Functional Maps and Its Application in Non-Rigid 3D Shape Correspondence

With the continuous development of 3D shape research technology, the issue of non-rigid 3D shape correspondence becomes increasingly important, with applications spanning multiple fields such as computer graphics, computer vision, and pattern recognition. The functional maps framework has achieved advanced results in non-rigid 3D shape correspondence, as it can capture complex relationships between shapes and exhibit robustness to the topological noise of non-rigid shapes. This paper first outlines the fundamental concepts and research directions of 3D shape correspondence, then it elaborates on the basic framework of functional maps. Building on this, it systematically reviews the classic works in the related field, including traditional functional maps methods and deep functional maps methods, highlighting the advantages and limitations of different approaches in addressing non-rigid shape correspondence. Subsequently, the paper introduces commonly used datasets in the field of non-rigid 3D shape correspondence, and conducts experimental comparisons and analysis of different methods. Finally, it provides an outlook on the future development trends of non-rigid 3D shape correspondence. © 2024 Journal of Computer Engineering and Applications Beijing Co., Ltd.; Science Press. All rights reserved.