Self-supervised learning for monocular depth estimation is widely investigated as an alternative to supervised learning approach, that requires a lot of ground truths. Previous works have successfully improved the accuracy of depth estimation by modifying the model structure, adding objectives, and masking dynamic objects and occluded area. However, when using such estimated depth image in applications, such as autonomous vehicles, and robots, we have to uniformly believe the estimated depth at each pixel position. This could lead to fatal errors in performing the tasks, because estimated depth at some pixels may make a bigger mistake. In this paper, we theoretically formulate a variational model for the monocular depth estimation to predict the reliability of the estimated depth image. Based on the results, we can exclude the estimated depths with low reliability or refine them for actual use. The effectiveness of the proposed method is quantitatively and qualitatively demonstrated using the KITTI benchmark and Make3D dataset.
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