New method for obtaining optimal polygonal approximations to solve the min-ε problem

A new method for obtaining optimal polygonal approximations in closed curves is proposed. The new method uses the suboptimal method proposed by Pikaz and an improved version of the optimal method proposed by Salotti. Firstly, the Pikaz’s method obtains a suboptimal polygonal approximation and then the improved Salotti’s method is used for obtaining many local optimal polygonal approximations with a prefixed starting point. The error value obtained in each polygonal approximation is used as value of pruning to obtain the next polygonal approximation. In order to select the starting point used by the Salotti’s method, five procedures have been tested. Tests have shown that by obtaining a small number of polygonal approximations, global optimal polygonal approximation is calculated. The results show that the computation time is significantly reduced, compared with existing methods.