  Monocular 360 depth estimation is challenging due to the inherent distortion
of the equirectangular projection (ERP). This distortion causes a problem:
spherical adjacent points are separated after being projected to the ERP plane,
particularly in the polar regions. To tackle this problem, recent methods
calculate the spherical neighbors in the tangent domain. However, as the
tangent patch and sphere only have one common point, these methods construct
neighboring spherical relationships around the common point. In this paper, we
propose spherical fully-connected CRFs (SF-CRFs). We begin by evenly
partitioning an ERP image with regular windows, where windows at the equator
involve broader spherical neighbors than those at the poles. To improve the
spherical relationships, our SF-CRFs enjoy two key components. Firstly, to
involve sufficient spherical neighbors, we propose a Spherical Window Transform
(SWT) module. This module aims to replicate the equator window's spherical
relationships to all other windows, leveraging the rotational invariance of the
sphere. Remarkably, the transformation process is highly efficient, completing
the transformation of all windows in a 512X1024 ERP with 0.038 seconds on CPU.
Secondly, we propose a Planar-Spherical Interaction (PSI) module to facilitate
the relationships between regular and transformed windows, which not only
preserves the local details but also captures global structures. By building a
decoder based on the SF-CRFs blocks, we propose CRF360D, a novel 360 depth
estimation framework that achieves state-of-the-art performance across diverse
datasets. Our CRF360D is compatible with different perspective image-trained
backbones (e.g., EfficientNet), serving as the encoder.
