- S. Borra and S. Sarkar,
**``A Framework for Performance Characterization of Intermediate Level Grouping Modules,''***IEEE Transactions on Pattern Analysis and Machine Intelligence,*vol. 19, no. 11, pp. 1306--1312, Nov. 1997.

We present five performance measures to evaluate grouping modules in the context of constrained search and indexing based object recognition. Using these measures, we demonstrate a sound experimental framework, based on statistical ANOVA tests, to compare and contrast three edge based organization modules, namely those of Etemadi et al., Jacobs, and Sarkar-Boyer in the domain of aerial objects using 50 images. With adapted parameters, the Jacobs module performs overall the best for constraint based recognition. For fixed parameters, the Sarkar-Boyer module is the best in terms of recognition accuracy and indexing speedup. Etemadi et al.'s module performs equally well with fixed and adapted parameters while the Jacobs module is most sensitive to fixed and adapted parameter choices. The overall performance ranking of the modules is Jacobs, Sarkar-Boyer, and Etemadi et al.

- M. Heath, S. Sarkar, T. Sanocki, and K.W. Bowyer,
**``A Robust Visual Method for Assessing the Relative Performance of Edge Detection Algorithms''***IEEE Transactions on Pattern Analysis and Machine Intelligence,*vol. 19, no. 12, pp. 1338--1359, Dec. 1997.

A new method for evaluating edge detection algorithms is presented and applied to measure the relative performance of algorithms by Canny, Nalwa-Binford, Iverson-Zucker, Bergholm and Rothwell. The basic measure of performance is a visual rating score which indicates the perceived quality of the edges for identifying an object. The process of evaluating edge detection algorithms with this performance measure requires the collection of a set of grey-scale images, optimizing the input parameters for each algorithm, conducting visual evaluation experiments and applying statistical analysis methods. The novel aspect of this work is the use of a visual task and real images of complex scenes in evaluating edge detectors. The method is appealing because, by definition, the results agree with visual evaluations of the edge images.

- L. Tsap, D. B. Goldgof, and S. Sarkar,
**``Efficient Nonlinear Finite Element Modeling of Nonrigid Objects via Optimization of Mesh Models,''**to appear in the special issue of*Computer Vision and Image Understanding*on CAD-Based Computer Vision, accepted 1997.

In this paper we propose a new general framework for the application of the Nonlinear Finite Element Method (FEM) to nonrigid motion analysis. We construct the models by integrating image data and prior knowledge, using well-established techniques from computer vision, structural mechanics and computer-aided design (CAD). These techniques guide the process of optimization of mesh models. Linear FEM proved to be a successful physically-based modeling tool in solving limited types of nonrigid motion problems. However, linear FEM can not handle nonlinear materials or large deformations. Application of nonlinear FEM to nonrigid motion analysis has been restricted by difficulties with high computational complexity and noise sensitivity. We tackle the problems associated with nonlinear FEM by changing the parametric description of the object to allow easy automatic control of the model, using physically motivated analysis of the possible displacements to address the worst effects of the noise, applying mesh control strategies and utilizing multiscale methods. The combination of these methods represents a new systematic approach to a class of nonrigid motion applications for which sufficiently precise and flexible FEM models can be built. The results from the skin elasticity experiments demonstrate the success of the proposed method. The model allows us to objectively detect the differences in elasticity between normal and abnormal skin. Our work demonstrates the possibility of accurate computation of point correspondences and force recovery from range image sequences containing nonrigid objects and large motion.

- S. Sarkar and Kim L. Boyer,
**``Quantitative Measures of Change based on Feature Organization: Eigenvalues and Eigenvectors''**to appear in*Computer Vision and Image Understanding,*accepted 1997.

One important task of site monitoring is change detection from aerial images. Change, in general, can be of various types. In this paper we address the problem of developmental change at a site. For instance, we would like to know about new construction at a previously undeveloped site and possibly monitor its progress. Model based approaches are not suited for this kind of change as it usually happens in unmodelled areas. Since it is difficult to infer construction activity by predicting and verifying specific local features, we rely on more global statistical indicators.

