In this paper, we develop two new algorithms based on the geometric moments and orthogonal moments to find the optimum solutions for polygonal approximation. For a given object contour, the purpose of the proposed methods is to determine a set of approximated polygons such that the moment difference between the approximated polygon and the initial contour is minimum. In the past two decades, many algorithms have been proposed for polygonal approximation. Most of them have the following characteristics: (1) they are sequential or iteratively sequential; (2) the cost functions depend only on the local relationship between the initial digital curves and the corresponding approximated polygon; (3) they output unique polygonal approximation resu and (4) the results depend on the selection of starting point. To surmount some of these drawbacks, Wu and Leou described a set of schemes that minimize the global area deviation between the approximated polygon and the initial curve. Their algorithms output a sequence of approximated polygons with different number of line segments, which can be used for various application situations. Furthermore, the methods proposed by Wu and Leou can be implemented in a parallel manner in order to speed up the computation time. By extending Wu and Leou's methods, we present in this paper two new algorithms based on geometric moments and orthogonal moments defined in terms of the Legendre polynomials to determine a set of the approximation polygons. In our methods, the geometric and orthogonal moments of order up to M are taken into account, respectively. The difference between the moments defined by the approximated polygon and those of the original polygon is taken as the cost function. A greedy strategy is adopted to establish a sequence of approximated polygons whose vertices are a subset of the points of the initial contour. Furthermore, fast algorithms for computation of the geometric and orthogonal moments are used to reduce the computational complexity. The application of the proposed approaches to some examples shows that our methods are efficient, and could give better resemblance to the initial contour in comparison with some known methods.%提出了两种基于矩的数字图像的多边形逼近方法.通过比较原始图形和近似图形之间几何矩或Legendre矩的偏差的大小，选择一个最佳的近似结果，进一步可以得到一个顶点数递减的近似多边形序列.与现存的方法比较，这种方法有效地避免了逼近结果依赖于起始点的选取的缺陷.
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