An Algorithm for Calculating Shape Correspondences Using Functional Maps by Calibrating Base Matrix of 3D Shapes

A new algorithm is proposed to calibrate the base matrix between 3D geometric shapes for calculating correspondences using functional maps, in which shape correspondences can be represented as the calibration operation between the base matrices constructed by the shape eigenfunctions. First, the Laplace operators of 3D shapes are calculated to obtain eigenvectors and eigenvalues, and the basis matrix is constructed using the eigenvectors. Second, a calibration algorithm based on covariance mini-mum is proposed to calculate a calibration matrix S between shapes, and used to calibrate the basis matrices of function space of the two given shapes. Third, the Gauss curvature of all points of the source shape is calculated to sample some feature points, and traverses all points on the calibrated target model in order to find the optimal corresponding points to construct the correspondence between 3D shapes with isometric transformation (or approximate isometric transformation). Finally, the matching accuracy of the proposed algorithm is measured by calculating the geodesic error between the sampling points and the optimal points. Experiment results show that our algorithm is better than existing methods for establishing an accurate correspondence between two or more shapes, moreover, it significantly solves symmetry ambiguities problem which influence calculation of shape correspondence.