Wreath products for edge detection

Wreath product group based spectral analysis has led to the development of the wreath product transform, a new multiresolution transform closely related to the wavelet transform. We derive the filter bank implementation of a simple wreath product transform and show that it is in fact, a multiresolution Roberts (1965) Cross edge detector. We also derive the relationship between this transform and the two-dimensional Haar wavelet transform. We prove that, using a non-traditional metric for measuring edge amplitude with the wreath product transform, yields a rotation and translation invariant edge detector. We introduce a novel method for measuring the orientation of an edge and show that it is without error in the noise-free case. The wreath product transform edge detection performance is shown to be superior to many standard edge detectors