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<p>Current deep functional map methods face a critical gap in map representation alignment. While shape correspondence can be represented as point-wise maps, functional maps, and complex functional maps in the spatial, spectral, and complex spectral domains, respectively, existing approaches typically integrate at most two representations, resulting in symmetry ambiguity or spatial inconsistency. In this paper, we propose the <b>TriAlign</b> (<b>Tri</b>ple Maps <b>Align</b>ment) framework, a novel three-branch deep functional map-based method that harmonizes map representations across spatial, spectral, and complex spectral domains. Additionally, we introduce an alignment loss function to align the point-wise map with the complex functional map. Extensive experiments on (near-)isometric and non-isometric datasets demonstrate the superior accuracy of our method and its generalization capabilities across different datasets and mesh discretizations. Furthermore, the new loss function improves the stability of network training.</p>

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TriAlign: revisiting deep functional map from map representation alignment perspectives

  • 期刊论文

  • 发表日期：

    2025年6月29日

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  • Haibo Wang,
  • Qinsong Li,
  • Ling Hu,
  • Haojun Xu,
  • Jing Meng,
  • Xinru Liu,
  • Yu-Kun Lai,
  • Shengjun Liu

摘要

Current deep functional map methods face a critical gap in map representation alignment. While shape correspondence can be represented as point-wise maps, functional maps, and complex functional maps in the spatial, spectral, and complex spectral domains, respectively, existing approaches typically integrate at most two representations, resulting in symmetry ambiguity or spatial inconsistency. In this paper, we propose the TriAlign (Triple Maps Alignment) framework, a novel three-branch deep functional map-based method that harmonizes map representations across spatial, spectral, and complex spectral domains. Additionally, we introduce an alignment loss function to align the point-wise map with the complex functional map. Extensive experiments on (near-)isometric and non-isometric datasets demonstrate the superior accuracy of our method and its generalization capabilities across different datasets and mesh discretizations. Furthermore, the new loss function improves the stability of network training.