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This paper introduces an efficient method for lossless compression of depth map images, using the representation of a depth image in terms of three entities: 1) the crack-edges; 2) the constant depth regions enclosed by them; and 3) the depth value over each region. The starting representation is identical with that used in a very efficient coder for palette images, the piecewise-constant image model coding, but the techniques used for coding the elements of the representation are more advanced and especially suitable for the type of redundancy present in depth images. Initially, the vertical and horizontal crack-edges separating the constant depth regions are transmitted by 2D context coding using optimally pruned context trees. Both the encoder and decoder can reconstruct the regions of constant depth from the transmitted crack-edge image. The depth value in a given region is encoded using the depth values of the neighboring regions already encoded, exploiting the natural smoothness of the depth variation, and the mutual exclusiveness of the values in neighboring regions. The encoding method is suitable for lossless compression of depth images, obtaining compression of about 10-65 times, and additionally can be used as the entropy coding stage for lossy depth compression.