SGER ACT: Stochastic Shape Analysis for Recognizing and Tracking Objects in Images and Videos

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Imaging devices have become ubiquitous tools of surveillance of public areas, remote locations, areas of restricted access, and other sites where additional security is needed. The detailed analysis of collected images can provide invaluable information about people, objects, their characteristics and patterns of behavior. Thus, combined with other strategies, image analysis can contribute significantly to the prevention of terrorism and national security. However, the execution of this task poses challenging problems due to the vast amount of imagery generated by surveillance devices. To make this task feasible, advanced automated systems are needed to screen images and route to human operators only material that is very likely to contain relevant information. The proposed interdisciplinary research addresses problems on the interface of shape and digital image analysis, whose solutions will contribute to the implementation of such intelligent surveillance systems, and will be useful in numerous other applications. Images contain information about two main attributes of objects: their shapes and textures. The proposers will develop a novel framework to represent and analyze planar shapes quantitatively using methods and tools of differential geometry, differential topology, and statistics. Statistical texture analysis and synthesis will be combined with the study of shapes to produce finer models of imaged objects. New algorithms of shape and image analysis will be developed, implemented, and applied to: (a) the detection and recognition of objects in noisy images; (b) tracking dynamic shapes possibly subject to occlusions in video sequences; (c) the organization of large databases of shapes for efficient retrieval and processing of information. Current techniques of algorithmic shape analysis are somewhat limited in scope or performance: some represent shapes using coarse collections of landmarks whose selection may be difficult to automate, and some involve heavy computational costs. Computational efficiency issues also limit the use of existing methods of image analysis; in spite of the remarkable success that methods based on partial differential equations have had in many applications, computational costs associated with typical implementations are high and the performance is not adequate for applications in video surveillance. There is a pressing need for efficient, robust algorithms that can analyze, process, and simulate the dynamics of shapes of continuous closed curves. The main idea proposed here is the use of computational stochastic differential geometry to study shapes, i.e., the algorithmic analysis of differential geometric representations of continuous curves in a statistical framework. The proposers will: (i) analyze closed shapes by representing them as elements of infinite-dimensional Riemannian manifolds via their angle or curvature functions; (ii) develop geometry-based tools for statistical inference problems on shape spaces; (iii) derive techniques for nonlinear filtering and tracking of shapes in infinite-dimensional shape manifolds; (iv) study completions of contours and textures with the goal of discovering hidden geometric features that follow an observable pattern; (v) implement algorithms and apply them to the solution of problems in shape and image analysis. The key new element in this approach is the use of the geometry of spaces of curves to study shapes, not only the geometry of individual curves. Results originating from this research may have far-reaching implications in shape, image and video analysis. The proposed algorithmic approach to shapes has the potential to set a new paradigm for the treatment of curve evolution. The team has expertise in the areas of differential geometry and topology, statistics, computing, and image analysis. This grouping reflects the interdisciplinary nature of the proposed investigation and will further enhance the atmosphere of collaborative research that exists among the PIs and their graduate students. Moreover, the applications to be investigated will contribute to the education and involvement of more students in areas related to national security. The PIs will continue to develop and offer courses and seminars from the introductory to the advanced levels targeting a broad audience of science students with the goal of increasing the overall impact of this line of research. To encourage the participation of undergraduates and students from underrepresented groups, motivated students will have full access to the Florida State University Laboratory of Computational Vision, where a hands-on learning environment will allow them to explore the area with their own experiments. To disseminate research results the proposers will continue to publish articles in well-circulated journals, post results in various electronic preprint archives, produce multimedia presentations on CD-ROMs, write introductory articles in magazines or handbooks, and present results at regional, national and international conferences.This award is supported jointly by the NSF and the Intelligence Community. The Approaches to Combat Terrorism Program in the Directorate for Mathematical and Physical Sciences supports new concepts in basic research and workforce development with the potential to contribute to national security.