Pairwise Harmonics for Shape Analysis

This is an author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by IEEE-Institute of Electrical and Electronics Engineers and can be found at: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2945. ©2013 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.This paper introduces a simple yet effective shape analysis mechanism for geometry processing. Unlike traditional shape\ud analysis techniques which compute descriptors per surface point up to certain neighborhoods, we introduce a shape analysis\ud framework in which the descriptors are based on pairs of surface points. Such a pairwise analysis approach leads to a new class of\ud shape descriptors that are more global, discriminative, and can effectively capture the variations in the underlying geometry.\ud Specifically, we introduce new shape descriptors based on the isocurves of harmonic functions whose global maximum and minimum\ud occur at the point pair. We show that these shape descriptors can infer shape structures and consistently lead to simpler and more\ud efficient algorithms than the state-of-the-art methods for three applications: intrinsic reflectional symmetry axis computation, matching\ud shape extremities, and simultaneous surface segmentation and skeletonization