# Neural Contourlet Network for Monocular 360 Depth Estimation

arXiv: https://arxiv.org/abs/2208.01817 · HTML: https://mlsanity.com/paper/2208.01817/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 44 references that are in the map.
- First posted on arXiv 3 Aug 2022.

## Builds on (most cited first, 29 of 29)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Non-local Neural Networks](https://mlsanity.com/paper/1711.07971/) (2017)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [Matterport3D: Learning from RGB-D Data in Indoor Environments](https://mlsanity.com/paper/1709.06158/) (2017)
- [Semantic Image Segmentation with Deep Convolutional Nets and Fully Connected CRFs](https://mlsanity.com/paper/1412.7062/) (2014)
- [Gibson Env: Real-World Perception for Embodied Agents](https://mlsanity.com/paper/1808.10654/) (2018)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [Joint 2D-3D-Semantic Data for Indoor Scene Understanding](https://mlsanity.com/paper/1702.01105/) (2017)
- [Deeper Depth Prediction with Fully Convolutional Residual Networks](https://mlsanity.com/paper/1606.00373/) (2016)
- [Rethinking ImageNet Pre-training](https://mlsanity.com/paper/1811.08883/) (2018)
- [Structured3D: A Large Photo-realistic Dataset for Structured 3D Modeling](https://mlsanity.com/paper/1908.00222/) (2019)
- [CondenseNet: An Efficient DenseNet using Learned Group Convolutions](https://mlsanity.com/paper/1711.09224/) (2017)
- [HoHoNet: 360 Indoor Holistic Understanding with Latent Horizontal Features](https://mlsanity.com/paper/2011.11498/) (2020)
- [OmniDepth: Dense Depth Estimation for Indoors Spherical Panoramas](https://mlsanity.com/paper/1807.09620/) (2018)
- [UniFuse: Unidirectional Fusion for 360circ Panorama Depth Estimation](https://mlsanity.com/paper/2102.03550/) (2021)
- [How do neural networks see depth in single images?](https://mlsanity.com/paper/1905.07005/) (2019)
- [Tangent Images for Mitigating Spherical Distortion](https://mlsanity.com/paper/1912.09390/) (2019)
- [Wavelet Integrated CNNs for Noise-Robust Image Classification](https://mlsanity.com/paper/2005.03337/) (2020)
- [Corners for Layout: End-to-End Layout Recovery from 360 Images](https://mlsanity.com/paper/1903.08094/) (2019)
- [Pano3D: A Holistic Benchmark and a Solid Baseline for 360o Depth Estimation](https://mlsanity.com/paper/2109.02749/) (2021)
- [Single Image Depth Prediction with Wavelet Decomposition](https://mlsanity.com/paper/2106.02022/) (2021)
- [Wavelet Domain Style Transfer for an Effective Perception-distortion Tradeoff in Single Image Super-Resolution](https://mlsanity.com/paper/1910.04074/) (2019)
- [S2R-DepthNet: Learning a Generalizable Depth-specific Structural Representation](https://mlsanity.com/paper/2104.00877/) (2021)
- [Distortion-aware Monocular Depth Estimation for Omnidirectional Images](https://mlsanity.com/paper/2010.08942/) (2020)
- [Monocular Depth Estimation with Augmented Ordinal Depth Relationships](https://mlsanity.com/paper/1806.00585/) (2018)
- [Mapped Convolutions](https://mlsanity.com/paper/1906.11096/) (2019)
- [Towards Interpretable Deep Networks for Monocular Depth Estimation](https://mlsanity.com/paper/2108.05312/) (2021)
- [Distortion-Tolerant Monocular Depth Estimation On Omnidirectional Images Using Dual-cubemap](https://mlsanity.com/paper/2203.09733/) (2022)
- [Monocular Spherical Depth Estimation with Explicitly Connected Weak Layout Cues](https://mlsanity.com/paper/2206.11358/) (2022)

## Built on by (most cited first, 3 of 3)

- [SGFormer: Spherical Geometry Transformer for 360 Depth Estimation](https://mlsanity.com/paper/2404.14979/) (2024)
- [SphereFusion: Efficient Panorama Depth Estimation via Gated Fusion](https://mlsanity.com/paper/2502.05859/) (2025)
- [Monocular Depth Estimation From the Perspective of Feature Restoration: A Diffusion Enhanced Depth Restoration Approach](https://mlsanity.com/paper/2604.07664/) (2026)

## Abstract (arXiv)

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.