Cosine Transform Generalized to Lie Groups SU(2)XSU(2) AND O(5): Application to Textural Image Processing

We propose to apply two of the multiple variants of the 2-dimensional cosine transform. We consider the Lie groups leading to square lattices, namely SU(2)xSU(2) and O(5) in the 2-dimensional space. Our aim is to evaluate the benefits of some discrete group transform (DGT) techniques, in particular the continuous extension of the discrete group transform (CEDGT), and to develop new techniques to refine image quality. The use of algorithms based on the 2-dimensional DGT is advantageous because these algorithms yield the exact value of the original data at all points of the grid lattice, and smoothly interpolate the data values between grid points. The quality of the interpolation is comparable with the most efficient data interpolation currently available in image zooming. In our application, we compare the two DGT techniques with the spline interpolation applied to analyse Brodatz textural images