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This paper proposes a minimal length difference algorithm for construction of a line in an image by solving the problem of optimal contour approximation. In this algorithm, a method for finding interest points is proposed, and the object matching (classification) is done by mapping interest points onto a vector space. In cases where the lines in the representation of the images are not smooth, the algorithm converges rapidly. The results of the experiments showed that for convergence of thedoi:10.3906/elk-1809-157 fatcat:vnxl6uj7b5hvtma7zlnrdgnswm