The thesis of this paper is that the change induced by human activity can be inferred from changes in the organization among the visual features. Not only will the attributes of the individual image features change but also the relationships among these features will evolve. With the progress of construction we expect to see increased structure among the image features. We exploit this emerging structure, or organization, to infer change. In this paper, we propose four measures to quantify the global statistical properties of the individual features and the relationships among them. We base these measures on the theory of graph spectra. We provide extensive analysis of the robustness of these measures under various imaging conditions and demonstrate the ability of these organization based measures to detect coarsely incremental developmental changes.

- M. Heath, S. Sarkar, T. Sanocki, and K.W. Bowyer,
**``Edge Detector Comparison: Initial Study and Methodology''**to appear in*Computer Vision and Image Understanding,*accepted 1997.

Because of the difficulty of obtaining ground truth for real images, the traditional technique for comparing low-level vision algorithms is to present image results, side by side, and to let the reader subjectively judge the quality. This is not a scientifically satisfactory strategy. However, human rating experiments can be done in a more rigorous manner, to provide useful quantitative conclusions. We present a paradigm based on experimental psychology and statistics, in which humans rate the output of low level vision algorithms. We demonstrate the proposed experimental strategy by comparing four well known edge detectors: Canny, Nalwa-Binford, Sarkar-Boyer, and Sobel. We answer the following questions: Is there a statistically significant difference in edge detector outputs as perceived by humans when considering an object recognition task? Do the edge detection results of an operator vary significantly with the choice of its parameters? For each detector, is it possible to choose a single set of optimal parameters for all the images without significantly affecting the edge output quality? Does an edge detector produce edges of the same quality for all images, or does the edge quality vary with the image?

- S. Sarkar and K. L. Boyer,
**``Perceptual Organization in Computer Vision: A Review and a proposal for a Classificatory Structure,''***IEEE Transactions on Systems, Man, and Cybernetics*, vol.~23, no.~2, pp.~382--399, Mar. 1993.

The evolution of perceptual organization in biological vision, and its necessity in advanced computer vision systems, arises from the characteristic that perception, the extraction of meaning from sensory input, is an intelligent process. This is particularly so for high order organisms and, analogically, for more sophisticated computational models. In this paper we explore the role of perceptual organization in computer vision systems. We do this from four vantage points. First, we offer a brief history of perceptual organization research in both humans and computer vision. Next, we propose a classificatory structure in which to cast perceptual organization research to clarify both the nomenclature and the relationships among the many contributions. Thirdly, we review the perceptual organization work in computer vision in the context of this classificatory structure. Finally, we survey the array of computational techniques applied to perceptual organization problems in computer vision.

- S. Sarkar and K. L. Boyer,
**``A Computational Structure for Preattentive Perceptual Organization: Graphical Enumeration and Voting Methods,''***IEEE Transactions on Systems, Man, and Cybernetics*, vol.~24, no.~2, pp.~246--267, Feb. 1994.

We present an efficient computational structure for preattentive perceptual organization. By perceptual organization we refer to the ability of a vision system to organize features detected in image based on viewpoint consistency and other Gestaltic perceptual phenomena. This usually has two components, a primarily bottom up preattentive part and a top down attentive part, with meaningful features emerging in a synergistic fashion from the original set of (very) primitive features. In this work we advance a computational structure for preattentive perceptual organization. We propose a hierarchical approach, using voting methods to build associations through consensus and relational graphs to represent the organization at each level. The voting method is very efficient in terms of time and space and performs impressively for a wide range of organizations. The graphical representation allows the ready extraction of higher order features, or perceptual tokens, because the relational information is rendered explicit.

