Consistency correspondence calculation of 3D shape collections using optimized spectral alignment

Abstract:

This paper focuses on the problems of computing correspondences among non-rigid 3D shape collections with a low accuracy rate, poor consistency, and difficult bijectivity. The novel approach proposed in this paper is based on the optimized spectral alignment algorithm and the canonical consistent latent basis. Firstly, we use the adjoint operator derived from the functional map to align the information between shapes in the spectral domain. The functional map matrix of each shape pair in the shape collections is calculated, resolving the problem of inconsistent direction between functional map and pointwise map. Secondly, we adapt the improved collections of shape maps approach to assign corresponding weights to the functional map matrix of each shape pair, reducing the impact of initialization parameter noise on the shape collection matching calculation results. Finally, we add the canonical consistent latent basis of the limit shape to compute the shape collections correspondence. The limit shape can be seen as a type structure of all shapes in the shape collection, which is an intermediate model with geometric variability, improving the consistency and bijectivity of the algorithm. The experimental results show that compared with the existing algorithms, this algorithm has the lowest geodesic error and the highest accuracy of global correspondence on FAUST, SCAPE, TOSCA, and SHERC’16 Topology datasets. Meanwhile, our method can reduce the noise of initialization parameters, solve the symmetric ambiguity problem, and more accurately compute the consistent and bijective correspondence of non-rigid 3D shape collections.