Comparison between Mexican Hat and Haar Wavelet Descriptors for Shape Representation

The wavelet transformation is a well known method in several engineering fields. In image processing and pattern recognition the wavelet transformation is used for the recognition of object shapes by deriving so called wavelet descriptors. In this context the Mexican Hat as well as the Haar function were used as mother wavelets. To derive wavelet descriptors the methods use a periodical angle function derived from the contour polygon. The angle function describes an object shape by calculating the angle changes along the object contour beginning from a given starting point. Since object shapes are described by polygons, the angle function is step-shaped and therefore it includes discontinuity at the existing polygon corners. This causes big changes of the Haar wavelet descriptors if the positions of the polygon corners change due to small changes of the object shape. Such changes can be caused at least by digitalization or binarization errors. The Mexican Hat wavelet descriptors are more adapted and suffer however from small changes. In this paper we present the results of the comparison between both methods in there accurateness of describing object shapes.