- S. Sarkar and K. L. Boyer,
**``Integration, Inference, and Management of Spatial Information Using Bayesian Networks: Perceptual Organization,''***IEEE Transactions on Pattern Analysis and Machine Intelligence*(Special Section on Probabilistic Reasoning), vol.~15, no.~3, pp.~256--274, Mar. 1993.

The use of knowledge bases has been advocated by many researchers to make computer vision more stable and reliable. The formalism of Bayesian networks provides a very elegant solution, in a probabilistic framework, to the problem of integrating top down and bottom up visual processes as well serving as a knowledge base. We modify the formalism to handle spatial data and thus extend the applicability of Bayesian networks to visual processing. We call the modified form the Perceptual Inference Network (PIN). We present the theoretical background of a PIN and demonstrate its viability in the context of perceptual organization. Perceptual organization imparts robustness, efficiency, and a qualitative and holistic nature to vision. So far the approaches to the problem of perceptual organization have been purely bottom up, without much top down knowledge base influence and hence entirely dependent on the inputs, which may be imperfect. The knowledge base, besides coping with such input imperfection, also allows us to integrate multiple organizations and form a composite organization hypothesis. The Perceptual Inference Network imparts an active inferential and integrating nature to perceptual organization in an elegant probabilistic framework.

- S. Sarkar and K. L. Boyer,
**``Using Perceputal Inference Networks to Manage Vision Processes,''***Computer Vision, Graphics, and Image Processing: Image Understanding*, vol. 62, no. 1, pp.27--46, July 1995.

We provide a probabilistic framework, based on Perceptual Inference Networks, for the management of computational resources such as special purpose modules, feature detectors, and highly domain dependent algorithms. Since these resources tend to be computationally expensive and have limited applicability, judicious management is warranted. The resources are used to build a comprehensive description of the scene. Resources are selected in an information theoretic framework with the maximization of information gain per unit of computation as the optimality criterion. The viability of the algorithm is demonstrated in perceptual organization tasks.

- S. V. Raman, S. Sarkar, and K. L. Boyer,
**``Hypothesizing Structures in Edge Focused Cerebral Magnetic Resonance Images Using Graph Theoretic Cycle Enumeration,"***Computer Vision, Graphics, and Image Processing: Image Understanding*, vol.~57, no. 1, pp. 81--98, Jan. 1993. - S. V. Raman, S. Sarkar, and K. L. Boyer,
**``Tissue boundary refinement in magnetic resonance images using contour-based scale space matching,''***IEEE Transactions on Medical Imaging*, vol. 10, pp. 109--121, June 1991.

Precise measurement or shape analysis of structures or lesion is required from cerebral magnetic resonance images for statistical studies of possible relationships between structural malformation and neuropsychiatric disorders, such as schizophrenia. Unfortunately, individual delineation of such image features by human operators is so cumbersome that it is done in only a few research centers. Tissue boundaries in magnetic resonance images can be identified as photometric edges in the visual representation. In recent years, the Laplacian-of-Gaussian (LoG) and Canny's edge detector have proven most interesting from the standpoint of mathematical optimality. These edge detection filters incorporate a scaling parameter allowing the tradeoff between edge localization and error rate to be made appropriately. At large scales, edges are inaccurately located with respect to the true underlying edge, but the boundaries detected arise from significant physical events. At small scales, edges are precisely located, but many false positive responses and excessive detail emerge, producing an overly rich edge image with a great deal of ``clutter.'' Point based scale space searching has been proposed as a mechanism for circumventing this problem but, to date, no robust, efficient algorithms have been reported. In contrast, we have developed a novel, whole contour based technique for tracing edges selected at a coarse scale into successively finer scales to recover the needed precision. The tracing algorithm builds consensus through a fast pixel voting scheme. We present a rigorous approach to setting the refinement schedule (quantizing the scale space) according to the information redundancy between adjacent filters by defining a {\it similarity functional}, which has broad applications. This has particular application to the mensuration of various structures in images of the brain. Although the LoG is used for many of the experiments, we also present results using a new edge detector which is mathematically superior to and faster to compute than the LoG and for which fewer steps are required to traverse the same effective span in scale space. We present experimental results on real data and outline other potential applications.

