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We propose a novel unsupervised region based criterion for multi-class texture segmentation. The proposed criterion relies on the maximization of a weighted sum of Kullback-Leibler measure between distributions of local texture features associated to the different image regions. Hence, the segmentation issue is stated as the maximization of the proposed criterion and a regularization term that imposes smoothness and regularity of region boundaries. The proposed approach is based on curve evolution techniques and is implemented using level-set methods. Curve evolution equations are expressed using shape derivative tools. As an application, we have tested the method using cooccurrence distributions, distributions of Gabor filter responses and wavelet packet to segment synthetic mosaics of textures from the Brodatz album, as well as real textured sonar images.