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In this paper, a new solution is introduced for the efficient compression of 3D video based on color and depth maps. While standard video codecs are designed for coding monoscopic videos, their application to depth maps is found to be suboptimal. With regard to the special properties of the depth maps, we propose an extension to conventional video coding in order to take advantage of object motion in the depth direction. Instead of performing a 2D motion search, as is common in conventional video codecs, we propose the use of a 3D motion search that is able to better exploit the temporal correlations of 3D content. In this new framework, the motion of blocks in depth maps are described using 3D motion vectors (x, y, z), representing the horizontal, vertical, and depth directions respectively. This leads to more accurate motion prediction and a smaller residual. The experimental results show that the proposed technique delivers an improvement in motion compensation, which leads to gains in compression efficiency.