TriAlign: revisiting deep functional map from map representation alignment perspectives

Wang, Haibo, Li, Qinsong, Hu, Ling, Xu, Haojun, Meng, Jing, Liu, Xinru, Lai, Yukun ORCID: https://orcid.org/0000-0002-2094-5680 and Liu, Shengjun 2025. TriAlign: revisiting deep functional map from map representation alignment perspectives. Visual Computer 41 (9) , 6999–7012. 10.1007/s00371-025-04038-w Item availability restricted.

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Abstract

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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Schools > Computer Science & Informatics
Publisher:	Springer
ISSN:	0178-2789
Date of First Compliant Deposit:	11 July 2025
Date of Acceptance:	29 May 2025
Last Modified:	15 Jul 2025 14:15
URI:	https://orca.cardiff.ac.uk/id/eprint/179761

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