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Shape Representation based on Integral Kernels Application to Image Matching and Segmentation Byung Woo Hong Emmanuel Prados Stefano Soatto Luminita Vese University of California Los Angeles CA 90095 hong eprados soatto cs ucla edu lvese math ucla edu Abstract This paper presents a shape representation and a variational framework for the construction of diffeomorphisms that establish meaningful correspondences between images in that they preserve the local geometry of singularities such as region boundaries At the same time the shape representation allows enforcing shape information locally in determining such region boundaries Our representation is based on a kernel descriptor that characterizes local shape This shape descriptor is robust to noise and forms a scale space in which an appropriate scale can be chosen depending on the size of features of interest in the scene In order to preserve local shape during the matching procedure we introduce a novel constraint to traditional energybased approaches to estimate diffeomorphic deformations and enforce it in a variational framework 1 Introduction Enforcing prior knowledge on the shape of structures of interest is a common way to facilitate bottom up segmentation for instance in the detection of anatomical structures in medical images Typically one exploits hand segmented samples to design a density in some space where shape is represented and such a density is used to bias the segmentation process towards shapes yielding a high posterior probability This enables overcoming problems such as low contrast occlusions illumination variations and other unmodeled phenomena collectively labeled as noise that would make purely bottom up segmentation unsuccessful While many researchers have been after a universal theory of shape including the determination of an appropriate space endowed with a metric and probabilistic structure that would enable reasoning on shape in a solid analytical framework such a theory does not exist



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