# Hierarchical Normalization for Robust Monocular Depth Estimation

arXiv: https://arxiv.org/abs/2210.09670 · HTML: https://mlsanity.com/paper/2210.09670/

## Key facts

- Cited by 52 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 49 references that are in the map.
- First posted on arXiv 18 Oct 2022.

## Builds on (most cited first, 30 of 35)

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [ScanNet: Richly-annotated 3D Reconstructions of Indoor Scenes](https://mlsanity.com/paper/1702.04405/) (2017)
- [Pyramid Scene Parsing Network](https://mlsanity.com/paper/1612.01105/) (2016)
- [RAFT: Recurrent All-Pairs Field Transforms for Optical Flow](https://mlsanity.com/paper/2003.12039/) (2020)
- [Arbitrary Style Transfer in Real-time with Adaptive Instance Normalization](https://mlsanity.com/paper/1703.06868/) (2017)
- [Vision Transformers for Dense Prediction](https://mlsanity.com/paper/2103.13413/) (2021)
- [Towards Robust Monocular Depth Estimation: Mixing Datasets for Zero-shot Cross-dataset Transfer](https://mlsanity.com/paper/1907.01341/) (2019)
- [Semantic Image Synthesis with Spatially-Adaptive Normalization](https://mlsanity.com/paper/1903.07291/) (2019)
- [Depth Map Prediction from a Single Image using a Multi-Scale Deep Network](https://mlsanity.com/paper/1406.2283/) (2014)
- [Instance Normalization: The Missing Ingredient for Fast Stylization](https://mlsanity.com/paper/1607.08022/) (2016)
- [Unsupervised Learning of Depth and Ego-Motion from Video](https://mlsanity.com/paper/1704.07813/) (2017)
- [MegaDepth: Learning Single-View Depth Prediction from Internet Photos](https://mlsanity.com/paper/1804.00607/) (2018)
- [Taskonomy: Disentangling Task Transfer Learning](https://mlsanity.com/paper/1804.08328/) (2018)
- [From Big to Small: Multi-Scale Local Planar Guidance for Monocular Depth Estimation](https://mlsanity.com/paper/1907.10326/) (2019)
- [Virtual Worlds as Proxy for Multi-Object Tracking Analysis](https://mlsanity.com/paper/1605.06457/) (2016)
- [GA-Net: Guided Aggregation Net for End-to-end Stereo Matching](https://mlsanity.com/paper/1904.06587/) (2019)
- [Unsupervised Scale-consistent Depth and Ego-motion Learning from Monocular Video](https://mlsanity.com/paper/1908.10553/) (2019)
- [DIODE: A Dense Indoor and Outdoor DEpth Dataset](https://mlsanity.com/paper/1908.00463/) (2019)
- [Enforcing geometric constraints of virtual normal for depth prediction](https://mlsanity.com/paper/1907.12209/) (2019)
- [CANet: Class-Agnostic Segmentation Networks with Iterative Refinement and Attentive Few-Shot Learning](https://mlsanity.com/paper/1903.02351/) (2019)
- [Learning to Recover 3D Scene Shape from a Single Image](https://mlsanity.com/paper/2012.09365/) (2020)
- [Single-Image Depth Perception in the Wild](https://mlsanity.com/paper/1604.03901/) (2016)
- [Feature-metric Loss for Self-supervised Learning of Depth and Egomotion](https://mlsanity.com/paper/2007.10603/) (2020)
- [Evaluation of CNN-based Single-Image Depth Estimation Methods](https://mlsanity.com/paper/1805.01328/) (2018)
- [Robust Learning Through Cross-Task Consistency](https://mlsanity.com/paper/2006.04096/) (2020)
- [Web Stereo Video Supervision for Depth Prediction from Dynamic Scenes](https://mlsanity.com/paper/1904.11112/) (2019)
- [OASIS: A Large-Scale Dataset for Single Image 3D in the Wild](https://mlsanity.com/paper/2007.13215/) (2020)
- [DeepEMD: Differentiable Earth Mover's Distance for Few-Shot Learning](https://mlsanity.com/paper/2003.06777/) (2020)
- [Virtual Normal: Enforcing Geometric Constraints for Accurate and Robust Depth Prediction](https://mlsanity.com/paper/2103.04216/) (2021)
- [Towards Accurate Reconstruction of 3D Scene Shape from A Single Monocular Image](https://mlsanity.com/paper/2208.13241/) (2022)

