Depth estimation is an essential component in understanding the 3D geometry
of a scene, with numerous applications in urban and indoor settings. These
scenes are characterized by a prevalence of human made structures, which in
most of the cases, are either inherently piece-wise planar, or can be
approximated as such. In these settings, we devise a novel depth refinement
framework that aims at recovering the underlying piece-wise planarity of the
inverse depth map. We formulate this task as an optimization problem involving
a data fidelity term that minimizes the distance to the input inverse depth
map, as well as a regularization that enforces a piece-wise planar solution. As
for the regularization term, we model the inverse depth map as a weighted graph
between pixels. The proposed regularization is designed to estimate a plane
automatically at each pixel, without any need for an a priori estimation of the
scene planes, and at the same time it encourages similar pixels to be assigned
to the same plane. The resulting optimization problem is efficiently solved
with ADAM algorithm. Experiments show that our method leads to a significant
improvement in depth refinement, both visually and numerically, with respect to
state-of-the-art algorithms on Middlebury, KITTI and ETH3D multi-view stereo
datasets.

本文提出了一种新颖的深度细化框架，旨在恢复逆深度图的分段平面特征，该框架将逆深度图建模为像素之间的加权图，设计了一种自动估计每个像素平面的正则化项，经过实验证明，该方法在视觉和数值上均相对于 Middlebury、KITTI 和 ETH3D 多视角立体数据集上的最先进算法有重大改进。