Mesh Optimization for Surface Approximation Using an Efficient Genetic Algorithm with a novel 2-D Orthogonal Crossover

In this paper, the surface approximation using a mesh optimization approach is investigated. 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 points as closely as possible. The resultant 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 points. A genetic-algorithm-based method has been proposed for establishing optimal 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 order of thousands. This paper proposes an efficient genetic algorithm with a novel 2-D orthogonal crossover for obtaining the optimal solution to the surface approximation problem using a triangular mesh. It is shown empirically that the proposed efficient genetic algorithm outperforms the existing GA-based method in solving the mesh optimization problem in terms of the approximation quality and the convergence speed, especially in solving large mesh optimization problems.