This paper describes an automatic dense correspondence approach to match two given isometric or nearly isometric 3D shapes which have non-rigid deformations. Our method is to improve the described ability of the assignment matrix as much as possible and solve the resolution composed of assignment matrices by using a combinatorial optimization algorithm. First, we construct two linear assignment matrices by using the SHOT and HKS descriptor, which can promote similar points into correspondence. Then, we construct a quadratic assignment matrix by using the heat distribution matrix, which can align a set of pairwise descriptors between a pair of points. In the final, we create a new objective function consisting of three assignment matrices which can adequately describe the matching relationship between points on two non-rigid deformed shapes, and the final optimal solution is obtained by solving the objective function using the projected descent optimization procedure. We show that high-quality dense correspondences can be established for a wide variety of model pairs which may have different poses, surface details. The effectiveness of this method is proven by geodesic error distance statistics from two commonly used datasets with ground truth, and we find that our algorithm is better than other state-of-the-art methods.
Graphic matching is a very critical issue in all aspects of computer vision. In this paper, a new graphics matching algorithm combining shape contexts and reweighted random walks was proposed. On the basis of the local descriptor, shape contexts, the reweighted random walks algorithm was modified to possess stronger robustness and correctness in the final result. Our main process is to use the descriptor of the shape contexts for the random walk on the iteration, of which purpose is to control the random walk probability matrix. We calculate bias matrix by using descriptors and then in the iteration we use it to enhance random walks’ and random jumps' accuracy, finally we get the one-to-one registration result by discretization of the matrix. The algorithm not only preserves the noise robustness of reweighted random walks but also possesses the rotation, translation, scale invariance of shape contexts. Through extensive experiments, based on real images and random synthetic point sets, and comparisons with other algorithms, it is confirmed that this new method can produce excellent results in graphic matching.
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