Ricci curvature tensor based volumetric segmentation

Huang, Jisui and Chen, Ke and Alpers, Andreas and Lei, Na (2025) Ricci curvature tensor based volumetric segmentation. International Journal of Computer Vision. 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

Chen, Ke ORCID: https://orcid.org/0000-0002-6093-6623

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  Item type:	Article
  ID code:	93045
  Dates:	Date Event 15 June 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:	17 Jun 2025 00:19
  URI:	https://strathprints.strath.ac.uk/id/eprint/93045