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 properties are: preservation of pixel ranges, arithmetic operations, non requirement of boundary processing, multiscale edge detection, elimination of the constant and the linear correlation, and the use of close neighboring information. In this study we describe this transformation and we propose a mixed scale visualization of the wavelet transform which makes it possible to show the transform result as an image. This visualization is used, with orientation information, to refine edge detection and image characterization by selecting regions with a high density of extrema wavelet coefficients.