# Sparsity Invariant CNNs

arXiv: https://arxiv.org/abs/1708.06500 · HTML: https://mlsanity.com/paper/1708.06500/

## Key facts

- Cited by 326 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Aug 2017.

## Built on by (most cited first, 30 of 326)

- [DSEC: A Stereo Event Camera Dataset for Driving Scenarios](https://mlsanity.com/paper/2103.06011/) (2021)
- [MoGe: Unlocking Accurate Monocular Geometry Estimation for Open-Domain Images with Optimal Training Supervision](https://mlsanity.com/paper/2410.19115/) (2024)
- [MoGe-2: Accurate Monocular Geometry with Metric Scale and Sharp Details](https://mlsanity.com/paper/2507.02546/) (2025)
- [The Temporal Opportunist: Self-Supervised Multi-Frame Monocular Depth](https://mlsanity.com/paper/2104.14540/) (2021)
- [BinsFormer: Revisiting Adaptive Bins for Monocular Depth Estimation](https://mlsanity.com/paper/2204.00987/) (2022)
- [Multimodal Virtual Point 3D Detection](https://mlsanity.com/paper/2111.06881/) (2021)
- [Panoptic NeRF: 3D-to-2D Label Transfer for Panoptic Urban Scene Segmentation](https://mlsanity.com/paper/2203.15224/) (2022)
- [SpatialBot: Precise Spatial Understanding with Vision Language Models](https://mlsanity.com/paper/2406.13642/) (2024)
- [PENet: Towards Precise and Efficient Image Guided Depth Completion](https://mlsanity.com/paper/2103.00783/) (2021)
- [MonoViT: Self-Supervised Monocular Depth Estimation with a Vision Transformer](https://mlsanity.com/paper/2208.03543/) (2022)
- [CoR-GS: Sparse-View 3D Gaussian Splatting via Co-Regularization](https://mlsanity.com/paper/2405.12110/) (2024)
- [DepthFormer: Exploiting Long-Range Correlation and Local Information for Accurate Monocular Depth Estimation](https://mlsanity.com/paper/2203.14211/) (2022)
- [Towards Zero-Shot Scale-Aware Monocular Depth Estimation](https://mlsanity.com/paper/2306.17253/) (2023)
- [CompletionFormer: Depth Completion with Convolutions and Vision Transformers](https://mlsanity.com/paper/2304.13030/) (2023)
- [RigNet: Repetitive Image Guided Network for Depth Completion](https://mlsanity.com/paper/2107.13802/) (2021)
- [Point Cloud Forecasting as a Proxy for 4D Occupancy Forecasting](https://mlsanity.com/paper/2302.13130/) (2023)
- [UltraLiDAR: Learning Compact Representations for LiDAR Completion and Generation](https://mlsanity.com/paper/2311.01448/) (2023)
- [Dynamic Spatial Propagation Network for Depth Completion](https://mlsanity.com/paper/2202.09769/) (2022)
- [RGB-D Local Implicit Function for Depth Completion of Transparent Objects](https://mlsanity.com/paper/2104.00622/) (2021)
- [Multi-Frame Self-Supervised Depth with Transformers](https://mlsanity.com/paper/2204.07616/) (2022)
- [Channel-Wise Attention-Based Network for Self-Supervised Monocular Depth Estimation](https://mlsanity.com/paper/2112.13047/) (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)
- [EPMF: Efficient Perception-aware Multi-sensor Fusion for 3D Semantic Segmentation](https://mlsanity.com/paper/2106.15277/) (2021)
- [OmniDet: Surround View Cameras based Multi-task Visual Perception Network for Autonomous Driving](https://mlsanity.com/paper/2102.07448/) (2021)
- [IEBins: Iterative Elastic Bins for Monocular Depth Estimation](https://mlsanity.com/paper/2309.14137/) (2023)
- [Radar-Camera Pixel Depth Association for Depth Completion](https://mlsanity.com/paper/2106.02778/) (2021)
- [Domain Randomization-Enhanced Depth Simulation and Restoration for Perceiving and Grasping Specular and Transparent Objects](https://mlsanity.com/paper/2208.03792/) (2022)
- [Marigold-DC: Zero-Shot Monocular Depth Completion with Guided Diffusion](https://mlsanity.com/paper/2412.13389/) (2024)
- [LRRU: Long-short Range Recurrent Updating Networks for Depth Completion](https://mlsanity.com/paper/2310.08956/) (2023)

## Abstract (arXiv)

In this paper, we consider convolutional neural networks operating on sparse inputs with an application to depth upsampling from sparse laser scan data. First, we show that traditional convolutional networks perform poorly when applied to sparse data even when the location of missing data is provided to the network. To overcome this problem, we propose a simple yet effective sparse convolution layer which explicitly considers the location of missing data during the convolution operation. We demonstrate the benefits of the proposed network architecture in synthetic and real experiments with respect to various baseline approaches. Compared to dense baselines, the proposed sparse convolution network generalizes well to novel datasets and is invariant to the level of sparsity in the data. For our evaluation, we derive a novel dataset from the KITTI benchmark, comprising 93k depth annotated RGB images. Our dataset allows for training and evaluating depth upsampling and depth prediction techniques in challenging real-world settings and will be made available upon publication.