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The paper proposes the concept of building the so-called medial width function - integral shape descriptor of figures used in image recognition tasks. Medial width function is determined based on the skeleton of the shape and the radial function. An algorithm to compute the medial width function for polygonal figures based on the line segment Voronoi diagram is also presented here. Generalized solution to the circular figures obtained by rounding corners in a polygonal figure is presented. Computational experiment demonstrates the efficiency and effectiveness of the approach to the problem of palm shapes comparing for personal identification.