  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.
