Detection and characterization of Intrinsic symmetry of 3D shapes

A comprehensive framework for detection and characterization of partial intrinsic symmetry over 3D shapes is proposed. To identify prominent symmetric regions which overlap in space and vary in form, the proposed framework is decoupled into a Correspondence Space Voting (CSV) procedure followed by a Transformation Space Mapping (TSM) procedure. In the CSV procedure, significant symmetries are first detected by identifying surface point pairs on the input shape that exhibit local similarity in terms of their intrinsic geometry while simultaneously maintaining an intrinsic distance structure at a global level. To allow detection of potentially overlapping symmetric shape regions, a global intrinsic distance-based voting scheme is employed to ensure the inclusion of only those point pairs that exhibit significant intrinsic symmetry. In the TSM procedure, the Functional Map framework is employed to generate the final map of symmetries between point pairs. The TSM procedure ensures the retrieval of the underlying dense correspondence map throughout the 3D shape that follows a particular symmetry. The TSM procedure is also shown to result in the formulation of a metric symmetry space where each point in the space represents a specific symmetry transformation and the distance between points represents the complexity between the corresponding transformations. Experimental results show that the proposed framework can successfully analyze complex 3D shapes that possess rich symmetries.