- S. Sarkar and K. L. Boyer,
**``On optimal infinite impulse response edge detection filters.''***IEEE Transactions on Pattern Analysis and Machine Intelligence*, vol.~13, no.~2, pp.~1154--1171, Nov. 1991.

In this paper we outline the design of an optimal, computationally efficient, infinite impulse response edge detection filter. We compute the optimal filter based on Canny's high signal to noise ratio, good localization criteria, and a criterion on the spurious response of the filter to noise. In our design procedure we incorporate an expression for the width of the filter, appropriate for infinite length filters, directly in the expression for spurious responses. The three criteria are maximized using the variational method and non-linear constrained optimization. The optimal filter parameters are tabulated for various values of the filter performance criteria. A complete methodology for implementing the optimal filters using approximating recursive digital filtering is presented. The approximating recursive digital filter is separable into two linear filters operating in two orthogonal directions. The implementation is very simple and computationally efficient. It has a constant time of execution for different sizes of the operator and is readily amenable to real time hardware implementation.

- S. Sarkar and K. L. Boyer,
**``Optimal infinite impulse response zero crossing based edge detectors,''***Computer Vision, Graphics, and Image Processing: Image Understanding*, vol.~54, no.~2, pp.~224--243, Sept. 1991.

We present formal optimality criteria and a complete design methodology for a family of zero crossing based, infinite impulse response (recursive) edge detection filters. In particular, we adapt the optimality criteria proposed by Canny to filters designed to respond with a zero crossing in the output at an edge location and {\em additionally} to impulse responses which are (allowed to be) infinite in extent. The spurious response criterion is captured directly by means of an appropriate measure of filter spatial extent for infinite responses. Infinite duration impulse responses may be implemented efficiently with recursive filtering techniques and so require constant computation time with respect to scale. As we will show, we can achieve both superior performance and increased speed by designing directly for an infinite impulse response than by any of the proposed finite duration approaches. We also show that the optimal filter which responds with a zero crossing in its output {\em may not} be implemented by designing the optimal peak responding filter (similar to Canny) and taking an additional derivative. It is necessary to formulate the criteria and design for a zero crossing response from the outset, else optimality is sacrificed. Filter parameters and performance criteria are presented for several designs, and experimental results are presented on a variety of images which demonstrate the behavior in the presence of very adverse noise, with respect to scale, and as compared to other ``optimal'' IIR filters which have been reported.

Click here for instructions to get Source Code

- K. L. Boyer and S. Sarkar,
**``Comments on ``On the Localization Performance Measure and Optimal Detection","***IEEE Transactions on Pattern Analysis and Machine Intelligence*, vol.~16, no.~1, pp.~106--107, Jan. 1994. In a recent paper, Tagare and deFigueiredo present a localization performance measure for edge detectors (PAMI-1990). They point out a flaw in Canny's formulation (subsequently used by Sarkar and Boyer of the localization criterion and motivate their form of the localization criterion from a different line of reasoning. In this correspondence we show that although Canny's derivation was wrong, the final form of the criterion is adequate and can in fact be derived from Tagare and deFigueiredo's formulation of the problem. We also point out disadvantages of using the form of Tagare and deFigueiredo's localization criterion.

- K. L. Boyer, D. M. Wuescher, and S. Sarkar,
**``Dynamic edge warping: An experimental system for recovering disparity maps in weakly constrained systems,''***IEEE Transactions on Systems, Man, and Cybernetics*, vol. 21, pp. 143--158, Jan. 1991.

