Mesh optimization for surface approximation using an efficient coarse-to-fine evolutionary algorithm

This paper investigates surface approximation using a mesh optimization approach. The mesh optimization problem is how to locate a limited number n of grid points such that the established mesh of n grid points approximates the digital surface of N sample points as closely as possible. The resulting combinatorial problem has an NP-hard search space of C(N, n) instances, i.e., the number of ways of choosing n grid points out of N sample points. A genetic-algorithm-based method has been proposed for establishing optimal approximating mesh surfaces. It was shown that the GA-based method is effective in searching the combinatorial space which is intractable when n and N are in the order of thousands. This paper proposes an efficient coarse-to-fine evolutionary algorithm with a novel 2-D orthogonal crossover for obtaining an optimal solution to the mesh optimization problem. It is shown empirically that the proposed coarse-to-fine evolutionary algorithm outperforms the existing GA-based method in solving the mesh optimization problem in terms of both approximation quality and convergence speed, especially in solving large mesh optimization problems.