# Sparse Depth Sensing for Resource-Constrained Robots

arXiv: https://arxiv.org/abs/1703.01398 · HTML: https://mlsanity.com/paper/1703.01398/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Mar 2017.

## Built on by (most cited first, 6 of 6)

- [Deep Depth Completion from Extremely Sparse Data: A Survey](https://mlsanity.com/paper/2205.05335/) (2022)
- [Event Guided Depth Sensing](https://mlsanity.com/paper/2110.10505/) (2021)
- [EVI-SAM: Robust, Real-time, Tightly-coupled Event-Visual-Inertial State Estimation and 3D Dense Mapping](https://mlsanity.com/paper/2312.11911/) (2023)
- [CFPNet: Improving Lightweight ToF Depth Completion via Cross-zone Feature Propagation](https://mlsanity.com/paper/2411.04480/) (2024)
- [Adaptive Illumination based Depth Sensing using Deep Superpixel and Soft Sampling Approximation](https://mlsanity.com/paper/2103.12297/) (2021)
- [Sparse Depth-Guided Attention for Accurate Depth Completion: A Stereo-Assisted Monitored Distillation Approach](https://mlsanity.com/paper/2303.15840/) (2023)

## Abstract (arXiv)

We consider the case in which a robot has to navigate in an unknown environment but does not have enough on-board power or payload to carry a traditional depth sensor (e.g., a 3D lidar) and thus can only acquire a few (point-wise) depth measurements. We address the following question: is it possible to reconstruct the geometry of an unknown environment using sparse and incomplete depth measurements? Reconstruction from incomplete data is not possible in general, but when the robot operates in man-made environments, the depth exhibits some regularity (e.g., many planar surfaces with only a few edges); we leverage this regularity to infer depth from a small number of measurements. Our first contribution is a formulation of the depth reconstruction problem that bridges robot perception with the compressive sensing literature in signal processing. The second contribution includes a set of formal results that ascertain the exactness and stability of the depth reconstruction in 2D and 3D problems, and completely characterize the geometry of the profiles that we can reconstruct. Our third contribution is a set of practical algorithms for depth reconstruction: our formulation directly translates into algorithms for depth estimation based on convex programming. In real-world problems, these convex programs are very large and general-purpose solvers are relatively slow. For this reason, we discuss ad-hoc solvers that enable fast depth reconstruction in real problems. The last contribution is an extensive experimental evaluation in 2D and 3D problems, including Monte Carlo runs on simulated instances and testing on multiple real datasets. Empirical results confirm that the proposed approach ensures accurate depth reconstruction, outperforms interpolation-based strategies, and performs well even when the assumption of structured environment is violated.