  We consider the problem of depth estimation from a single monocular image in
this work. It is a challenging task as no reliable depth cues are available,
e.g., stereo correspondences, motions, etc. Previous efforts have been focusing
on exploiting geometric priors or additional sources of information, with all
using hand-crafted features. Recently, there is mounting evidence that features
from deep convolutional neural networks (CNN) are setting new records for
various vision applications. On the other hand, considering the continuous
characteristic of the depth values, depth estimations can be naturally
formulated into a continuous conditional random field (CRF) learning problem.
Therefore, we in this paper present a deep convolutional neural field model for
estimating depths from a single image, aiming to jointly explore the capacity
of deep CNN and continuous CRF. Specifically, we propose a deep structured
learning scheme which learns the unary and pairwise potentials of continuous
CRF in a unified deep CNN framework.
  The proposed method can be used for depth estimations of general scenes with
no geometric priors nor any extra information injected. In our case, the
integral of the partition function can be analytically calculated, thus we can
exactly solve the log-likelihood optimization. Moreover, solving the MAP
problem for predicting depths of a new image is highly efficient as closed-form
solutions exist. We experimentally demonstrate that the proposed method
outperforms state-of-the-art depth estimation methods on both indoor and
outdoor scene datasets.
