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Full resolution depth is required in many realworld engineering applications. However, exist depth sensorsonly offer sparse depth sample points with limited resolutionand noise, e.g., LiDARs. We here propose a deep learningbased full resolution depth recovery method from monocularimages and corresponding sparse depth measurements of targetenvironment. The novelty of our idea is that the structure similarinformation between the RGB image and depth image is used torefine the dense depth estimation result. This important similarstructure information can be found using a correlation layerin the regression neural network. We show that the proposedmethod can achieve higher estimation accuracy compared tothe state of the art methods. The experiments conducted on theNYU Depth V2 prove the novelty of our idea.