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This paper presents a lossy coding method for depth images using a segmentation constructed by selecting regions of pixels having the depth values obeying constraints defined in terms of some bounds, which are tuned in order to obtain the target distortion. The contours describing the segmentation are transmitted using an efficient chain coding method and are thus available also at the decoder for the next stage, which is region based predictive coding with a tunable precision level. The rate comprises the cost of losslessly transmission of the contours and the cost of transmitting the residuals with the decided precision, which is the main factor influencing the distortion. We introduce a procedure optimizing the parameters involved in the segmentation and in the prediction for a given image. As a side result, the segmentations residing on the convex hull of the RD curve can be seen as optimal segmentations with various granularity.