# Dense Depth Posterior (DDP) from Single Image and Sparse Range

arXiv: https://arxiv.org/abs/1901.10034 · HTML: https://mlsanity.com/paper/1901.10034/

## Key facts

- Cited by 57 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jan 2019.

## Built on by (most cited first, 30 of 57)

- [RigNet: Repetitive Image Guided Network for Depth Completion](https://mlsanity.com/paper/2107.13802/) (2021)
- [Unsupervised Depth Completion with Calibrated Backprojection Layers](https://mlsanity.com/paper/2108.10531/) (2021)
- [Bilateral Propagation Network for Depth Completion](https://mlsanity.com/paper/2403.11270/) (2024)
- [Depth Completion with Twin Surface Extrapolation at Occlusion Boundaries](https://mlsanity.com/paper/2104.02253/) (2021)
- [Learning Topology from Synthetic Data for Unsupervised Depth Completion](https://mlsanity.com/paper/2106.02994/) (2021)
- [WorDepth: Variational Language Prior for Monocular Depth Estimation](https://mlsanity.com/paper/2404.03635/) (2024)
- [Deep Depth Completion from Extremely Sparse Data: A Survey](https://mlsanity.com/paper/2205.05335/) (2022)
- [Not Just Streaks: Towards Ground Truth for Single Image Deraining](https://mlsanity.com/paper/2206.10779/) (2022)
- [An Adaptive Framework for Learning Unsupervised Depth Completion](https://mlsanity.com/paper/2106.03010/) (2021)
- [DesNet: Decomposed Scale-Consistent Network for Unsupervised Depth Completion](https://mlsanity.com/paper/2211.10994/) (2022)
- [Test-Time Adaptation for Depth Completion](https://mlsanity.com/paper/2402.03312/) (2024)
- [Monitored Distillation for Positive Congruent Depth Completion](https://mlsanity.com/paper/2203.16034/) (2022)
- [Bayesian Deep Basis Fitting for Depth Completion with Uncertainty](https://mlsanity.com/paper/2103.15254/) (2021)
- [ALTO: Alternating Latent Topologies for Implicit 3D Reconstruction](https://mlsanity.com/paper/2212.04096/) (2022)
- [RSA: Resolving Scale Ambiguities in Monocular Depth Estimators through Language Descriptions](https://mlsanity.com/paper/2410.02924/) (2024)
- [RadarCam-Depth: Radar-Camera Fusion for Depth Estimation with Learned Metric Scale](https://mlsanity.com/paper/2401.04325/) (2024)
- [A Surface Geometry Model for LiDAR Depth Completion](https://mlsanity.com/paper/2104.08466/) (2021)
- [Stereoscopic Universal Perturbations across Different Architectures and Datasets](https://mlsanity.com/paper/2112.06116/) (2021)
- [AugUndo: Scaling Up Augmentations for Monocular Depth Completion and Estimation](https://mlsanity.com/paper/2310.09739/) (2023)
- [Advancing Self-supervised Monocular Depth Learning with Sparse LiDAR](https://mlsanity.com/paper/2109.09628/) (2021)
- [Completion as Enhancement: A Degradation-Aware Selective Image Guided Network for Depth Completion](https://mlsanity.com/paper/2412.19225/) (2024)
- [Towards 3D Scene Reconstruction from Locally Scale-Aligned Monocular Video Depth](https://mlsanity.com/paper/2202.01470/) (2022)
- [RigNet++: Semantic Assisted Repetitive Image Guided Network for Depth Completion](https://mlsanity.com/paper/2309.00655/) (2023)
- [ProtoDepth: Unsupervised Continual Depth Completion with Prototypes](https://mlsanity.com/paper/2503.12745/) (2025)
- [Rapid Network Adaptation: Learning to Adapt Neural Networks Using Test-Time Feedback](https://mlsanity.com/paper/2309.15762/) (2023)
- [Distilling Diffusion Models to Efficient 3D LiDAR Scene Completion](https://mlsanity.com/paper/2412.03515/) (2024)
- [Simultaneous Acquisition of High Quality RGB Image and Polarization Information using a Sparse Polarization Sensor](https://mlsanity.com/paper/2209.13106/) (2022)
- [Clutter Detection and Removal in 3D Scenes with View-Consistent Inpainting](https://mlsanity.com/paper/2304.03763/) (2023)
- [Extending Foundational Monocular Depth Estimators to Fisheye Cameras with Calibration Tokens](https://mlsanity.com/paper/2508.04928/) (2025)
- [RGB Guided ToF Imaging System: A Survey of Deep Learning-based Methods](https://mlsanity.com/paper/2405.10357/) (2024)

## Abstract (arXiv)

We present a deep learning system to infer the posterior distribution of a dense depth map associated with an image, by exploiting sparse range measurements, for instance from a lidar. While the lidar may provide a depth value for a small percentage of the pixels, we exploit regularities reflected in the training set to complete the map so as to have a probability over depth for each pixel in the image. We exploit a Conditional Prior Network, that allows associating a probability to each depth value given an image, and combine it with a likelihood term that uses the sparse measurements. Optionally we can also exploit the availability of stereo during training, but in any case only require a single image and a sparse point cloud at run-time. We test our approach on both unsupervised and supervised depth completion using the KITTI benchmark, and improve the state-of-the-art in both.