  Depth maps captured by modern depth cameras such as Kinect and Time-of-Flight
(ToF) are usually contaminated by missing data, noises and suffer from being of
low resolution. In this paper, we present a robust method for high-quality
restoration of a degraded depth map with the guidance of the corresponding
color image. We solve the problem in an energy optimization framework that
consists of a novel robust data term and smoothness term. To accommodate not
only the noise but also the inconsistency between depth discontinuities and the
color edges, we model both the data term and smoothness term with a robust
exponential error norm function. We propose to use Iteratively Re-weighted
Least Squares (IRLS) methods for efficiently solving the resulting highly
non-convex optimization problem. More importantly, we further develop a
data-driven adaptive parameter selection scheme to properly determine the
parameter in the model. We show that the proposed approach can preserve fine
details and sharp depth discontinuities even for a large upsampling factor
($8\times$ for example). Experimental results on both simulated and real
datasets demonstrate that the proposed method outperforms recent
state-of-the-art methods in coping with the heavy noise, preserving sharp depth
discontinuities and suppressing the texture copy artifacts.
