterative process that alternatively estimates the rotation and translation using an original correlation optimization scheme. The evaluation procedure implied comparisons with both manual (11 cases) and stereotactic frame based (9 cases) registration. The results encompass that manual registration is not a viable method of reference for registering such volumes whereas stereotactic frame (or equivalent means) is acceptable for validation purpose. A maximum error of 4 mm was measured for our automated algorithm while variations of up to 5 mm were considered on the initial point location. Convergence time was below 1 minute while an average time of 30 minutes was required to perform manual registration. This validation procedure demonstrates a good precision for the automated algorithm when compared to a stereotactic frame based matching. Such an algorithm could make the intra-cranial pathology assessment more reliable, enable frameless radiotherapy planning of AVMs in 3D, ease biopsy planning in neurosurgery or be helpful for educational purpose.

Common problems in medical image analysis involve surface-based registration. The applications range from atlas matching to tracking an object's boundary in an image sequence, or segmenting anatomical structures out of images. Most proposed solutions are based on deformable surface algorithms. The main problem of such methods is that the local accuracy of the matching must often be traded off against global smoothness of the surface in order to reach global convergence of the deformation process. Our contribution is to first build a Multi-Resolution (M-R) surface from a reference segmented image, and then match this surface onto the target image in an M-R fashion using a deformable surface-like algorithm. As we proceed from lower to higher resolution, the smoothing effect of the deformable surface is more and more localized, and the surface gets closer and closer to the target boundary. We present initial results of our algorithm for atlas registration onto brain MRI showing improved convergence and accuracy over classical deformable surface methods.

Since an image data compression technique is usually associated with a low-pass filter, the unsharpness of calcifications and edges are of clinical concerns in mammography. The same effect may turn film defects into calcification-like spots and could produce false-positive detection by the radiologist. In this study, we employed a highly sensitive calcification detection system to guide an S+P integer wavelet compression, so that the data fidelity of calcifications or unknown spots are fully preserved. The prediction component of the S+P decomposition is based on Daubechies'D8. Our results indicated that the modified CAD program detected an average of 1,193 potential calcifications on CC view mammograms and an average of 948 potential calcifications on MLO view mammograms, respectively. Compressed data rates between 0.1 to 0.43 bit/pixel were studied. The compressed images were evaluated by subjective comparison studies. The results indicated that no difference could be observed between the original and the 0.43 bit rate decompressed images. The radiologist identifies 20% of the compressed images at 0.1 bit rate suffering from minor blurry artifacts and 6% of the compressed images possessing greater edge sharpness. Without a lossless compression for microcalcifications, the radiologist identified 20% of the microcalcifications on the compressed mammograms at 0.1 bit rate suffering from minor compression artifacts.

We used the correspondence of detected structures on two views of the same breast for false-positive (FP) reduction in computerized detection of mammographic masses. For each initially detected object on one view, we considered all possible pairings with objects on the other view that fell within a radial band defined by the nipple-to-object distances. We designed a 'correspondence classifier' to classify these pairs as either the same mass (a TP-TP pair) or a mismatch (a TP-FP, FP-TP or FP-FP pair). For each pair, similarity measures of morphological and texture features were derived and used as input features in the correspondence classifier. Two-view mammograms from 94 cases were used as a preliminary data set. Initial detection provided 6.3 FPs/image at 96% sensitivity. Further FP reduction in single view resulted in 1.9 FPs/image at 80% sensitivity and 1.1 FPs/image at 70% sensitivity. By combining single-view detection with the correspondence classifier, detection accuracy improved to 1.5 FPs/image at 80% sensitivity and 0.7 FPs/image at 70% sensitivity. Our preliminary results indicate that the correspondence of geometric, morphological, and textural features of a mass on two different views provides valuable additional information for reducing FPs.

We have developed computerized methods for the analysis of lesions that combine results from different imaging modalities, in this case digitized mammograms and sonograms of the breast, for distinguishing between malignant and benign lesions. The computerized classification method -- applied here to mass lesions seen on both digitized mammograms and sonograms, includes: (1) automatic lesion extraction, (2) automated feature extraction, and (3) automatic classification. The results for both modalities are then merged into an estimate of the likelihood of malignancy. For the mammograms, computer-extracted lesion features include degree of spiculation, margin sharpness, lesion density, and lesion texture. For the ultrasound images, lesion features include margin definition, texture, shape, and posterior acoustic attenuation. Malignant and benign lesions are better distinguished when features from both mammograms and ultrasound images are combined.

