Wreath Products for Edge Detection
V. Chickanosky and G. Mirchandani
ICASSP1999
(Paper (pdf) / Paper (ps))
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. In this work
we derive the filter bank implementation of a simple wreath
product transform and show that it is in fact, a multiresolution
Roberts 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.