Bayesian 3D Reconstruction of Subsampled Multispectral Single-Photon Lidar Signals

Abstract

Light detection and ranging (Lidar) single-photon devices capture range and intensity information from a 3D scene. This modality enables long range 3D reconstruction with high range precision and low laser power. A multispectral single-photon Lidar system provides additional spectral diversity, allowing the discrimination of different materials. However, the main drawback of such systems can be the long acquisition time needed to collect enough photons in each spectral band. In this work, we tackle this problem in two ways: first, we propose a Bayesian 3D reconstruction algorithm that is able to find multiple surfaces per pixel, using few photons, i.e., shorter acquisitions. In contrast to previous algorithms, the novel method processes jointly all the spectral bands, obtaining better reconstructions using less photon detections. The proposed model promotes spatial correlation between neighbouring points within a given surface using spatial point processes. Secondly, we account for different spatial and spectral subsampling schemes, which reduce the total number of measurements, without significant degradation of the reconstruction performance. In this way, the total acquisition time, memory requirements and computational time can be significantly reduced. The experiments performed using both synthetic and real single-photon Lidar data demonstrate the advantages of tailored sampling schemes over random alternatives. Furthermore, the proposed algorithm yields better estimates than other existing methods for multi-surface reconstruction using multispectral Lidar data.

Robust and Guided Bayesian Reconstruction of Single-Photon 3D Lidar Data: Application to Multispectral and Underwater Imaging

“…In a similar fashion to depth, spatial smoothness can be enforced on the reflectivity by considering latent variables as in the gamma Markov random field prior [47]. However, this prior will lead to underestimated reflectivity values as already highlighted in [27]. In this work, we introduce an N ×K latent variable M assigned a Gaussian prior distribution as follows…”

“…• The RT3D algorithm [34]: assumes the presence of multiple surfaces per-pixel and is used when analysing robustness to noise and photon-sparse regime imaging on single spectral data. • The MUSAPOP algorithm [27]: assumes the presence of multiple surfaces per-pixel and is used when analysing multi-spectral Lidar data.…”

“…where N represents the number of pixels having a target, and . In addition, we consider the metrics used in [27] to evaluate point clouds. More precisely, we consider the percentage of true detections as a function of the distance τ , where a true detection occurs if an estimated point of a given nth pixel has a reference point in its surrounding such that |d n − d ref n | ≤ τ .…”

“…We distinguish three broad families: statistical, learning-based and hybrid methods. The former builds on a statistical model and solves the resulting inference using stochastic simulation methods [6], [15], [26], [27], or optimization algorithms [19], [25], [28]. These principled methods benefit from a good interpretability but are subject to the definition of good features to represent the data.…”

Expectation-Maximization Based Approach to 3D Reconstruction From Single-Waveform Multispectral Lidar Data

“…Sampling the auxiliary variablẽ t needed in (23) can be achieved as when Φ = ∅. Optimizing (24) globally is challenging as the problem is not convex and alternating optimization w.r.t. W and Φ can be adopted to ensure local convergence.…”