# Predicting High-precision Depth on Low-Precision Devices Using 2D Hilbert Curves

arXiv: https://arxiv.org/abs/2405.14024 · HTML: https://mlsanity.com/paper/2405.14024/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 40 of its 61 references that are in the map.
- First posted on arXiv 22 May 2024.

## Builds on (most cited first, 30 of 40)

- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [ScanNet: Richly-annotated 3D Reconstructions of Indoor Scenes](https://mlsanity.com/paper/1702.04405/) (2017)
- [BEiT: BERT Pre-Training of Image Transformers](https://mlsanity.com/paper/2106.08254/) (2021)
- [Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inference](https://mlsanity.com/paper/1712.05877/) (2017)
- [Depth Anything: Unleashing the Power of Large-Scale Unlabeled Data](https://mlsanity.com/paper/2401.10891/) (2024)
- [Depth Map Prediction from a Single Image using a Multi-Scale Deep Network](https://mlsanity.com/paper/1406.2283/) (2014)
- [A Large Dataset to Train Convolutional Networks for Disparity, Optical Flow, and Scene Flow Estimation](https://mlsanity.com/paper/1512.02134/) (2015)
- [ScanNet++: A High-Fidelity Dataset of 3D Indoor Scenes](https://mlsanity.com/paper/2308.11417/) (2023)
- [Open3D: A Modern Library for 3D Data Processing](https://mlsanity.com/paper/1801.09847/) (2018)
- [Simple Baselines for Human Pose Estimation and Tracking](https://mlsanity.com/paper/1804.06208/) (2018)
- [A White Paper on Neural Network Quantization](https://mlsanity.com/paper/2106.08295/) (2021)
- [Pseudo-LiDAR from Visual Depth Estimation: Bridging the Gap in 3D Object Detection for Autonomous Driving](https://mlsanity.com/paper/1812.07179/) (2018)
- [HAQ: Hardware-Aware Automated Quantization with Mixed Precision](https://mlsanity.com/paper/1811.08886/) (2018)
- [Virtual KITTI 2](https://mlsanity.com/paper/2001.10773/) (2020)
- [RAFT-Stereo: Multilevel Recurrent Field Transforms for Stereo Matching](https://mlsanity.com/paper/2109.07547/) (2021)
- [Repurposing Diffusion-Based Image Generators for Monocular Depth Estimation](https://mlsanity.com/paper/2312.02145/) (2023)
- [DeepPose: Human Pose Estimation via Deep Neural Networks](https://mlsanity.com/paper/1312.4659/) (2013)
- [Iterative Geometry Encoding Volume for Stereo Matching](https://mlsanity.com/paper/2303.06615/) (2023)
- [LSQ+: Improving low-bit quantization through learnable offsets and better initialization](https://mlsanity.com/paper/2004.09576/) (2020)
- [Pseudo-LiDAR++: Accurate Depth for 3D Object Detection in Autonomous Driving](https://mlsanity.com/paper/1906.06310/) (2019)
- [PTQ4ViT: Post-training quantization for vision transformers with twin uniform quantization](https://mlsanity.com/paper/2111.12293/) (2021)
- [Revisiting ResNets: Improved Training and Scaling Strategies](https://mlsanity.com/paper/2103.07579/) (2021)
- [Quantization Networks](https://mlsanity.com/paper/1911.09464/) (2019)
- [Delving Deeper into Convolutional Networks for Learning Video Representations](https://mlsanity.com/paper/1511.06432/) (2015)
- [Revisiting Single Image Depth Estimation: Toward Higher Resolution Maps with Accurate Object Boundaries](https://mlsanity.com/paper/1803.08673/) (2018)
- [APQ: Joint Search for Network Architecture, Pruning and Quantization Policy](https://mlsanity.com/paper/2006.08509/) (2020)
- [Selective-Stereo: Adaptive Frequency Information Selection for Stereo Matching](https://mlsanity.com/paper/2403.00486/) (2024)
- [FastDepth: Fast Monocular Depth Estimation on Embedded Systems](https://mlsanity.com/paper/1903.03273/) (2019)
- [Post-Training Piecewise Linear Quantization for Deep Neural Networks](https://mlsanity.com/paper/2002.00104/) (2020)

## Abstract (arXiv)

Dense depth prediction deep neural networks (DNN) have achieved impressive results for both monocular and binocular data, but still they are limited by high computational complexity, restricting their use on low-end devices. For better on-device efficiency and hardware utilization, weights and activations of the DNN should be converted to low-bit precision. However, this precision is not sufficient to represent high dynamic range depth. In this paper, we aim to overcome this limitation and restore high-precision depth from low-bit precision predictions. To achieve this, we propose to represent high dynamic range depth as two low dynamic range components of a Hilbert curve, and to train the full-precision DNN to directly predict the latter. For on-device deployment, we use standard quantization methods and add a post-processing step that reconstructs depth from the Hilbert curve components predicted in low-bit precision. Extensive experiments demonstrate that our method increases the bit precision of predicted depth by up to three bits with little computational overhead. We also observed a positive side effect of quantization error reduction by up to 4.6 times. Our method enables effective and accurate depth prediction with DNN weights and activations quantized to eight-bit precision.