Symmetry Map and Symmetry Transforms for Shape Recovery and Object Recognition

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This project is concerned with the problem of recovery, representation, and recognition of shapes in images. The PI proposes to use the symmetry map, the shock graph of an edge map, as an intermediate-level representation for 2D shape. Deformations of shape are then expressed as a sequence of symmetry transforms which correspond to the inherent instabilities of skeletons (shock transitions). The optimal deformation path between two shapes is found using an edit distance approach to finding the least action sequence of transforms, or edits, on the shock graph. The cost of this path is used as a dissimilarity measure for indexing into image databases. This approach also allows for shape modeling and design, the construction of morphing sequences, and deformable templates. In 3D, The PI proposes to reduce the three-dimensional skeleton to a shock scaffold consisting of 1D space curves on which the 3D skeleton can be analytically constructed, leading to significant savings in recovery and storage of complex shapes, e.g., Michelangelo's Pieta, human lungs, etc. The research is generic and can potentially significantly impact a number of industrial and medical applications, including shape-based retrieval and construction of computational atlases.