A Local-Global Commutative Preserving Functional Map for Shape Correspondence

Existing non-rigid shape matching methods mainly involve two disadvantages. (a) Local details and global features of shapes can not be carefully explored. (b) A satisfactory trade-off between the matching accuracy and computational efficiency can be hardly achieved. To address these issues, we propose a local-global commutative preserving functional map (LGCP) for shape correspondence. The core of LGCP involves an intra-segment geometric submodel and a local-global commutative preserving submodel, which accomplishes the segment-to-segment matching and the point-to-point matching tasks, respectively. The first submodel consists of an ICP similarity term and two geometric similarity terms which guarantee the correct correspondence of segments of two shapes, while the second submodel guarantees the bijectivity of the correspondence on both the shape level and the segment level. Experimental results on both segment-to-segment matching and point-to-point matching show that, LGCP not only generate quite accurate matching results, but also exhibit a satisfactory portability and a high efficiency.