Abstract

No abstract

We present a purely isometric method that establishes 3D correspondence between two (nearly) isometric shapes. Our method evenly samples high-curvature vertices from the given mesh representations, and then seeks an injective mapping from one vertex set to the other that minimizes the isometric distortion. We formulate the problem of shape correspondence as combinatorial optimization over the domain of all possible mappings, which then reduces in a probabilistic setting to a log-likelihood maximization problem that we solve via the Expectation-Maximization (EM) algorithm. The EM algorithm is initialized in the spectral domain by transforming the sampled vertices via classical Multidimensional Scaling (MDS). Minimization of the isometric distortion, and hence maximization of the log-likelihood function, is then achieved in the original 3D euclidean space, for each iteration of the EM algorithm, in two steps: by first using bipartite perfect matching, and then a greedy optimization algorithm. The optimal mapping obtained at convergence can be one-to-one or many-to-one upon choice. We demonstrate the performance of our method on various isometric (or nearly isometric) pairs of shapes for some of which the ground-truth correspondence is available.

We present an automatic method that establishes 3D correspondence between isometric shapes. Our goal is to find an optimal correspondence between two given (nearly)

We exploit the permutation creation ability of genetic optimization to find the permutation of one point set that puts it into correspondence with another one. To this end, we provide a genetic algorithm for the 3D shape correspondence problem, which is the main contribution of this article. As another significant contribution, we present an adaptive sampling approach that relocates the matched points based on the currently available correspondence via an alternating optimization. The point sets to be matched are sampled from two isometric (or nearly isometric) shapes. The sparse one-to-one correspondence, i.e., bijection, that we produce is validated both in terms of running time and accuracy in a comprehensive test suite that includes four standard shape benchmarks and state-of-the-art techniques.