  We consider the case of inpainting single depth images. Without corresponding
color images, previous or next frames, depth image inpainting is quite
challenging. One natural solution is to regard the image as a matrix and adopt
the low rank regularization just as inpainting color images. However, the low
rank assumption does not make full use of the properties of depth images.
  A shallow observation may inspire us to penalize the non-zero gradients by
sparse gradient regularization. However, statistics show that though most
pixels have zero gradients, there is still a non-ignorable part of pixels whose
gradients are equal to 1. Based on this specific property of depth images , we
propose a low gradient regularization method in which we reduce the penalty for
gradient 1 while penalizing the non-zero gradients to allow for gradual depth
changes. The proposed low gradient regularization is integrated with the low
rank regularization into the low rank low gradient approach for depth image
inpainting. We compare our proposed low gradient regularization with sparse
gradient regularization. The experimental results show the effectiveness of our
proposed approach.