A new classification scheme was developed to classify mammographic masses as malignant and benign by using interval change information. The masses on both the current and the prior mammograms were automatically segmented using an active contour method. From each mass, 20 run length statistics (RLS) texture features, 3 spiculation features, and mass size were extracted. Additionally, 20 difference RLS features were obtained by subtracting the prior RLS features from the corresponding current RLS features. The feature space consisted of the current RLS features, the difference RLS features, the current and prior spiculation features, and the current and prior mass sizes. Stepwise feature selection and linear discriminant analysis classification (LDA) were used to select and merge the most useful features. A leave-one-case-out resampling scheme was applied to train and test the classifier using 140 temporal image pairs (85 malignant, 55 benign) obtained from 57 biopsy-proven masses (33 malignant, 24 benign) in 56 patients. An average of 10 features were selected from the 56 training subsets: 4 difference RLS features, 4 RLS features and 1 spiculation feature from the current image, and 1 spiculation feature from the prior, were most often chosen. The classifier achieved an average training A_z of 0.92 and a test A_z of 0.88. For comparison, a classifier was trained and tested using features extracted from the 120 current single images. This classifier achieved an average training A_z of 0.90 and a test A_z of 0.82. The information on the prior image significantly (p=0.01) improved the accuracy for classification of the masses.

A Computer-assisted Chest Radiograph Reader System (CARRS) was developed for the detection of pathological features in lungs presenting with pneumoconioses. CARRS applies novel techniques in automatic image segmentation, incorporates neural network-based pattern classification, and integrates these into a graphical user interface. The three aspects of CARRS are described: Chest radiograph digitization and display, rib and parenchyma characterization, and classification. The quantization of the chest radiograph film was optimized to maximize the information content of the digital images. Entropy was used as the benchmark for optimizing the quantization. From the rib-segmented images, regions of interest were selected by the pulmonologist. A feature vector composed of image characteristics such as entropy, textural statistics, etc. was calculated. A laterally primed adaptive resonance theory (LAPART) neural network was used as the classifier. LAPART classification accuracy averaged 86.8 %. Truth was determined by the two pulmonologists. The CARRS has demonstrated potential as a screening device. Today, 90% or more of the chest radiographs seen by the pulmonologist are normal. A computer-based system that can screen 50% or more of the chest radiographs represents a large savings in time and dollars.

Our research builds on the hypothesis that white matter damage resulting from therapy spans a continuum of severity that can be reliably probed using non-invasive MR technology. This project focuses on children treated for ALL with a regimen containing seven courses of high-dose methotrexate (HDMTX) which is known to cause leukoencephalopathy. Axial FLAIR, T1-, T2-, and PD-weighted images were acquired, registered and then analyzed with a hybrid neural network segmentation algorithm to identify normal brain parenchyma and leukoencephalopathy. Quantitative T1 and T2 maps were also analyzed at the level of the basal ganglia and the centrum semiovale. The segmented images were used as mask to identify regions of normal appearing white matter (NAWM) and leukoencephalopathy in the quantitative T1 and T2 maps. We assessed the longitudinal changes in volume, T1 and T2 in NAWM and leukoencephalopathy for 42 patients. The segmentation analysis revealed that 69% of patients had leukoencephalopathy after receiving seven courses of HDMTX. The leukoencephalopathy affected approximately 17% of the patients' white matter volume on average (range 2% - 38%). Relaxation rates in the NAWM were not significantly changed between the 1st and 7th courses. Regions of leukoencephalopathy exhibited a 13% elevation in T1 and a 37% elevation in T2 relaxation rates.

We are developing a computer-aided diagnosis (CAD) system for lung nodule detection on thoracic helical computed tomography (CT) images. In the first stage of this CAD system, lung regions are identified and suspicious structures are segmented. These structures may include true lung nodules or normal structures that consist mainly of vascular structures. We have designed rule-based classifiers to distinguish nodules and normal structures using 2D and 3D features. After rule-based classification, linear discriminant analysis (LDA) is used to further reduce the number of false positive (FP) objects. We have performed a preliminary study using CT images from 17 patients with 31 lung nodules. When only LDA classification was applied to the segmented objects, the sensitivity was 84% (26/31) with 2.53 (1549/612) FP objects per slice. When the LDA followed the rule-based classifier, the number of FP objects per slice decreased to 1.75 (1072/612) at the same sensitivity. These preliminary results demonstrate the feasibility of our approach for nodule detection and FP reduction on CT images. The inclusion of rule-based classification leads to an improvement in detection accuracy for the CAD system.

