Faber-Schauder wavelet transform, application to edge detection and image characterization

The Faber-Schauder wavelet transform is a simple multiscale transformation with many interesting properties in image processing. Some of these propert ies are: preservation of pixel ranges, arithmetic operations, non requireme nt of boundary processing, multiscale edge detection, elimination of the co nstant and the linear correlation, and the use of close neighboring informa tion. In this study we describe this transformation and we propose a mixed scale visualization of the wavelet transform which makes it possible to sho w the transform result as an image. This visualization is used, with orient ation information, to refine edge detection and image characterization by s electing regions with a high density of extrema wavelet coefficients.