# Parametric Modeling and Estimation of Photon Registrations for 3D Imaging

arXiv: https://arxiv.org/abs/2407.02712 · HTML: https://mlsanity.com/paper/2407.02712/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jul 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)

In single-photon light detection and ranging (SP-LiDAR) systems, the histogram distortion due to hardware dead time fundamentally limits the precision of depth estimation. To compensate for the dead time effects, the photon registration distribution is typically modeled based on the Markov chain self-excitation process. However, this is a discrete process and it is computationally expensive, thus hindering potential neural network applications and fast simulations. In this paper, we overcome the modeling challenge by proposing a continuous parametric model. We introduce a Gaussian-uniform mixture model (GUMM) and periodic padding to address high noise floors and noise slopes respectively. By deriving and implementing a customized expectation maximization (EM) algorithm, we achieve accurate histogram matching in scenarios that were deemed difficult in the literature.