The purpose of this work is to automatically detect lung nodules in CT images, and then relocalize them in follow-up scans so that changes in size or morphology can be measured. We propose a new method that uses a patient's baseline image data to assist in the segmentation of subsequent images. The system uses a generic, a priori model to analyze the baseline scan of a previously unseen patient and then a user confirms or rejects nodule candidates. For analysis of follow-up scans of that particular patient, a patient- specific model is derived that narrows the search in feature-space for previously labeled nodules based on the feature values measured on the baseline scan. Also, some previously identified false positives can be automatically relocalized and eliminated. In the baseline scans of eleven patients, a radiologist identified a total of 14 nodules. All 14 nodules were detected automatically by the system with an average of 11 false positives per case. In follow- up scans, using patient-specified models, 12 of the 14 nodules were relocalized. There was one previously unseen nodule, that was detected by the system, with 9 false positives per follow-up case.

Computed tomography of the chest can be used as a screening method for lung cancer in a high-risk population. However, the detection of lung nodules is a difficult and time-consuming task for radiologists. The developed technique should improve the sensitivity of the detection of lung nodules without showing too many false positive nodules. In the first step the CAD technique for nodule detection in CT examinations of the lung eliminates all air outside the patient, then soft tissue and bony structures are removed. In the remaining lung fields a three-dimensional region detection is performed and rule-based analysis is used to detect possible lung nodules. In a study, which should evaluate the feasibility of screening lung cancer, about 2000 thoracic examinations were performed. The CAD system was used for reporting in a consecutive subset (n=100) of those studies. Computation time is about 5 min on an Silicon Graphics O2 workstation. Of the total number of found nodules >= 5 mm (n=68) 26 were found by the CAD scheme, 59 were detected by the radiologist. The CAD workstation helped the radiologist to identify 9 additional nodules. The false positive rate was less than 0.1 per image. The nodules missed by the CAD scheme were analyzed and the reasons for failure categorized into the density of the nodule is too low, nodules is connected to chest wall, segmentation error, and misclassification. Possible solutions for those problems are presented. We have developed a technique, which increased the detection rate of the radiologist in the detection of pulmonary nodules in CT exams of the chest. Correction of the CAD scheme using the analysis of the missed nodules will further enhance the performance of this method.

This paper describes the development of a computer-aided diagnosis (CAD) tool for solitary pulmonary nodules. This CAD tool is built upon physically meaningful features that were selected because of their relevance to shape and texture. These features included a modified version of the Hotelling statistic (HS), a channelized HS, three measures of fractal properties, two measures of spicularity, and three manually measured shape features. These features were measured from a difficult database consisting of 237 regions of interest (ROIs) extracted from digitized chest radiographs. The center of each 256x256 pixel ROI contained a suspicious lesion which was sent to follow-up by a radiologist and whose nature was later clinically determined. Linear discriminant analysis (LDA) was used to search the feature space via sequential forward search using percentage correct as the performance metric. An optimized feature subset, selected for the highest accuracy, was then fed into a three layer artificial neural network (ANN). The ANN's performance was assessed by receiver operating characteristic (ROC) analysis. A leave-one-out testing/training methodology was employed for the ROC analysis. The performance of this system is competitive with that of three radiologists on the same database.

We are developing a micro-computed tomography (micro CT) system for imaging pulmonary nodules. The purpose is to enhance the physician performance in accessing the micro- architecture of the nodule for classification between malignant and benign nodules. The basic components of the micro CT system consist of microfocus X-ray source, a specimen manipulator, and an image intensifier detector coupled to charge-coupled device (CCD) camera. 3D image reconstruction was performed by the slice. A standard fan- beam convolution and backprojection algorithm was used to reconstruct the center plane intersecting the X-ray source. The preprocessing of the 3D image reconstruction included the correction of the geometrical distortions and the shading artifact introduced by the image intensifier. The main advantage of the system is to obtain a high spatial resolution which ranges between b micrometers and 25 micrometers . In this work we report on preliminary studies performed with the micro CT for imaging resected tissues of normal and abnormal lung. Experimental results reveal micro architecture of lung tissues, such as alveolar wall, septal wall of pulmonary lobule, and bronchiole. From the results, the micro CT system is expected to have interesting potentials for high confidential differential diagnosis.

Layer decomposition is a promising technique for background removal and noise reduction in coronary angiograms. Our layer decomposition algorithm decomposes a projection image sequence into multiple 2D layers undergoing translation, rotation, and scaling. We apply this layer decomposition algorithm to simulated angiograms containing stenotic vessels with and without thrombus. We constructed 85 pairs of simulated angiographic sequences by embedding each of 5 simulated vessels (with and without thrombus) in 17 clinical angiograms. We computed the response of a matched eye filter applied to (1) one raw image of each sequence at the time of minimal motion (RAW), (2) a layered digital subtraction angiography (LDSA) image of the same frame, and (3) the time-averaged vessel layer image (LAYER). We find that on average the LAYER and LDSA images have higher signal-to-noise ration and larger area under the receiver- operator characteristic curves (AUC) than the raw images.

