New statistical textural transforms for non-stationary signals; Application to generalized multifractal analysis

We introduce a method to generate statistical textural transforms that improves the treatment of non-stationarity and leads to a sharper detection of the boundaries between distinct textures (texture segmentation). This method is based on a sliding window processing with fixed size. The basic idea proposed by the authors is to readjust the measuring window around each pixel so as to maximize homogeneity. We use this method with the dimensions D-n(q) that are derived from the Generalized Multifractal Analysis formalism to show that the D-n(q)s can detect and quantify departures from multifractality, while providing the analogue of the classical generalized dimension if the measure is multifractal.