# Bayesian Deep Basis Fitting for Depth Completion with Uncertainty

arXiv: https://arxiv.org/abs/2103.15254 · HTML: https://mlsanity.com/paper/2103.15254/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 50 of its 78 references that are in the map.
- First posted on arXiv 29 Mar 2021.

## Builds on (most cited first, 30 of 50)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Depth Map Prediction from a Single Image using a Multi-Scale Deep Network](https://mlsanity.com/paper/1406.2283/) (2014)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Virtual KITTI 2](https://mlsanity.com/paper/2001.10773/) (2020)
- [Snapshot Ensembles: Train 1, get M for free](https://mlsanity.com/paper/1704.00109/) (2017)
- [Virtual Worlds as Proxy for Multi-Object Tracking Analysis](https://mlsanity.com/paper/1605.06457/) (2016)
- [Sparsity Invariant CNNs](https://mlsanity.com/paper/1708.06500/) (2017)
- [Scalable Bayesian Optimization Using Deep Neural Networks](https://mlsanity.com/paper/1502.05700/) (2015)
- [Being Bayesian, Even Just a Bit, Fixes Overconfidence in ReLU Networks](https://mlsanity.com/paper/2002.10118/) (2020)
- [Non-Local Spatial Propagation Network for Depth Completion](https://mlsanity.com/paper/2007.10042/) (2020)
- [Evaluating Scalable Bayesian Deep Learning Methods for Robust Computer Vision](https://mlsanity.com/paper/1906.01620/) (2019)
- [On the uncertainty of self-supervised monocular depth estimation](https://mlsanity.com/paper/2005.06209/) (2020)
- [BA-Net: Dense Bundle Adjustment Network](https://mlsanity.com/paper/1806.04807/) (2018)
- [Sparse-to-Dense: Depth Prediction from Sparse Depth Samples and a Single Image](https://mlsanity.com/paper/1709.07492/) (2017)
- [CodeSLAM - Learning a Compact, Optimisable Representation for Dense Visual SLAM](https://mlsanity.com/paper/1804.00874/) (2018)
- [PENet: Towards Precise and Efficient Image Guided Depth Completion](https://mlsanity.com/paper/2103.00783/) (2021)
- [Self-supervised Sparse-to-Dense: Self-supervised Depth Completion from LiDAR and Monocular Camera](https://mlsanity.com/paper/1807.00275/) (2018)
- [Uncertainty Estimates and Multi-Hypotheses Networks for Optical Flow](https://mlsanity.com/paper/1802.07095/) (2018)
- [DeepLiDAR: Deep Surface Normal Guided Depth Prediction for Outdoor Scene from Sparse LiDAR Data and Single Color Image](https://mlsanity.com/paper/1812.00488/) (2018)
- [A General Framework for Uncertainty Estimation in Deep Learning](https://mlsanity.com/paper/1907.06890/) (2019)
- [Learning Guided Convolutional Network for Depth Completion](https://mlsanity.com/paper/1908.01238/) (2019)

## Built on by (most cited first, 23 of 23)

- [RigNet: Repetitive Image Guided Network for Depth Completion](https://mlsanity.com/paper/2107.13802/) (2021)
- [Conditional-Flow NeRF: Accurate 3D Modelling with Reliable Uncertainty Quantification](https://mlsanity.com/paper/2203.10192/) (2022)
- [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)
- [Domain Randomization-Enhanced Depth Simulation and Restoration for Perceiving and Grasping Specular and Transparent Objects](https://mlsanity.com/paper/2208.03792/) (2022)
- [Learning Topology from Synthetic Data for Unsupervised Depth Completion](https://mlsanity.com/paper/2106.02994/) (2021)
- [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)
- [GraphCSPN: Geometry-Aware Depth Completion via Dynamic GCNs](https://mlsanity.com/paper/2210.10758/) (2022)
- [DebSDF: Delving into the Details and Bias of Neural Indoor Scene Reconstruction](https://mlsanity.com/paper/2308.15536/) (2023)
- [AugUndo: Scaling Up Augmentations for Monocular Depth Completion and Estimation](https://mlsanity.com/paper/2310.09739/) (2023)
- [Estimating 3D Uncertainty Field: Quantifying Uncertainty for Neural Radiance Fields](https://mlsanity.com/paper/2311.01815/) (2023)
- [Uncertainty Quantification for Machine Learning in Healthcare: A Survey](https://mlsanity.com/paper/2505.02874/) (2025)
- [RigNet++: Semantic Assisted Repetitive Image Guided Network for Depth Completion](https://mlsanity.com/paper/2309.00655/) (2023)
- [Sources of Uncertainty in 3D Scene Reconstruction](https://mlsanity.com/paper/2409.06407/) (2024)
- [Dense Uncertainty Estimation](https://mlsanity.com/paper/2110.06427/) (2021)
- [All-day Depth Completion](https://mlsanity.com/paper/2405.17315/) (2024)
- [Uncertainty-Aware Autonomous Vehicles: Predicting the Road Ahead](https://mlsanity.com/paper/2510.22680/) (2025)
- [ETA: Energy-based Test-time Adaptation for Depth Completion](https://mlsanity.com/paper/2508.05989/) (2025)
- [Uncertainty in Real-Time Semantic Segmentation on Embedded Systems](https://mlsanity.com/paper/2301.01201/) (2022)
- [PEdger++: Practical Edge Detection via Assembling Cross Information](https://mlsanity.com/paper/2508.11961/) (2025)

## Abstract (arXiv)

In this work we investigate the problem of uncertainty estimation for image-guided depth completion. We extend Deep Basis Fitting (DBF) for depth completion within a Bayesian evidence framework to provide calibrated per-pixel variance. The DBF approach frames the depth completion problem in terms of a network that produces a set of low-dimensional depth bases and a differentiable least squares fitting module that computes the basis weights using the sparse depths. By adopting a Bayesian treatment, our Bayesian Deep Basis Fitting (BDBF) approach is able to 1) predict high-quality uncertainty estimates and 2) enable depth completion with few or no sparse measurements. We conduct controlled experiments to compare BDBF against commonly used techniques for uncertainty estimation under various scenarios. Results show that our method produces better uncertainty estimates with accurate depth prediction.