Magnetic Resonance Imaging (MRI) is a powerful technique for imaging cardiovascular diseases. The introduction of cardiovascular MRI into clinical practice is however hampered by the lack of efficient and accurate image analysis methods. This paper focuses on the evaluation of blood perfusion in the myocardium (the heart muscle) from MR images, using contrast-enhanced ECG-triggered MRI. We have developed an automatic quantitative analysis method, which works as follows. First, image registration is used to compensate for translation and rotation of the myocardium over time. Next, the boundaries of the myocardium are detected and for each position within the myocardium a time-intensity profile is constructed. The time interval during which the contrast agent passes for the first time through the left ventricle and the myocardium is detected and various parameters are measured from the time-intensity profiles in this interval. The measured parameters are visualized as color overlays on the original images. Analysis results are stored, so that they can later on be compared for different stress levels of the heart. The method is described in detail in this paper and preliminary validation results are presented.

Conventional reconstructions from intravascular ultrasound (IVUS) stack the frames as acquired during the pullback of the catheter to form a straight three-dimensional volume, thus neglecting the vessel curvature and merging images from different heart phases. We are developing a comprehensive system for fusion of the IVUS data with the pullback path as determined from x-ray angiography, to create a geometrically accurate 4-D (3-D plus time) model of the coronary vasculature as basis for computational hemodynamics. The overall goal of our work is to correlate shear stress with plaque thickness. The IVUS data are obtained in a single pullback using an automated pullback device; the frames are afterwards assigned to their respective heart phases based upon the ECG signal. A set of 3-D models is reconstructed by fusion of IVUS and angiographic data corresponding to the same ECG-gated heart phase; methods of computational fluid dynamics (CFD) are applied to obtain important hemodynamic data. Combining these models yields the final 4-D reconstruction. Visualization is performed using the platform-independent VRML standard for a user-friendly manipulation of the scene. An extension for virtual angioscopy allows an easy assessment of the vessel features within their local context. Validation was successfully performed both in-vitro and in-vivo.

A model is developed for the automated classification of bone fractures via image analysis techniques. The model is based on the widely used fracture classification system developed by the M.E. Mueller Foundation of Bern, Switzerland. The system describes a hierarchy of fractures, six layers deep. It also describes a series of questions to be asked about a given fracture, in which each question answered classifies the fracture into more descriptive subcategories. The model developed considers fracture classification as a tree traversal problem, in which the lower layers of the tree represent more precise categorizations. At each of the tree's nodes, algorithms specific to that subcategory determine which of the child nodes will be visited. Digital image processing techniques are most readily applicable to the largest number of nodes. Thus, the initial algorithms in this work are based on image processing techniques. The main contributions of this paper include a model for automated bone fracture classification and the algorithms for classification of a subset of long bone fractures. This work aims to provide a solid model and initial results that will serve as the basis for further research into this challenging and potentially rewarding field.

Methods exist for extracting vascular tree structures from very large 3D medical images, such as those arising from micro-CT scanners. Techniques have not been well addressed, however, for characterizing the detailed statistical structure of the tree or for interacting with such data. In this paper, we present our ongoing efforts on the detailed generational analysis of large 3D vascular trees. Our previously proposed system discussed the initial image analysis and tree representation of 3D vascular images. Our current work improves the performance of the image analysis process and gives new means for evaluating the quantitative information and geometrical characteristics of the vasculature. Furthermore, we have made it more feasible to perform multigenerational analysis and topology manipulation interactively by incorporating visualization tools. Our current implementation of the image processing and analysis methods generates varied details of the branching geometry at generation, inter-branch, and intra-branch levels. Variations of vessel surfaces, blood volumes, cross-sectional areas, and branch lengths in a whole tree are studied. The visualization tools provide functionality of displaying slices, projections of the 3D images, and surface rendering of the segmented trees. Also, tree-editing capability permits a user to interactively manipulate the vascular topology, such as modification of extraneous, generally peripheral artifactual, branches and generations, and update the statistical details of the tree in real time. We present results for 3D micro-CT rat heart images.

We propose a novel technique for ultrasound speckle reduction based on iterative solutions to the coherent diffusion equation with the speckled image considered as the initial heat distribution. According to the extent of speckle, the model changes progressively from isotropic diffusion through anisotropic coherent diffusion to mean curvature motion. This structure maximally low-pass filters those parts of the image corresponding to fully-formed speckle, while preserving information associated with resolved object structures. The distance measure used to assess the deviation between images is embedded within the diffusivity tensor and is utilized as an intrinsic stopping criterion that ends the diffusion process completely in all directions when the deviation between the original and the filtered image exceeds the speckle limit. This model is termed pseudo-biased diffusion due to this unique formulation. Hence, there is no need for specifying the number of iterations in advance as with previous methods. Moreover, the steady state solution does not converge to the trivial single gray level solution, but rather to an image that is close in structure to the original but with speckle noise substantially reduced. Efficient discretization schemes allow large time steps to be used in obtaining the solution to achieve real-time processing.

