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This workshop will concentrate on mathematical and practical issues arising in the higher level processes in image analysis. These include object recognition, optical character and handwriting recognizers, printed-circuit board inspection systems, and quality control devices, motion detection, robotic control by visual feedback, theory of shape, reconstruction of objects from stereoscopic view and/or motion, and many others. Shape theory is of fundamental importance since it is the bottleneck between high and low level vision, and forms the bridge between the two workshops on vision. The recent geometric partial differential equation methods have been essential in throwing new light on this very difficult problem area. There are two classical approaches to approximating the shape of objects. The first is based on diffusion and often leads to the (Gaussian) smoothing of contour information. The resulting scale-space may often be viewed as generated by parabolic operators which progressively and globally smooth shapes. The second approach is based on morphological morphology operations that represent the interior of shapes as sets, e.g., a collection of disks. The resulting morphological space can be viewed as being defined via a hyperbolic operator whose weak or viscosity solutions progressively smooth shapes in a local manner. The geometric PDE approach based on abstract conservation principles, Hamilton-Jacobi theory, and curvature driven flows leads to a computational theory of shape that naturally characterizes its computational elements including protrusions, parts, bends, and seeds (which show where to place the components of a shape). Stochastic processes, including Markov random fields, have been used in a Bayesian framework to incorporate prior constraints on a smoothness and the regularities of discontinuities into algorithms for image restoration and reconstruction. Sequential decision theory has been used to develop algorithms for efficient identification of objects in a scene, including handwritten characters, roads in satellite imagery, and faces. Deformable templates have been used to automate the identification of structures, both normal and pathological, in medical imagery. Since human vision relies on a variety of symmetry transformations, including Euclidean, affine and projective invariance, the incorporation of group theory and invariants into the image processing equations has been of great importance in the design of algorithms, both continuous and numerical.

A primary goal of this workshop is to educate and interest mathematicians in the mathematical and scientific problems that arise in the study of computer and natural vision. There will be a mix of tutorials in natural and artificial vision and mathematical talks on the theoretical foundations of existing and proposed vision systems. An additional goal is to bring together researchers working in these areas to compare results and to collaborate on ways to integrate these approaches into a powerful overall mathematical approach to vision. Unlike numerical analysis, the computer vision community has yet to establish "benchmark" tests for comparison of the various visual processing systems that are available, making direct and rigorous comparisons difficult. In this workshop we propose to initiate the development of a set of benchmark visual images that can be used for overall comparison purposes.

WORKSHOP SCHEDULE

Talk Abstracts

2000-2001 Program: Mathematics in Multimedia

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