Object Shape Description Using Haar-Wavelet Functions

Similar to the shape description using Mexican Hat Wavelet functions we present in this paper the derivation of object descriptors using Haar Wavelets. The derivation is based on the continuous wavelet transformation of an angle function using the Haar function as mother wavelet. The angle function which represents a given object shape is derived from the extracted contour polygon by computing the angle differences between the angles at every position on the contour and the angle at the starting point. This angle function is periodical but with 2 pi offset and can be normalized in order to be independent of the object's size, it's position and orientation. The angle function depends only on the starting point on the given contour. Moreover, the used angle function doesn't include any singularity which might arise due to object rotations. The derived Wavelet descriptors were used in an agricultural application to recognize weed species. The paper presents in this context some derived results as well as possible solution for the problem of starting point.