In this paper we present a parallel code which performs in iterative image deconvolution using either a spatially- invariant point spread function (SI-PSF) or a spatially- variant point spread function (SV-PSF). The basic algorithm is described as well as a description of the parallel implementation. Applications and results in the area of medical x-ray imaging is discussed.

We are developing a 3-D spherical navigator (SNAV) echo technique for MRI that can measure rigid body motion in all six degrees of freedom simultaneously, in a single echo, by sampling a spherical shell in k-space. MRI pulse sequences were developed to acquire varying amounts of data on such a shell. 3-D rotations of an imaged object simply rotate the data on this shell, and can be detected by registration of magnitude values. 3-D translations add phase shifts to the data on the shell, and can be detected with a weighted least squares fit to the phase differences at corresponding points. Data collected with a computer controlled motion phantom with known rotational and translational motions was used to evaluate the technique. The accuracy and precision of the technique depend on the sampling density, with roughly 1000 sample points necessary for accurate detection to within the error limits of the motion phantom. This number of samples can be captured in a single SNAV echo with a 3-D helical spiral trajectory. Motion detection in MRI with spherical navigator echoes is thus feasible and practical. Accurate motion measurements about all three axes, suitable for retrospective or prospective correction, can be obtained in a single pulse sequence.

Patient motion in gamma camera coincidence imaging results in severe reconstruction artifacts. A protocol is proposed to automatically detect and correct motion from SPECT coincidence studies. The method is based on fractionating the acquisition into three full temporal sets of coincidence data. For each set and camera position, partial sinograms are calculated by rebinning events acquired at the same rotation. Partial sinograms from successive angular positions as well as from successive sets are cross- correlated along their common range of projections. Decreases in the cross-correlation values indicate that data from two successive rotations or sets became inconsistent and permit localization of the motion that occurred during the study. Events acquired during motion are eliminated while pre and post motion events are recombined into sets of consistent rebinned data that are reconstructed independently and fused to provide a motion-artifact free reconstructed image. The methods were tested using a wide range of experimental motion data obtained from cylindrical phantoms containing spheres filled with Fluorine-18. Single arbitrary motions that occurred during the study could be detected and further corrected in all phantom studies when the total number of coincident events acquired was greater than 5x10⁶ for lesion-to-background ratios greater than 5.

This paper presents a hierarchical tetrahedral mesh model to represent the bone density atlas. We propose and implement an efficient and automatic method to construct hierarchical tetrahedral meshes from CT data sets of bony anatomy. The tetrahedral mesh is built based on contour tiling between CT slices. The mesh is then smoothed using an enhanced Laplacian algorithm. And we approximate bone density variations by means of continuous density functions written as smooth Bernstein polynomial spline expressed in terms of barycentric coordinates associated with each tetrahedron. We further perform the tetrahedral mesh simplification by collapsing the tetrahedra and build hierarchical structure with multiple resolutions. Both the shape and density error bound are preserved during the simplification. Furthermore a deformable prior model is computed from a collection of training models. Point Distribution Model is used to compute the variability of the prior model. Both the shape information and the density statistics are parameterized in the prior model. Our model demonstrates good accuracy, high storage efficiency and processing efficiency. We also compute the Digitally Reconstructed Radiographs from our model and use them to evaluate the accuracy and efficiency of our model. Our method has been tested on femur and pelvis data sets. This research is part of our effort of building density atlases for bony anatomies and applying them in deformable density based registrations.

Today's solid state flat panel radiography detectors provide images which contain artifacts caused by lines, columns and clusters of inactive pixels. If not too large, such defects can be filled by interpolation algorithms which usually work in the spatial domain. This paper describes an alternative spectral domain approach to defect interpolation. The acquired radiograph is modeled as the undistorted image multiplied by a known binary defect window. The window effect is then removed by deconvolving the window spectrum from the spectrum of the observed, distorted radiograph. The basic ingredient of our interpolation algorithm is an earlier approach to block transform coding of arbitrarily shaped image segments, that extrapolates the segment internal intensities over a block into which the segment is embedded. For defect interpolation, the arbitrarily shaped segment is formed by a local image region with defects, thus turning extrapolation into defect interpolation. Our algorithm reconstructs both oriented structures and noise- like information in a natural-looking manner, even for large defects. Moreover, our concept can also be applied to non- binary defect windows, e.g. for gain correction.

