In this paper, we propose a new global geometry constraint for depth completion. By assuming depth maps often lay on low dimensional subspaces, a dense depth map can be approximated by a weighted sum of full-resolution principal depth bases. The principal components of depth fields can be learned from natural depth maps. The given sparse depth points are served as a data term to constrain the weighting process. When the input depth points are too sparse, the recovered dense depth maps are often over smoothed. To address this issue, we add a colour-guided auto-regression model as another regularization term. It assumes the reconstructed depth maps should share the same nonlocal similarity in the accompanying colour image. Our colour-guided PCA depth completion method has closed-form solutions, thus can be efficiently solved and is significantly more accurate than PCA only method. Extensive experiments on KITTI and Middlebury datasets demonstrate the superior performance of our proposed method.
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