Multiscale Transforms for Region-based Texture Segmentation

In this paper we propose a rigorous and elegant framework for texture image segmentation relying on region-based active contours (RBAC), shape derivative tools and multiscale geometrical texture representations. After transforming the texture in a dictionary of appropriate waveforms (atoms), the obtained transform coefficients are intended to efficiently capture the essential spectral and geometrical contents of the texture, and to allow to discriminate it from other textures. Hence, to measure the dissimilarity between two different textures, we use a divergence between the non-parametric kernel density estimates of the probability density functions (PDFs) of their respective transform coefficients. The divergence measure is then either minimized (supervised segmentation) or maximized (unsupervised) after appropriately incorporating it within an RBAC variational functional. The functional is then optimized by taking benefit from shape derivative tools to derive the evolution equation of the active contour. Our framework is applied to both supervised (with exemplar reference textures), and unsupervised texture segmentation. A series of experiments on synthetic and real images are reported to illustrate the versatility and applicability of our approach.