Simulations and measurements of triple head PET acquisitions of a hot sphere phantom were performed to evaluate the performance of two different reconstruction algorithms (projection based ML-EM and listmode ML-EM)for triple head gamma camera coincidence systems. A geometric simulator assuming a detector with 100 percent detection efficiency and only detection of trues was used. The resolution was equal to the camera system. The measurements were performed with a triple headed gamma camera. Simulated and measured data were stored in listmode format, which allowed the flexibility for different reconstruction algorithms. As a measure for the performance the hot spot detectability was taken because tumor imaging is the most important clinical application for gamma camera coincidence systems. The detectability was evaluated by calculating the recovered contrast and the contrast-to-noise ratio. Results show a slightly improved contrast but a clearly higher contrast-to-noise ratio for list mode reconstruction.

Magnetic resonance imaging exhibits technical characteristics that make it invaluable in medical diagnosis. However its full potential has been severely limited by the presence of imaging artifacts. These artifacts cause distortions in the obtained images, which no longer represent faithfully the object being imaged. In this work, we study the particular type of artifact known as magnetic susceptibility differences artifacts, caused by the presence of a ferromagnetic source. Previously, we have quantified these artifacts from three different perspectives: (1) pixel displacement, (2) blurring and (3) non-linearity. However, the non-linear distortions were quantified using a single-parameter non-linear function. In the present study, a multiparameter non-linear function based on polynomial series is used in the optimization. The results show that this modification allows for more flexibility and, as a result, improves the optimization algorithm.

The ability to correct certain types of MR images for motion artifacts from the raw data alone by iterative optimization of an image quality measure has recently been demonstrated. In the first study on a large data set of clinical images, we showed that such an autocorrection technique significantly improved the quality of clinical rotator cuff images, and performed almost as well as navigator echo correction while never degrading an image. One major criticism of such techniques is that they are computationally intensive, and reports of the processing time required have ranged form a few minutes to tens of minutes per slice. In this paper we describe a variety of improvements to our algorithm as well as approaches to correct sets of adjacent slices efficiently. The resulting algorithm is able to correct 256x256x20 clinical shoulder data sets for motion at an effective rate of 1 second/image on a standard commercial workstation. Future improvements in processor speeds and/or the use of specialized hardware will translate directly to corresponding reductions in this calculation time.

Diffraction tomography (DT) is a tomographic inversion technique that reconstructs the spatially variant refractive index distribution of a scattering object, and it can be viewed as a generalization of conventional X-ray computed tomography (CT) where X-rays have been replaced with a diffracting acoustical or electromagnetic wavefield. It is widely believed that measurements from a full angular range of 2(pi) are generally required to exactly reconstruct a complex-valued refractive index distribution. However, we have recently revealed that one needs measurements only over the angular range zero to 270 degrees to perform an exact reconstruction, and we developed minimal-scan filtered backpropagation (MS-FBPP) algorithms to achieve this. In this work, we review and numerically implement a recently developed family of minimal-scan reconstruction algorithms for DT that effectively operate by transforming the minimal-scan DT reconstruction problem into a conventional full-scan X-ray CT reconstruction problem.

All of the exact cone-beam reconstruction algorithms for so called long-object problem do not use equi-angular sampling but use equi-space sampling. However, cylindrical detectors (equi-angular sampling in xy and equi-spatial in z) have advantage in their compact design. Therefore, toward the long-object problem with equi-angular sampling, the purpose of this study is to develop a cone-beam reconstruction algorithm using equi-angular sampling for short-object problem. A novel implementation of Grangeat's algorithm using equi-angular sampling has been developed for short- object problem with and without detector truncation. First, both cone-beam projection g^(Psi )((Theta) ,(phi) ) and the first derivative of plane integral (3D Radon transform) p^(Psi )((Theta) ,(phi) ) are described using spherical harmonics with equi-angular sampling. Then, using Grangeat's formula, relationship between coefficients of spherical harmonics for g^(Psi )((Theta) ,(phi) ) and p^(Psi )((Theta) ,(phi) ) are found. Finally, a method has been developed to obtain p^(Psi )((Theta) ,(phi) ) from cone- beam projection data in which the object is partially scanned. Images are reconstructed using the 3D Radon backprojection with rebinning. Computer simulations were performed in order to verify this approach: Isolated (axially bounded) objects were scanned both with circular and helical orbits. Wen the orbit of the cone vertex does not satisfy Tuy's data sufficiency conditions, strong oblique shadows and blurring in the axial direction were shown in reconstructed coronal images. ON the other hand, if the trajectory satisfied Tuy's data sufficiency condition, the proposed algorithm provides an exact reconstruction. In conclusion, a novel implementation of the Grangeat's algorithm for cone-beam image reconstruction using equi-angular sampling has been developed.

