Bayesian estimation methods have been used with success in a great number of applications. One major domain is the inverse problems of image reconstruction and restoration.

Bayesian methods have formed the core of the development of reconstruction algorithms for emission tomography. In particular, there has been considerable interest in edge-preserving prior models, which are associated with smoothing penalty functions that are nonquadratic functions of nearby pixel differences. In spite of several advantages of nonconvex prior models, their use in routine applications has been hindered by several factors, such as the computational expense due to the nonconvexity of penalty functions and the difficulty in the selection of hyperparameters. We note here that, by choosing a penalty function which is nonquadratic but is still convex, both the problem of nonconvexity involved in some nonquadratic priors and the edge-oversmoothing problem of conventional quadratic priors may be avoided. In this paper, we use a class of two-dimensional smoothing splines with low (first) and high (second) spatial derivatives applied to convex-nonquadratic (CNQ) penalty functions. To compare quantitative performance of our new priors, we use the quantitation of bias/variance and total squared error over noise trials. Our numerical results show that a linear combination of first- and second-order spatial derivatives applied to CNQ penalty functions improves reconstructions in terms of total squared error.

Noninvasive imaging based on wave scattering remains a difficult problem in those cases where the forward map can only be adequately simulated by solving the appropriate partialdifferential equation subject to boundary conditions. We develop a method for solving these linear boundary-value problems which is efficient and exact, trading off storage requirements against computation time. The method is based on using the present solution within the Woodbury formula for updating solutions given changes in the trial image, or state. Hence the method merges well with the Metropolis-Hastings algorithm using localized updates. The scaling of the method as a function of image size and measurement set size is given. We conclude that this method is considerably more efficient than earlier algorithms that we have used to demonstrate sampling for inverse problems in this class. We give examples of sampling for imaging electrical conductivity from a simple synthetic data set. Full Bayesian inference is demonstrated with expectations calculated over the posterior for Potts-type prior distributions.

A novel image prior with mixed continuity constraints is proposed for the Bayesian positron emission tomography image reconstruction of human brains. Assume that a human brain can be partitioned into four tissue classes: gray matter, white matter, cerebral spinal fluid, and partial volume. And each partial volume image voxel consists of an arbitrary mixture among pure tissues. The brain image is then modeled as a piece-wise smooth function through a Gibbs prior with the image intensity of each region governed by the thin-plate energy function. We apply first and second order edge detection techniques to estimate region boundaries, and then categorize these boundaries based on the resulting edge maps. Rather than use the binary processes representing region boundaries such as weak-membrane or weak-plate (WP) models, we adopt a controlled-continuity approach to influence boundary formation. We refer to this model as a modified (WP) model with controlled continuity. We present the results of a computer simulated phantom study in which partial volume effects are explicitly modeled. Results indicate that we obtain superior region of interest quantitation using this approach in comparison to a partial volume correction method that has previously been proposed for quantitation using filtered back-projection image.

Emission computed tomography is widely applied in medical diagnostic imaging, especially to determine physiological function. The available set of measurements is, however, often incomplete and corrupted, and the quality of image reconstruction is enhanced by the computation of a statistically optimal estimate. Most formulations of the estimation problem use the Poisson model to measure fidelity to data. The intuitive appeal and operational simplicity of quadratic approximations to the Poisson log likelihood make them an attractive alternative, but they imply a potential loss of reconstruction quality which has not often been studied. This paper presents quantitative comparisons between the two models and shows that a judiciously chosen quadratic, as part of a short series of Newton-style steps, yields reconstructions nearly indistinguishable from those under the exact Poisson model.

This paper discusses a multiresolution approach to Bayesian design of binary filters. The key problem with Bayesian design is that for any window one needs enough observations of a template across the states of nature to estimate its prior distribution, thus introducing severe constraints on single window Bayesian filter designs. By using a multiresolution approach and optimized training methods, we take advantage of prior probability information in designing large-window multiresolution filters. The key point is that we define each filter value at the largest resolution for which we have sufficient prior knowledge to form a prior distribution for the relevant conditional probability, and move to a subwindow when a nonuniform prior is not available. This is repeated until we are able to make a filtering decision at some window size with a known prior for the probability P(Y=1|x), which is guaranteed for smaller windows. The optimized training algorithm overcomes computational issues that are associated with larger window filter designs. Further the Bayesian multiresolution filter is compared with the differencing multiresolution filter. The robustness of the Bayesian design is demonstrated over variation of the distributions of the states of nature. We consider edge noise for our experiments with emphasis on realistically degraded document images.

