Modelling textured images as AM-FM functions has been applied during the last years to texture analysis and segmentation tasks. In this paper we present some advances in two directions, namely the improvement of modulation feature extraction and texture vs. non texture discrimination. First we present a modified dominant AM-FM component analysis scheme based on non-linear energy operators. Subsequently we propose a novel approach to the discrimination between textured and non-textured image areas using multiband filter responses which is formulated as a statistical multiple hypothesis testing problem. The theoretical insights of this approach are supported by experimental validation using natural images.