A practical method for scatter compensation in SPECT imaging is the triple energy window technique (TEW) which estimates the fraction of scattered photons in the projection data pixel by pixel. This technique requires an acquisition of counts in three windows of the energy spectrum for each projection bin, which is not possible on every gamma camera. The aim of this study is to set up a scatter template for brain perfusion SPECT imaging by means of the scatter data acquired with the triple energy window technique. This scatter template can be used for scatter correction as follows: the scatter template is realigned with the acquired, by scatter degraded and reconstructed image by means of the corresponding emission template, which also includes scatter counts. The ratios between the voxel values of this emission template and the acquired and reconstructed image are used to locally adjust the scatter template. Finally the acquired and reconstructed image is corrected for scatter by subtracting the thus obtained scatter estimates. We compared the template based approach with the TEW scatter correction technique for data acquired with same gamma camera system and found a similar performance for both correction methods.

Magnetic resonance signals that have very short relaxation times are conveniently sampled in a spherical fashion. We derive a least squares framework for reconstructing three-dimensional source distribution images from such data. Using a finite-series approach, the image is represented as a weighted sum of translated Kaiser-Bessel window functions. The Radon transform thereof establishes the connection with the projection data that one can obtain from the radial sampling trajectories. The resulting linear system of equations is sparse, but quite large. To reduce the size of the problem, we introduce focus of attention. Based on the theory of support functions, this data-driven preprocessing scheme eliminates equations and unknowns that merely represent the background. The image reconstruction and the focus of attention both require a least squares solution to be computed. We describe a projected gradient approach that facilitates a non-negativity constrained version of the powerful LSQR algorithm. In order to ensure reasonable execution times, the least squares computation can be distributed across a network of PCs and/or workstations. We discuss how to effectively parallelize the NN-LSQR algorithm. We close by presenting results from experimental work that addresses both computational issues and image quality using a mathematical phantom.

We previously introduced a new Bayesian reconstruction method for transmission tomographic reconstruction that is useful in attenuation correction in SPECT and PET. To make it practical, we apply a deterministic annealing algorithm to the method in order to avoid the dependence of the MAP estimate on the initial conditions. The Bayesian reconstruction method used a novel pointwise prior in the form of a mixture of gamma distributions. The prior models the object as comprising voxels whose values (attenuation coefficients) cluster into a few classes (e.g. soft tissue, lung, bone). This model is particularly applicable to transmission tomography since the attenuation map is usually well-clustered and the approximate values of attenuation coefficients in each region are known. The algorithm is implemented as two alternating procedures, a regularized likelihood reconstruction and a mixture parameter estimation. The Bayesian reconstruction algorithm can be effective, but has the problem of sensitivity to initial conditions since the overall objective is non-convex. To make it more practical, it is important to avoid such dependence on initial conditions. Here, we implement a deterministic annealing (DA) procedure on the alternating algorithm. We present the Bayesian reconstructions with/out DA and show the independence of initial conditions with DA.

A fully automatic method to deform medical images is proposed. The procedure is based on the application of a set of consecutive local linear transformations at fixed landmarks, generating a global non-linear deformation. Continuity is guaranteed by a smooth change form the landmark point to the neighborhood, which is a homotopy between an affine transformation and the identity map. Landmarks are distributed uniformly throughout both reference and target images and their density is increased to reach the desired similarity between both images. A hybrid genetic optimization algorithm is used to search for the transformation parameters by maximizing the normalized mutual information. It is shown, by means of the transformation of a circle into a triangle and vice versa, that the method has the capability to generate either sharp of smooth deformations. For magnetic resonance images, it is proved that the successive application of the local linear transformations allows us to increase the similarity between geometrically deformed images and target. The results suggest that the method can be applied to a wide range of non-rigid image registration problems.

This study investigates the efficacy of filtering two-dimensional (2D) projection images of Computer Tomography (CT) by the nonlinear diffusion filtration in removing the statistical noise prior to reconstruction. The projection images of Shepp-Logan head phantom were degraded by Gaussian noise. The variance of the Gaussian distribution was adaptively changed depending on the intensity at a given pixel in the projection image. The corrupted projection images were then filtered using the nonlinear anisotropic diffusion filter. The filtered projections as well as original noisy projections were reconstructed using filtered backprojection (FBP) with Ram-Lak filter and/or Hanning window. The ensemble variance was computed for each pixel on a slice. The nonlinear filtering of projection images improved the SNR substantially, on the order of fourfold, in these synthetic images. The comparison of intensity profiles across a cross-sectional slice indicated that the filtering did not result in any significant loss of image resolution.

