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In this paper, we propose a novel depth upsampling method by residual interpolation (RI) that uses both a low-resolution depth map and a high-resolution intensity image. Our method is an application of the RI to depth upsampling, where the upsampling is performed in a residual domain following its success in the field of image demosaicking. Experimental results demonstrate that our method preserves the sharpness of depth discontinuities and outperforms existing well-known methods such as joint bilateral upsampling and guided filtering.