# Propagating Confidences through CNNs for Sparse Data Regression

arXiv: https://arxiv.org/abs/1805.11913 · HTML: https://mlsanity.com/paper/1805.11913/

## Key facts

- Cited by 36 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 May 2018.

## Built on by (most cited first, 30 of 36)

- [PENet: Towards Precise and Efficient Image Guided Depth Completion](https://mlsanity.com/paper/2103.00783/) (2021)
- [Unsupervised Depth Completion with Calibrated Backprojection Layers](https://mlsanity.com/paper/2108.10531/) (2021)
- [Learning Topology from Synthetic Data for Unsupervised Depth Completion](https://mlsanity.com/paper/2106.02994/) (2021)
- [Deep Depth Completion from Extremely Sparse Data: A Survey](https://mlsanity.com/paper/2205.05335/) (2022)
- [An Adaptive Framework for Learning Unsupervised Depth Completion](https://mlsanity.com/paper/2106.03010/) (2021)
- [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)
- [GraphCSPN: Geometry-Aware Depth Completion via Dynamic GCNs](https://mlsanity.com/paper/2210.10758/) (2022)
- [A Surface Geometry Model for LiDAR Depth Completion](https://mlsanity.com/paper/2104.08466/) (2021)
- [Improving Monocular Visual Odometry Using Learned Depth](https://mlsanity.com/paper/2204.01268/) (2022)
- [RGB Guided ToF Imaging System: A Survey of Deep Learning-based Methods](https://mlsanity.com/paper/2405.10357/) (2024)
- [All-day Depth Completion](https://mlsanity.com/paper/2405.17315/) (2024)
- [Learning an Efficient Multimodal Depth Completion Model](https://mlsanity.com/paper/2208.10771/) (2022)
- [CU-Net: LiDAR Depth-Only Completion With Coupled U-Net](https://mlsanity.com/paper/2210.14898/) (2022)
- [PDC: Piecewise Depth Completion utilizing Superpixels](https://mlsanity.com/paper/2107.06711/) (2021)
- [SelfTune: Metrically Scaled Monocular Depth Estimation through Self-Supervised Learning](https://mlsanity.com/paper/2203.05332/) (2022)
- [Revisiting Deformable Convolution for Depth Completion](https://mlsanity.com/paper/2308.01905/) (2023)
- [ETA: Energy-based Test-time Adaptation for Depth Completion](https://mlsanity.com/paper/2508.05989/) (2025)
- [Normalized Convolution Upsampling for Refined Optical Flow Estimation](https://mlsanity.com/paper/2102.06979/) (2021)
- [DVMN: Dense Validity Mask Network for Depth Completion](https://mlsanity.com/paper/2107.06709/) (2021)
- [Self-Supervised Depth Completion for Active Stereo](https://mlsanity.com/paper/2110.03234/) (2021)
- [DOC-Depth: A novel approach for dense depth ground truth generation](https://mlsanity.com/paper/2502.02144/) (2025)
- [SparseFormer: Attention-based Depth Completion Network](https://mlsanity.com/paper/2206.04557/) (2022)
- [Prior based Sampling for Adaptive LiDAR](https://mlsanity.com/paper/2304.07099/) (2023)
- [Gated Cross-Attention Network for Depth Completion](https://mlsanity.com/paper/2309.16301/) (2023)
- [RoofDiffusion: Constructing Roofs from Severely Corrupted Point Data via Diffusion](https://mlsanity.com/paper/2404.09290/) (2024)
- [Depth on Demand: Streaming Dense Depth from a Low Frame Rate Active Sensor](https://mlsanity.com/paper/2409.08277/) (2024)
- [Monocular Depth Estimation Primed by Salient Point Detection and Normalized Hessian Loss](https://mlsanity.com/paper/2108.11098/) (2021)
- [FCDSN-DC: An Accurate and Lightweight Convolutional Neural Network for Stereo Estimation with Depth Completion](https://mlsanity.com/paper/2209.06525/) (2022)

## Abstract (arXiv)

In most computer vision applications, convolutional neural networks (CNNs) operate on dense image data generated by ordinary cameras. Designing CNNs for sparse and irregularly spaced input data is still an open problem with numerous applications in autonomous driving, robotics, and surveillance. To tackle this challenging problem, we introduce an algebraically-constrained convolution layer for CNNs with sparse input and demonstrate its capabilities for the scene depth completion task. We propose novel strategies for determining the confidence from the convolution operation and propagating it to consecutive layers. Furthermore, we propose an objective function that simultaneously minimizes the data error while maximizing the output confidence. Comprehensive experiments are performed on the KITTI depth benchmark and the results clearly demonstrate that the proposed approach achieves superior performance while requiring three times fewer parameters than the state-of-the-art methods. Moreover, our approach produces a continuous pixel-wise confidence map enabling information fusion, state inference, and decision support.