LiDAR
Analysis and Improvement of Rank-Ordered Mean Algorithm in Single-Photon LiDAR
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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.
Publication:
William C Yau, Weijian Zhang, Hashan Kavinga Weerasooriya, Stanley H Chan,
‘‘Analysis and Improvement of Rank-Ordered Mean Algorithm in Single-Photon LiDAR’’,
MMSP 2024.
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Parametric Modeling and Estimation of Photon Registrations for 3D Imaging
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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.
Publication:
Weijian Zhang, Hashan K. Weerasooriya, Prateek Chennuri, Stanley H. Chan,
‘‘Parametric Modeling and Estimation of Photon Registrations for 3D Imaging’’,
MMSP 2024.
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Resolution limit of Single-Photon LiDAR
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Single-photon Light Detection and Ranging (LiDAR) systems are often equipped
with an array of detectors for improved spatial resolution and sensing speed.
However, given a fixed amount of flux produced by the laser transmitter
across the scene, the per-pixel Signal-to-Noise Ratio (SNR) will decrease
when more pixels are packed in a unit space. This presents a fundamental
trade-off between the spatial resolution of the sensor array and the SNR
received at each pixel. Theoretical characterization of this fundamental
limit is explored. By deriving the photon arrival statistics and introducing
a series of new approximation techniques, the Mean Squared Error (MSE) of the
maximum-likelihood estimator of the time delay is derived. The theoretical
predictions align well with simulations and real data.
Publication:
Stanley H. Chan, Hashan K. Weerasooriya, Weijian Zhang, Pamela Abshire, Istvan Gyongy, Robert K. Henderson,
‘‘Resolution Limit of Single-Photon LiDAR’’,
CVPR 2024.
Code: https://github.itap.purdue.edu/StanleyChanGroup
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