# Analysis and Improvement of Rank-Ordered Mean Algorithm in Single-Photon LiDAR

arXiv: https://arxiv.org/abs/2407.20399 · HTML: https://mlsanity.com/paper/2407.20399/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 17 references that are in the map.
- First posted on arXiv 29 Jul 2024.

## Builds on (most cited first, 3 of 3)

- [Asynchronous Single-Photon 3D Imaging](https://mlsanity.com/paper/1908.06372/) (2019)
- [Dead Time Compensation for High-Flux Ranging](https://mlsanity.com/paper/1810.11145/) (2018)
- [Resolution Limit of Single-Photon LiDAR](https://mlsanity.com/paper/2403.17719/) (2024)

## Built on by (most cited first, 1 of 1)

- [Joint Depth and Reflectivity Estimation using Single-Photon LiDAR](https://mlsanity.com/paper/2505.13250/) (2025)

## Abstract (arXiv)

Depth estimation using a single-photon LiDAR is often solved by a matched filter. It is, however, error-prone in the presence of background noise. A commonly used technique to reject background noise is the rank-ordered mean (ROM) filter previously reported by Shin textitet al. (2015). ROM rejects noisy photon arrival timestamps by selecting only a small range of them around the median statistics within its local neighborhood. Despite the promising performance of ROM, its theoretical performance limit is unknown. In this paper, we theoretically characterize the ROM performance by showing that ROM fails when the reflectivity drops below a threshold predetermined by the depth and signal-to-background ratio, and its accuracy undergoes a phase transition at the cutoff. Based on our theory, we propose an improved signal extraction technique by selecting tight timestamp clusters. Experimental results show that the proposed algorithm improves depth estimation performance over ROM by 3 orders of magnitude at the same signal intensities, and achieves high image fidelity at noise levels as high as 17 times that of signal.