We present a novel method for the automatic generation of strcture hypotheses suitable for recognition in medical images. We base the approach on segment-based edge-focusing to precisely delineate significant boundaries, and graph-theoretic cycle enumeration to produce natural closures and, therefore, plausible tissue structures of interest from incomplete boundary information. An efficient edge focusing algorithm selects significant fine scale boundaries as those natural descendants (in scale space) of prominent coarse scale edges. The fine scale representation provides the localization precision necessary, while the focusing ensures that only significant contours surviving over a range of scales are considered and so eliminates much of the ``clutter'' associated with a fine scale edge map. The spatial relationships among the edge segments are stored in the form a directed graph. Possible extensions (closures) of broken edge segments are searched using time- and space-efficient voting methods. Cycle enumeration techniques for directed graphs then generate the structure hypotheses. The overall paradigm is fairly general and can be used in other problem domains, certainly for images of other parts of the anatomy. We demonstrate the effectiveness of the method with extensive experimental results on various magnetic resonance images of the human brain.

A new technique called dynamic edge warping (DEW) for recovering reasonably accurate disparity maps from

- S. Sarkar,
**``Context Dependent Perceptual Organization: Graph Spectral Partitioning and Learning Automata,''**submitted to*IEEE Transactions on Pattern Analysis and Machine Intelligence,*Dec. 1997.

Perceptual organization using Gestalt principles offers an elegant framework to group low level features that are likely to come from a single object. We offer a novel strategy to adapt this grouping process to an object and its context in a scene. Given a set of training images of an object in context, the associated learning process decides on the relative importance of the basic Gestalt relationships such as proximity, parallelness, similarity, symmetry, closure, and common region towards segregating the object from the background. This learning is accomplished using a team of stochastic automata in a N-player cooperative game framework. The grouping process which is based on graph partitioning is able to form {\em large} groups from relationships defined over a small set of primitives and is fast. We demonstrate the robust performance of the grouping system on a variety of real images. Among the interesting conclusions is the significant role of photometric attributes in grouping and the ability to perform figure-ground segmentation from a set of local relations, each defined over a small number of primitives.

- L. Tsap, D. B. Goldgof, S. Sarkar, and P. Powers,
**``A vision-based technique for objective assessment of burn scars,''**submitted to*IEEE Transactions on Medical Imaging,*Oct.~1997.

In this paper we propose a method for the objective assessment of burn scars. The quantitative measures developed in this research provide an objective way to calculate scar elasticity. The approach combines range data and the mechanics and motion dynamics of human tissues. Active contours are employed to locate regions of interest and to find displacements of feature points using automatically established correspondences. We are able to evaluate the changes in strain distribution over time. Given images at two time instances and their corresponding features, we use Finite Element Method (FEM) to synthesize strain distributions of the underlying tissues. This results in a physically-based framework for motion and strain analysis. Elasticity of the burn scar is then recovered using iterative descent search for the best nonlinear finite element model that approximates stretching behavior of the region containing the burn scar. The results from the skin elasticity experiments illustrate the ability to objectively detect differences in elasticity between normal and abnormal tissue. These estimated differences in elasticity are correlated against the subjective judgments of physicians which are presently the practice.

- L. Tsap, D. B. Goldgof, and S. Sarkar,
**``Accurate tracking of non-rigid motion through iterative refinement of finite element models,''**submitted to*IEEE Transactions on Pattern Analysis and Machine Intelligence*, Nov. 1997.

In this paper we propose new algorithms for accurate nonrigid motion tracking. Given only a set of sparse correspondences and incomplete or missing information about geometry or material properties, we can recover dense motion vectors using finite element models. The method is based on the iterative analysis of the differences between the actual and predicted behavior. Large differences indicate that an object's properties are not captured properly by the model describing it. Feedback from the images during the motion allows the refinement of the model by minimizing the error between the expected and true position of the object's points. These errors are due to flaws in the model parameter estimation such as geometry and material properties. Unknown parameters are recovered using an iterative descent search for the best nonlinear finite element model that approximates nonrigid motion of the given object. During this search process we not only estimate material properties, but also infer dense point correspondences from our initial set of sparse correspondences. Thus, during tracking the model is refined which, in turn, improves tracking quality. As a result, we obtain a more precise description of nonrigid motion. Experimental results demonstrate the success of the proposed algorithm. The method was applied to man-made elastic materials and human skin to recover unknown elasticity, to complex 3-D objects to find details of their geometry, and to a hand motion analysis application. Our work demonstrates the possibility of accurate quantitative analysis of nonrigid motion in range image sequences with objects consisting of multiple materials and 3-D volumes.

