  For a monocular 360 image, depth estimation is a challenging because the
distortion increases along the latitude. To perceive the distortion, existing
methods devote to designing a deep and complex network architecture. In this
paper, we provide a new perspective that constructs an interpretable and sparse
representation for a 360 image. Considering the importance of the geometric
structure in depth estimation, we utilize the contourlet transform to capture
an explicit geometric cue in the spectral domain and integrate it with an
implicit cue in the spatial domain. Specifically, we propose a neural
contourlet network consisting of a convolutional neural network and a
contourlet transform branch. In the encoder stage, we design a spatial-spectral
fusion module to effectively fuse two types of cues. Contrary to the encoder,
we employ the inverse contourlet transform with learned low-pass subbands and
band-pass directional subbands to compose the depth in the decoder. Experiments
on the three popular panoramic image datasets demonstrate that the proposed
approach outperforms the state-of-the-art schemes with faster convergence. Code
is available at
https://github.com/zhijieshen-bjtu/Neural-Contourlet-Network-for-MODE.
