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This paper studies the lossless compression of depth images realized by first transmitting contours of suitably chosen regions and subsequently performing predictive coding inside each region and transmitting the prediction residuals. For the large constant depth regions only the contour needs to be transmitted along with the value of the depth inside each region, while for the rest of the image we find suitable regions where the local variation of the depth level from one pixel to another is constrained above. The nonlinear predictors used for each region combine the results of several linear predictors, each fitting optimally a subset of pixels belonging to the local neighborhood. Overall the obtained results exceed by a wide margin the performance of standard image compression algorithms.