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Discretization of Laplace-Beltrami Operator Based on Cotangent Scheme and Its Applications

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Human Centered Computing (HCC 2019)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 11956))

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Abstract

Laplace-Beltrami operator (LBO) is the basis of describing geometric partial differential equation. It also plays an important role in computational geometry, computer graphics and image processing, such as surface parameterization, shape analysis, matching and interpolation. Due to the different application fields of Laplace-Beltrami operator need to meet the mathematical properties of different, has produced many discretization methods but cannot replace each other discretization method, different discretization method can reduce the time complexity, at the same time can improve an inefficient algorithm. In this article, We are mainly aimed at discretization based on the Laplace-Beltrami cotangent operator. We improve the original discretization method and apply it to non-rigid 3D shape retrieval tasks. Experimental results shows the effectiveness of our discretization method.

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Acknowledgment

We acknowledge the National Natural Science Foundation of China for its financial support (Grant No. 61502284).

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Authors and Affiliations

  1. Business School, Shandong Normal University, Jinan, China

    Qingqing Zhang & Chunmei Duan

Authors
  1. Qingqing Zhang
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  2. Chunmei Duan
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Corresponding author

Correspondence to Chunmei Duan .

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Editors and Affiliations

  1. University of Kragujevac, Čačak, Serbia

    Danijela Milošević

  2. South China Normal University, Guangzhou, China

    Yong Tang

  3. Wuhan University of Technology, Wuhan, Hubei, China

    Qiaohong Zu

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Zhang, Q., Duan, C. (2019). Discretization of Laplace-Beltrami Operator Based on Cotangent Scheme and Its Applications. In: Milošević, D., Tang, Y., Zu, Q. (eds) Human Centered Computing. HCC 2019. Lecture Notes in Computer Science(), vol 11956. Springer, Cham. https://doi.org/10.1007/978-3-030-37429-7_62

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  • DOI: https://doi.org/10.1007/978-3-030-37429-7_62

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-37428-0

  • Online ISBN: 978-3-030-37429-7

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