A supervised classification model based on a variational approach is presented. This model is specifically devoted to textured images. We want to get a partition of an image, composed of texture regions separated by regular interfaces. Each kind of texture defines a class. We use a wavelet packet transform to analyze the textures, characterized by their energy distribution in each sub-band. In order to have an image segmentation according to the classes, we model the regions and their interfaces by level set functions. We define a functional on these level sets whose minimizers define the optimal classification according to textures. A system of coupled PDEs is deduced from the functional. By solving this system, each region evolves according to its wavelet coefficients and interacts with the neighbour region in order to obtain a partition with regular contours. Experiments are shown on synthetic and real images.