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Multi-scale anisotropic heat diffusion based on normal-driven shape representation

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Abstract

Multi-scale geometric processing has been a popular and powerful tool in graphics, which typically employs isotropic diffusion across scales. This paper proposes a novel method of multi-scale anisotropic heat diffusion on manifold, based on the new normal-driven shape representation and Edge-weighted Heat Kernels (EHK). The new shape representation, named as Normal-Controlled Coordinates (NCC), can encode local geometric details of a vertex along its normal direction and rapidly reconstruct surface geometry. Moreover, the inner product of NCC and its corresponding vertex normal, called Normal Signature (NS), defines a scalar/heat field over curved surface. The anisotropic heat diffusion is conducted using the weighted heat kernel convolution governed by local geometry. The convolution is computed iteratively based on the semigroup property of heat kernels toward accelerated performance. This diffusion is an efficient multi-scale procedure that rigorously conserves the total heat. We apply our new method to multi-scale feature detection, scalar field smoothing and mesh denoising, and hierarchical shape decomposition. We conduct various experiments to demonstrate the effectiveness of our method. Our method can be generalized to handle any scalar field defined over manifold.

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Authors and Affiliations

  1. Dalian University of Technology, Dalian, 116024, China

    Shengfa Wang & Zhixun Su

  2. Stony Brook University (SUNY), Stony Brook, NY, 11794-4400, USA

    Shengfa Wang, Tingbo Hou & Hong Qin

Authors
  1. Shengfa Wang
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  2. Tingbo Hou
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  3. Zhixun Su
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  4. Hong Qin
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Correspondence to Shengfa Wang.

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Wang, S., Hou, T., Su, Z. et al. Multi-scale anisotropic heat diffusion based on normal-driven shape representation. Vis Comput 27, 429–439 (2011). https://doi.org/10.1007/s00371-011-0582-y

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