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A representation method for 2D object shapes using contour polygons and Daubechies wavelet transform is presented for image processing and pattern recognition applications. Wavelet descriptors is derived using an angle function which is obtained from an extracted contour polygon. An approximation method is used which describes the contours as polygons. The method is qualified to approximate the contours depending on the local curvature, since this is necessary to avoid distortion of the contour characteristics. The resulting polygons are then described in polar coordinates. To reconstruct the original signal from the approximation the IWT (inverse wavelet transform) is used.