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Intrinsic Geometric Scale Space by Shape Diffusion
November/December 2009 (vol. 15 no. 6)
pp. 1193-1200
Guangyu Zou, Wayne State University
Jing Hua, Wayne State University
Zhaoqiang Lai, Wayne State University
Xianfeng Gu, Stony Brook University
Ming Dong, Wayne State University
This paper formalizes a novel, intrinsic geometric scale space (IGSS) of 3D surface shapes. The intrinsic geometry of a surface is diffused by means of the Ricci flow for the generation of a geometric scale space. We rigorously prove that this multiscale shape representation satisfies the axiomatic causality property. Within the theoretical framework, we fur ther present a feature-based shape representation derived from IGSS processing, which is shown to be theoretically plausible and practically effective. By integrating the concept of scale-dependent saliency into the shape description, this representation is not only highly descriptive of the local structures, but also exhibits several desired characteristics of global shape representations, such as being compact, robust to noise and computationally efficient. We demonstrate the capabilities of our approach through salient geometric feature detection and highly discriminative matching of 3D scans.

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Index Terms:
Scale space, feature extraction, geometric flow, Riemannian manifolds
Guangyu Zou, Jing Hua, Zhaoqiang Lai, Xianfeng Gu, Ming Dong, "Intrinsic Geometric Scale Space by Shape Diffusion," IEEE Transactions on Visualization and Computer Graphics, vol. 15, no. 6, pp. 1193-1200, Nov.-Dec. 2009, doi:10.1109/TVCG.2009.159
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