Optimal polygonal approximation of digital curves

An algorithm for optimal polygonal approximation is presented. Given a value for the maximal allowed distance between the approximation and the curve, the algorithm finds an approximation with the minimal number of vertices. The city-block metric is used to measure the distance between the approximation and the curve. The algorithm worst case complexity is O(n²) where n is the number of points in the curve. This complexity is attractive compared to the complexity of other algorithms for optimal approximations. An efficient and optimal solution for the case of closed curves where no initial point is given, is also presented