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Pairwise Harmonics for Shape Analysis
July 2013 (vol. 19 no. 7)
pp. 1172-1184
Youyi Zheng, Geometric Modeling & Sci. Visualization Center, King Abdullah Univ. of Sci. & Technol., Thuwal, Saudi Arabia
Chiew-Lan Tai, Dept. of Comput. Sci. & Eng., Hong Kong Univ. of Sci. & Technol., Kowloon, China
E. Zhang, Sch. of Electr. Eng. & Comput. Sci., Oregon State Univ., Corvallis, OR, USA
Pengfei Xu, Dept. of Comput. Sci. & Eng., Hong Kong Univ. of Sci. & Technol., Kowloon, China
This paper introduces a simple yet effective shape analysis mechanism for geometry processing. Unlike traditional shape analysis techniques which compute descriptors per surface point up to certain neighborhoods, we introduce a shape analysis framework in which the descriptors are based on pairs of surface points. Such a pairwise analysis approach leads to a new class of shape descriptors that are more global, discriminative, and can effectively capture the variations in the underlying geometry. Specifically, we introduce new shape descriptors based on the isocurves of harmonic functions whose global maximum and minimum occur at the point pair. We show that these shape descriptors can infer shape structures and consistently lead to simpler and more efficient algorithms than the state-of-the-art methods for three applications: intrinsic reflectional symmetry axis computation, matching shape extremities, and simultaneous surface segmentation and skeletonization.
Index Terms:
Shape,Harmonic analysis,Geometry,Surface treatment,Shape measurement,Complexity theory,Face,segmentation and skeletonization,Shape analysis,pairwise harmonics,intrinsic symmetry,shape correspondence
Citation:
Youyi Zheng, Chiew-Lan Tai, E. Zhang, Pengfei Xu, "Pairwise Harmonics for Shape Analysis," IEEE Transactions on Visualization and Computer Graphics, vol. 19, no. 7, pp. 1172-1184, July 2013, doi:10.1109/TVCG.2012.309
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