Moment-based methods for polygonal approximation of digitized curves

Object shape representation plays an important role in the area of image processing, pattern recognition and computer vision. In the past two decades, many algorithms have been suggested for creating approximated polygons. In this study, two new polygonal approximation methods based on the geometric moments and the orthogonal moments defined in terms of Legendre polynomials are proposed. The difference between the moments defined by the initial contour and those of the approximated polygon is taken as the objective function. Each algorithm provides various polygonal approximation results with different number of line segments for different application situations. For a given error bound, we can determine the optimal polygon with a minimum number of line segments. The procedures are applied to some digital curves and better results are obtained in comparison with some known methods.