## Built on by (most cited first, 30 of 52)

- [Metric3Dv2: A Versatile Monocular Geometric Foundation Model for Zero-shot Metric Depth and Surface Normal Estimation](https://mlsanity.com/paper/2404.15506/) (2024)
- [Metric3D: Towards Zero-shot Metric 3D Prediction from A Single Image](https://mlsanity.com/paper/2307.10984/) (2023)
- [Repurposing Diffusion-Based Image Generators for Monocular Depth Estimation](https://mlsanity.com/paper/2312.02145/) (2023)
- [GeoWizard: Unleashing the Diffusion Priors for 3D Geometry Estimation from a Single Image](https://mlsanity.com/paper/2403.12013/) (2024)
- [DNGaussian: Optimizing Sparse-View 3D Gaussian Radiance Fields with Global-Local Depth Normalization](https://mlsanity.com/paper/2403.06912/) (2024)
- [Lotus: Diffusion-based Visual Foundation Model for High-quality Dense Prediction](https://mlsanity.com/paper/2409.18124/) (2024)
- [Learning Temporally Consistent Video Depth from Video Diffusion Priors](https://mlsanity.com/paper/2406.01493/) (2024)
- [Fine-Tuning Image-Conditional Diffusion Models is Easier than You Think](https://mlsanity.com/paper/2409.11355/) (2024)
- [Marigold: Affordable Adaptation of Diffusion-Based Image Generators for Image Analysis](https://mlsanity.com/paper/2505.09358/) (2025)
- [DepthFM: Fast Monocular Depth Estimation with Flow Matching](https://mlsanity.com/paper/2403.13788/) (2024)
- [What Matters When Repurposing Diffusion Models for General Dense Perception Tasks?](https://mlsanity.com/paper/2403.06090/) (2024)
- [Depth Any Video with Scalable Synthetic Data](https://mlsanity.com/paper/2410.10815/) (2024)
- [Pixel-Perfect Depth with Semantics-Prompted Diffusion Transformers](https://mlsanity.com/paper/2510.07316/) (2025)
- [RoboDepth: Robust Out-of-Distribution Depth Estimation under Corruptions](https://mlsanity.com/paper/2310.15171/) (2023)
- [One Diffusion to Generate Them All](https://mlsanity.com/paper/2411.16318/) (2024)
- [LBM: Latent Bridge Matching for Fast Image-to-Image Translation](https://mlsanity.com/paper/2503.07535/) (2025)
- [BetterDepth: Plug-and-Play Diffusion Refiner for Zero-Shot Monocular Depth Estimation](https://mlsanity.com/paper/2407.17952/) (2024)
- [DepthLab: From Partial to Complete](https://mlsanity.com/paper/2412.18153/) (2024)
- [Flowing from Words to Pixels: A Noise-Free Framework for Cross-Modality Evolution](https://mlsanity.com/paper/2412.15213/) (2024)
- [StyleAvatar3D: Leveraging Image-Text Diffusion Models for High-Fidelity 3D Avatar Generation](https://mlsanity.com/paper/2305.19012/) (2023)
- [DaRF: Boosting Radiance Fields from Sparse Inputs with Monocular Depth Adaptation](https://mlsanity.com/paper/2305.19201/) (2023)
- [RSA: Resolving Scale Ambiguities in Monocular Depth Estimators through Language Descriptions](https://mlsanity.com/paper/2410.02924/) (2024)
- [DepthMaster: Taming Diffusion Models for Monocular Depth Estimation](https://mlsanity.com/paper/2501.02576/) (2025)
- [Distill Any Depth: Distillation Creates a Stronger Monocular Depth Estimator](https://mlsanity.com/paper/2502.19204/) (2025)
- [PrimeDepth: Efficient Monocular Depth Estimation with a Stable Diffusion Preimage](https://mlsanity.com/paper/2409.09144/) (2024)
- [Buffer Anytime: Zero-Shot Video Depth and Normal from Image Priors](https://mlsanity.com/paper/2411.17249/) (2024)
- [The Third Monocular Depth Estimation Challenge](https://mlsanity.com/paper/2404.16831/) (2024)
- [Boost 3D Reconstruction using Diffusion-based Monocular Camera Calibration](https://mlsanity.com/paper/2411.17240/) (2024)
- [QuartDepth: Post-Training Quantization for Real-Time Depth Estimation on the Edge](https://mlsanity.com/paper/2503.16709/) (2025)
- [The Fourth Monocular Depth Estimation Challenge](https://mlsanity.com/paper/2504.17787/) (2025)

## Abstract (arXiv)

In this paper, we address monocular depth estimation with deep neural networks. To enable training of deep monocular estimation models with various sources of datasets, state-of-the-art methods adopt image-level normalization strategies to generate affine-invariant depth representations. However, learning with image-level normalization mainly emphasizes the relations of pixel representations with the global statistic in the images, such as the structure of the scene, while the fine-grained depth difference may be overlooked. In this paper, we propose a novel multi-scale depth normalization method that hierarchically normalizes the depth representations based on spatial information and depth distributions. Compared with previous normalization strategies applied only at the holistic image level, the proposed hierarchical normalization can effectively preserve the fine-grained details and improve accuracy. We present two strategies that define the hierarchical normalization contexts in the depth domain and the spatial domain, respectively. Our extensive experiments show that the proposed normalization strategy remarkably outperforms previous normalization methods, and we set new state-of-the-art on five zero-shot transfer benchmark datasets.