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The article is devoted to use wavelet transform, that have properties of frequency-spatial selectivity, and detect information elements of object (for example, contour) with required detailed elaboration. The morphological operator on wavelet transform base was developed. It allows receiving the contour description at different hierarchy levels. The algorithm of getting contour points on a base of iterative quasi Newton method of extremum search of function at wavelet transform space was developed. The algorithm of image contour analysis based on iterative search algorithms in wavelet transform space was offered.