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Multiview color information used jointly with depth maps is a widespread technique for 3D video. Using this depth information, 3D functionalities such as free view point video can be provided by means of depth-image-based rendering techniques. In this paper, a new technique to encode depth maps is proposed. Based on the usually smooth structure and the sharp edges of depth map, our proposal segments the depth map into homogeneous regions of arbitrary shape and encodes the contents of these regions using different texture coding strategies. An optimal lagrangian approach is applied to the hierarchical region representation provided by our segmentation technique. This approach automatically selects the best encoding strategy for each region and the optimal partition to encode the depth map. To avoid the high coding costs of coding the resulting partition, a prediction is made using the associated decoded color image.