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

TL;DR

This paper analyzes the limitations of the rank-ordered mean (ROM) algorithm in single-photon LiDAR depth estimation under noise, providing a theoretical characterization and proposing an improved method that significantly enhances accuracy and noise robustness.

Contribution

It offers the first theoretical analysis of ROM's performance limits and introduces a new clustering-based technique that outperforms ROM in noisy conditions.

Findings

ROM fails below a certain reflectivity threshold.

Proposed method improves depth accuracy by 1000x at the same signal levels.

Achieves high image fidelity even with noise 17 times the signal level.

Abstract

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 \textit{et 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.