Wavelet-based affine invariant representation: a tool for recognizing planar objects in 3D space

A technique is developed to construct a representation of planar objects undergoing a general affine transformation. The representation can be used to describe planar or nearly planar objects in a three-dimensional space, observed by a camera under arbitrary orientations. The technique is based upon object contours, parameterized by an affine invariant parameter and the dyadic wavelet transform. The role of the wavelet transform is the extraction of multiresolution affine invariant features from the affine invariant contour representation. A dissimilarity function is also developed and used to distinguish among different object representations. This function makes use of the extrema on the representations, thus making its computation very efficient. A study of the effect of using different wavelet functions and their order or vanishing moments is also carried out. Experimental results show that the performance of the proposed representation is better than that of other existing methods, particularly when objects are heavily corrupted with noise.