Adaptive Use of LBO Bases by Shape Feature Scales for High‐Quality and Efficient Shape Correspondence

Abstract Bases from the eigenfunctions of the Laplace–Beltrami operator (LBO), called LBO bases, are popularly used to construct functional mappings for shape correspondence. Although many efforts have been made to improve LBO basis construction and their application in shape correspondence, they often overlook the role of shape feature scales in determining the suitability of LBO bases. This mismatch between the selected LBO bases and shape features results in poor representation, hindering shape correspondence and requiring more iterations for convergence, ultimately reducing efficiency. In this paper, we present an attention‐based module that adaptively learns weights based on the scales of shape features to better utilise LBO bases. This ensures that the selected LBO bases have frequencies that align with the scales of shape features, addressing the mismatch problem and improving feature representation. By filtering out LBO bases with incompatible frequencies, our approach enhances shape correspondence while reducing the number of iterations required for convergence, thereby improving efficiency. Additionally, the selected LBO bases can be easily integrated with existing methods, such as the test‐time adaptation strategy, to further enhance shape correspondence. Experimental results demonstrate that our method achieves higher‐quality results than state‐of‐the‐art methods while at a high efficiency.