Wreath Products For Image Processing
D. Healy, G. Mirchandani, T. Olson and D. Rockmore
ICASSP1996
(Paper (pdf) / Paper (ps))
We present a wreath product approach for matched filtering to
detect rotated copies of a template in an image. We view the
image as a homogeneous space for a wreath product, a
noncommutative symmetry group. The corresponding Fourier analysis has
a natural multiresolution structure and accompanying efficient
algorithm which we explain and illustrate with an example. The
associated matched filter is a new example of the use of
noncommutative convolution for image processing. Numerical
experiments are described in which this noncommutative approach
outperforms standard Fourier-based methods.