Ricci curvature tensor based volumetric segmentation

Tools

Huang, Jisui and Chen, Ke and Alpers, Andreas and Lei, Na (2025) Ricci curvature tensor based volumetric segmentation. International Journal of Computer Vision, 133 (9). pp. 6491-6512. ISSN 1573-1405 (https://doi.org/10.1007/s11263-025-02492-6)

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Abstract

Existing level set models employ regularization based only on gradient information, 1D curvature or 2D curvature. For 3D image segmentation, however, an appropriate curvature-based regularization should involve a well-defined 3D curvature energy. This is the first paper to introduce a regularization energy that incorporates 3D scalar curvature for 3D image segmentation, inspired by the Einstein-Hilbert functional. To derive its Euler-Lagrange equation, we employ a two-step gradient descent strategy, alternately updating the level set function and its gradient. The paper also establishes the existence and uniqueness of the viscosity solution for the proposed model. Experimental results demonstrate that our proposed model outperforms other state-of-the-art models in 3D image segmentation.

ORCID iDs

Huang, Jisui, Chen, Ke ORCID logoORCID: https://orcid.org/0000-0002-6093-6623, Alpers, Andreas and Lei, Na;
  • Item type:Article
    ID code:93045
    Dates:
    Date
    Event
    1 September 2025
    Published
    15 June 2025
    Published Online
    26 May 2025
    Accepted
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:06 Jun 2025 14:36
    Last modified:09 Jan 2026 04:55
    URI:https://strathprints.strath.ac.uk/id/eprint/93045
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