- N. Saxena, S. Sarkar, and N. Ranganathan,
**``Mapping and Parallel Implementation of Bayesian Belief Networks,''**submitted to*IEEE Transactions on Parallel and Distributed Systems,*Apr. 1996.

Bayesian belief networks are used for graphically representing uncertainty and probabilistic dependence. Bayesian networks are applied in computer vision, object recognition, feature detection, medicine, CAM, troubleshooting and other applications wherein decisions are conditionally dependent on many controlling factors. Since most real time applications require fast response, parallelization of Bayesian networks becomes important. This paper presents an efficient technique for mapping polytree structured Bayesian belief networks, onto the hypercube parallel machine architecture. The proposed mapping is deadlock free since all the messages are received and processed in the order of the structural hierarchy of the nodes in a tree. The mapping scheme maintains parent-child adjacency and single hop message passing throughout the computation. The scheme was implemented and verified on a 64 node nCUBE. The task allocation is static and is done at the beginning of the computation. The proposed scheme allows for efficient mapping of arbitrarily large trees onto a fixed size hypercube. It is shown that the overall speed up corresponds to the height of the tree.

- T. K. Das and S. Sarkar,
**``Optimal Preventive Maintenance in a Single Machine Production Inventory System,''**Submitted to*IIE Transactions on Quality,*revised 1997.

In this paper we consider a production inventory system. The system produces a single product type of which inventory is maintained according to a ($S,s$) policy. Exogenous demand for the product arrives according to a random process. Unsatisfied demands are not back ordered. Such a make-to-stock production inventory policy is found very commonly in discrete part manufacturing industry, e.g., automotive spare parts manufacturing.

It is assumed that the demand arrival process is Poisson, and the production time of a unit has a general probability distribution. The system is failure prone and the time between failures has a general probability distribution. We conjecture that, for any such system, the down time due to failures can be reduced through preventive maintenance resulting in possible increases in the service level (\% of satisfied demands) and the cost benefit. We develop a mathematical model for systems whose repair time and maintenance time have general probability distributions. Subsequently we develop expressions for system performance measures. These performance measures, which are functions of the preventive maintenance parameters, are used as basis for optimal determination of the maintenance parameters. The optimization approach is exemplified through a numerical example problem. Interesting results from our numerical study together with a outline of the solution procedure is presented to motivate and facilitate the application of the modeling approach. Exact numerical results obtained from the example problem can be used to benchmark performance of other computationally attractive (perhaps, non optimal) solution approaches.

- S. Sarkar and K. L. Boyer,
**``Automated Design of Bayesian Perceptual Inference Networks,''**Tech. Rep. SAMPL-93-03, SAMP-Lab, Dept. of EE, OSU, March 1993, Presented at the*International Conference on Computer Vision and Pattern Recognition, 1994*

In our previous work we presented the Perceptual Inference Network (PIN), a formalism based on Bayesian Networks, to reason among a set of object or feature hypotheses and to integrate multiple sources of information in the context of perceptual organization. The design of a PIN requires knowledge of the dependency structure among the organizations of interest and the specification of the conditional probabilities. Heretofore, this design was done manually. In this paper we present an algorithm based on structural entropic measures and Random Parametric Structural Descriptions (RPSDs) to design a PIN automatically. Experimental results present evidence of the robustness of the algorithm and make performance comparisons on real image data with a manually structured PIN. Since PINs are a form of Bayesian Network, we hope that this work will also prove useful towards structuring Bayesian Networks in other computer vision contexts.

Sudeep Sarkar Last modified: Wed Feb 25 09:29:50 EST 1998