Non-rigid Shape Correspondence Between Partial Shape and Full Shape

  Objectives  Constructing meaningful correspondence between two or more models is a very important basic research work. Regards the calculation issue of the correspondence between the partial 3D isometric shape and full shape, a new method for constructing the correspondence among shapes by computing 3D shape feature descriptors with partial functional map and localized manifold harmonics (LMH) operators is proposed.

  Methods  Firstly, the LMH operator is generated by the spectral decomposition from the improved Laplace and the feature descriptor of the shape is calculated. Secondly, the initial correspondence between the partial shape and the full shape is constructed by the partial functional map theory. Then the dense correspondence between the partial shape and the full shape is iteratively calculated. Finally, the correspondence can be optimized by the greedy algorithm till convergence.

  Results  Compared with the existing algorithms in TOSCA dataset, the feature descriptors constructed by the LMH operator used in this paper better reflects the intrinsic properties of some shapes than the feature descriptors constructed by Laplace-Beltrami operators, and the calculated correspondences between full and partial shapes (some with holes) are more accurate as well.

  Conclusions  The new operator generated by the local manifold harmonics and the sparse correspondence calculated by the partial functional map method can be used to construct a more accurate dense correspondence and therefore it can reduce the isometric error to some extent.