  In this paper we propose a method for estimating depth from a single image
using a coarse to fine approach. We argue that modeling the fine depth details
is easier after a coarse depth map has been computed. We express a global
(coarse) depth map of an image as a linear combination of a depth basis learned
from training examples. The depth basis captures spatial and statistical
regularities and reduces the problem of global depth estimation to the task of
predicting the input-specific coefficients in the linear combination. This is
formulated as a regression problem from a holistic representation of the image.
Crucially, the depth basis and the regression function are {\bf coupled} and
jointly optimized by our learning scheme. We demonstrate that this results in a
significant improvement in accuracy compared to direct regression of depth
pixel values or approaches learning the depth basis disjointly from the
regression function. The global depth estimate is then used as a guidance by a
local refinement method that introduces depth details that were not captured at
the global level. Experiments on the NYUv2 and KITTI datasets show that our
method outperforms the existing state-of-the-art at a considerably lower
computational cost for both training and testing.
