U of U CS 7960 - A Shock Grammar For Recognition (7 pages)

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A Shock Grammar For Recognition



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A Shock Grammar For Recognition Kaleem Siddiqi Benjamin B Kimia Department of Electrical Engineering McGill University Montreal Canada H3A lY2 Division of Engineering Brown University Providence RI 02912 Abstract properties of its region e g symmetry and thickness l or of its boundary e g curvature extrema I 20 and inflection points or of both 2 An alternate classification is according to those where shape is viewed statically as a combination of primitives e g generalized cylinders versus those where shape is explained developmentally via a set of processes acting on a simpler shape 14 Returning to the region based symmetrac axis transform SAT l this view has spawned a vast literature on the theoretical and computational aspects of skeletons However it is unfortunate that Blum s key insig ht that the SAT provides for qualitative shape descriptions in terms of shape morphemes e g disc worm wedge flare etc is usually forgotten Curiously an evolutionary a p proach to shape description supports and complements this view and gives it a sound mathematical foundation 8 101 To elaborate Kimia et al explore deformations of the shape s boundary a special case of which is deformation by a linear function of curvature K We confront the theoretical and practical difficulties of computing a representation for two dimensional shape based on shocks or singularities that arise as the shape s boundary is deformed First we develop subpixel local detectors for finding and classifying shocks Second we show that shock patterns are not arbitrary but obey the rules of a grammar and in addition satisfy specific topological and geometric constraints Shock hypotheses that violate the grammar or are topologically or geometrically invalid are pruned to enforce global consistency Survivors are organized into a hierarchical graph of shock groups computed in the reaction diffusion space where diffusion plays a role of regularization to determine the significance of each shock group The shock



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