Many methods on form document image analysis have been proposed, but only a few of them have treated the extraction of logical structure. A new method called global-local-global (GLG) method for the logical structure extraction of a form document is proposed in this paper. Its algorithm consists of three phases: global division, local logical structure analysis, and global redivision of the whole document. GLG method emphasizes the global layout structure analysis and has a high accuracy. It is robust for treating with the accidental direct adjacent relationship between two unrelated cells. In addition, a logical structure tree is proposed to represent the logical structure of a form document.

This paper proposes a new operator called the surfaceshape operator for describing image structure. We consider an image function as a bivariate surface, then established the surfaceshape operator for describing the shape of each pixel compared with its neighborhood. From a geometry viewpoint, the types of surface shapes are elliptic, hyperbolic, cylindrical, etc. To give clearer meanings, in general, here we label them based on the topographic structure such as hill, dale, ridge, valley, etc. We also extend the surface-shape operator to have the capability of describing multiscale topographic structures by incorporating in scale-space representation. The surface-shape operator has invariant properties under linear and monotonic gray-tone transformations, and is insensitive to additive noises modeled by linear functions, so it has robustness with brightness variations and shading effects. Finally, we illustrate applicability of the surface-shape operator with applications to image classifications. The proposed method is compared with the spatial gray-level-dependence method and the multiresolution simultaneous autoregressive method. The results show that the proposed method works better, and has much more robustness with brightness variations and shading effects than those methods.

Recently Latecki and Lakämper [Computer Vision and Image Understanding 73(3) (1999)] reported a process called discrete curve evolution. This process has various application possibilities, in particular, for noise removal and shape simplification of boundary curves in digital images. In this paper we prove that the process of the discrete curve evolution is continuous: if polygon Q is close to polygon P, then the polygons obtained by their evolution remain close. This result follows directly from the fact that the evolution of Q corresponds to the evolution of P if Q approximates P. This intuitively implies that first all vertices of Q are deleted that are not close to any vertex of P, and then, whenever a vertex of P is deleted, then a vertex of Q that is close to it is deleted in the corresponding evolution step of Q.

Programmable media processors have been emerging to meet the continuously increasing computational demand in complex digital media applications, such as HDTV and MPEG-4, at an affordable cost. These media processors provide the flexibility to implement various image computing algorithms along with high performance, unlike the hardwired approach that has provided high performance for a particular algorithm, but lacks flexibility. However, to achieve high performance on these media processors, a careful and sometimes innovative design of algorithms is essential. In addition, programming techniques, e.g., software pipelining and loop unrolling, are needed to speed up the computations while the data flow can be optimized using a programmable DMA controller. In this paper, we describe an algorithm for two-dimensional convolution, which can be implemented efficiently on many media processors. Implemented on a new media processor called the MAP1000, it takes 7.9 ms to convolve a 512x512 image with a 7x7 kernel, which is much faster than the previously reported software-based convolution and is comparable with the hardwired implementations. High performance in two-dimensional convolution and other algorithms on the MAP1000 clearly demonstrates the feasibility of software-based solutions in demanding imaging and video applications.

As an application of smart cameras, this paper presents an algorithm and its real-time implementation for detecting and tracking multiple people moving in a surveillance scene. The algorithm is devised to work for low resolution image frames and any camera angle. First an adaptive background subtraction module is used to obtain potential moving target areas. Second a human body detection module is activated to locate the heads. Third a multitarget tracking module is deployed to resolve ambiguities associated with crosspaths and merged targets. The algorithm is implemented on the Texas Instruments TMS320C6201 fixed-point DSP processor for real-time processing of video signals. This real-time capability allows field deployment for the purpose of collecting surveillance data such as the number of people and their crossing frequency in a certain area.

Programmers involved in the electronic imaging industry are often confronted with developing image file format libraries. While in many cases simply purchasing a third party library is the most efficient way to do this, there are many new applications requiring code written from scratch. Embedded operating systems in digital cameras, printers, and scanners are examples of applications where the support of third party vendors is lacking.