Symmetry-based Representation of 2D and 3D shapes and images for category-level recognition

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This project investigates the development and use of 2D and 3D shape and image representations for category-level recognition, as organized in four closely related streams. First, low-distortion embeddings of the shape space that capture both its local topology and its high order structure will be investigated for efficient and practical indexing in a database of several tens of thousands of shapes. Query search will then be guided in the embedding space via hierarchically structured categories motivated by cognitive science notions. Second, a novel free-form deformable template will be developed by constructing a parametric space for generating shapes constrained to have a given shock-graph topology and by sampling this space with a low-dimensional dense and complete approximation. This will lead to a formal complete language for describing shape via symmetry representations and has fundamental implications in a number of areas including segmentation, shape averaging, and !shape design. Third, viewing symmetry-based representations primarily as the joint representation of the spatial configuration of pairs of features, a formal and complete symmetry-based representation of images will be developed based on a partitioning of the image into patches called "visual fragments". The proposed advantage of the visual fragments is that they allow for perceptual grouping based on both boundary and regional attributes, and also for top-down feedback from partially recognized portions of the grouping. Fourth, in a track parallel to investigations of 2D shape representations, the local form and transitions of the graph-structured shock scaffold as a representation of 3D shape will be explored. Two graph matching techniques, graduated assignment and edit distance, will be investigated for indexing into 3D shape models and applied to a large database of 3D shapes.The broader impact of this research activity spans a number of areas, such as tracking and recognition of vehicles for surveillance, homeland security, and defense applications, generation of computational atlases and registration of datasets in medical imaging, fragment assembly and integration of multiple range datasets in archaeology, virtual sculpting in visual arts, signature and fingerprint recognition in biometric identification, indexing into large databases by shape content, key frame animation for entertainment applications, among others. The concepts developed here are also of interest for both modeling shape perception and cortical activity as related to shape recognition.