Affine invariant wavelet transform

We present a two-dimensional wavelet transform that is invariant to affine distortions of the input signal. Affine distortions include geometric effects such as translation, reflection, uniform and anisotropic scaling, rotation, and shearing of the input signal. Invariance of the wavelet transform to affine distortions is achieved in our work by developing an algorithm that reduces replicas of a signal related by affine distortions to a unique prototype signal. The affine invariant wavelet transform is then defined as the two-dimensional wavelet transform of the prototype signal, which provides the wavelet coefficients that are invariant to affine distortions of the input signal. We describe our algorithm and show examples that demonstrate our claims.