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We present an algorithm to synthetically increase the resolution of a solitary depth image using only a generic database of local patches. Modern range sensors measure depths with non-Gaussian noise and at lower starting resolutions than typical visible-light cameras. While patch based approaches for upsampling intensity images continue to improve, this is the first exploration of patching for depth images. We match against the height field of each low resolution input depth patch, and search our database for a list of appropriate high resolution candidate patches. Selecting the right candidate at each location in the depth image is then posed as a Markov random field labeling problem. Our experiments also show how important further depth-specific processing, such as noise removal and correct patch normalization, dramatically improves our results. Perhaps surprisingly, even better results are achieved on a variety of real test scenes by providing our algorithm with only synthetic training depth data.