In Computed Tomography, axial resolution is determined by the slice collimation and the spiral algorithm, while in-plane resolution is determined by the reconstruction kernel. Both choices select a tradeoff between image resolution (sharpness) and pixel noise. We investigated an alternative approach using default settings for image reconstruction which provide narrow reconstructed slice-width and high in-plane resolution. If smoother images are desired, we filter the original (sharp) images, instead of performing a new reconstruction with a smoother kernel. A suitable filter function in the frequency domain is the ratio of smooth and original (sharp) kernel. Efficient implementation was achieved by a Fourier transform of this ratio to the spatial domain. Separating the 2D spatial filtering into two subsequent 1D filtering stages in x- and y-direction further reduces computational complexity. Using this approach, arbitrarily oriented multi-planar reformats (MPRs) can be treated in exactly the same way as axial images. Due to efficient implementation, interactive modification of the filter settings becomes possible, which completely replace the variety of different reconstruction kernels. We implemented a further promising application of the method to thorax imaging, where different regions of the thorax (lungs and mediastinum) are jointly presented in the same images using different filter settings and different windowing.

The purpose of this study was to evaluate performance of the EM-IntraSPECT (EMIS) algorithm for non-uniform attenuation correction in the chest. EMIS is a maximum-likelihood expectation maximization (MLEM) algorithm for simultaneously estimating SPECT emission and attenuation parameters from emission data alone. EMIS uses the activity within the patient as transmission tomography sources, with which attenuation coefficients can be estimated. A thorax phantom with a normal heart was used. The activity images reconstructed by EMIS were compared to images reconstructed using a conventional MLEM with a fixed uniform attenuation map. Uniformity of normal heart was improved with EMIS as compared to a conventional MLEM.

A correction method for inhomogeneity of magnetic resonance (MR) images was developed based on renormalization transformation. It is a post-processing algorithm on images. Unlike previous post-processing methods, which need to determine either a filter size or a free adjustable parameter for different applications, this presented method is fully automated. Tests on physical phantom data, patients' brain and neck MR images were presented.

A theoretically based transformation, which reorders SPECT sinograms degraded by the Poisson noise according to their signal-to-noise ratio (SNR), has been proposed. The transformation is equivalent to the maximum noise fraction (MNF) approach developed for Gaussian noise treatment. It is a two-stage transformation. The first stage is the Anscombe transformation, which converts Poisson distributed variable into Gaussian distributed one with constant variance. The second one is the Karhunen-Loeve (K-L) transformation along the direction of the slices, which simplifies the complex task of three-dimensional (3D) filtering into 2D spatial process slice-by-slice. In the K-L domain, the noise property of constant variance remains for all components, while the SNR of each component decreases proportional to its eigenvalue, providing a measure for the significance of each components. The availability of the noise covariance matrix in this method eliminates the difficulty of separating noise from signal. Thus we can construct an accurate 2D Wiener filter for each sinogram component in the K-L domain, and design a weighting window to make the filter adaptive to the SNR of each component, leading to an improved restoration of SPECT sinograms. Experimental results demonstrate that the proposed method provides a better noise reduction without sacrifice of resolution.

This paper presents implementation of an algorithm termed as oblique surface reconstruction (OSR) on cone-beam multi-slice reconstruction. Simulations on several mathematical phantoms are performed. Theoretical consideration is reviewed and the reconstruction of simulated phantom data in comparison to the current standard 180# LI is presented. The OSR is shown to produce images with high quality when practical spiral cone-beam scanning utilizing the multi-slice configuration is considered.

Cone beam reconstruction has attracted a great deal of attention in the medical imaging community. However, high-resolution cone beam reconstruction (CBR) involves a huge set of data and very time consuming computing. It usually needs customized hardware or a large-scale computer to achieve acceptable speed. Although the Feldkamp algorithm is an approximate CBR algorithm, it is a practical and efficient 3D reconstruction algorithm and is a basic component in several exact cone-beam reconstruction algorithms (CBRA). In this paper, we present a practical implementation for high-speed CBR on a commercially available PC based on hybrid computing (HC). We implement Feldkamp CBR with multi-level acceleration. We use HC utilizing single instruction multiple data (SIMD) and making execution units (EU) in the processor work effectively. We also utilize the multi-thread and fiber support on the operating system, which automatically enable the reconstruction parallelism in the multi-processor environment, and makes data I/O to the hard disk more effective. Memory and cache access optimization is done by properly data partition. This approach was tested on an Intel Pentium III 500Mhz computer and was compared to the traditional implementation. It decreases more than 75% the filtering time for 288 pieces projections, saves more than 60% of the reconstruction time for the 512³ cube, and maintains good precision with less than 0.08% average error. Our system is cost-effective and high-speed. An effective reconstruction engine can be built with a market-available Symmetric Multi-processor (SMP) computer. This is an easy and cheap upgrade and is compatible with newer PC processors.