Bayesian methods for inverse problems with point clouds : applications to single-photon lidar

Single-photon light detection and ranging (lidar) has emerged as a prime candidate technology for depth imaging through challenging environments. This modality relies on constructing, for each pixel, a histogram of time delays between emitted light pulses and detected photon arrivals. The problem of estimating the number of imaged surfaces, their reflectivity and position becomes very challenging in the low-photon regime (which equates to short acquisition times) or relatively high background levels (i.e., strong ambient illumination). In a general setting, a variable number of surfaces can be observed per imaged pixel. The majority of existing methods assume exactly one surface per pixel, simplifying the reconstruction problem so that standard image processing techniques can be easily applied. However, this assumption hinders practical three-dimensional (3D) imaging applications, being restricted to controlled indoor scenarios. Moreover, other existing methods that relax this assumption achieve worse reconstructions, suffering from long execution times and large memory requirements. This thesis presents novel approaches to 3D reconstruction from single-photon lidar data, which are capable of identifying multiple surfaces in each pixel. The resulting algorithms obtain new state-of-the-art reconstructions without strong assumptions about the sensed scene. The models proposed here differ from standard image processing tools, being designed to capture correlations of manifold-like structures. Until now, a major limitation has been the significant amount of time required for the analysis of the recorded data. By combining statistical models with highly scalable computational tools from the computer graphics community, we demonstrate 3D reconstruction of complex outdoor scenes with processing times of the order of 20 ms, where the lidar data was acquired in broad daylight from distances up to 320 m. This has enabled robust, real-time target reconstruction of complex moving scenes, paving the way for single-photon lidar at video rates for practical 3D imaging applications

Probabilistic modeling for single-photon lidar

Lidar is an increasingly prevalent technology for depth sensing, with applications including scientific measurement and autonomous navigation systems. While conventional systems require hundreds or thousands of photon detections per pixel to form accurate depth and reflectivity images, recent results for single-photon lidar (SPL) systems using single-photon avalanche diode (SPAD) detectors have shown accurate images formed from as little as one photon detection per pixel, even when half of those detections are due to uninformative ambient light. The keys to such photon-efficient image formation are two-fold: (i) a precise model of the probability distribution of photon detection times, and (ii) prior beliefs about the structure of natural scenes. Reducing the number of photons needed for accurate image formation enables faster, farther, and safer acquisition. Still, such photon-efficient systems are often limited to laboratory conditions more favorable than the real-world settings in which they would be deployed. This thesis focuses on expanding the photon detection time models to address challenging imaging scenarios and the effects of non-ideal acquisition equipment. The processing derived from these enhanced models, sometimes modified jointly with the acquisition hardware, surpasses the performance of state-of-the-art photon counting systems. We first address the problem of high levels of ambient light, which causes traditional depth and reflectivity estimators to fail. We achieve robustness to strong ambient light through a rigorously derived window-based censoring method that separates signal and background light detections. Spatial correlations both within and between depth and reflectivity images are encoded in superpixel constructions, which fill in holes caused by the censoring. Accurate depth and reflectivity images can then be formed with an average of 2 signal photons and 50 background photons per pixel, outperforming methods previously demonstrated at a signal-to-background ratio of 1. We next approach the problem of coarse temporal resolution for photon detection time measurements, which limits the precision of depth estimates. To achieve sub-bin depth precision, we propose a subtractively-dithered lidar implementation, which uses changing synchronization delays to shift the time-quantization bin edges. We examine the generic noise model resulting from dithering Gaussian-distributed signals and introduce a generalized Gaussian approximation to the noise distribution and simple order statistics-based depth estimators that take advantage of this model. Additional analysis of the generalized Gaussian approximation yields rules of thumb for determining when and how to apply dither to quantized measurements. We implement a dithered SPL system and propose a modification for non-Gaussian pulse shapes that outperforms the Gaussian assumption in practical experiments. The resulting dithered-lidar architecture could be used to design SPAD array detectors that can form precise depth estimates despite relaxed temporal quantization constraints. Finally, SPAD dead time effects have been considered a major limitation for fast data acquisition in SPL, since a commonly adopted approach for dead time mitigation is to operate in the low-flux regime where dead time effects can be ignored. We show that the empirical distribution of detection times converges to the stationary distribution of a Markov chain and demonstrate improvements in depth estimation and histogram correction using our Markov chain model. An example simulation shows that correctly compensating for dead times in a high-flux measurement can yield a 20-times speed up of data acquisition. The resulting accuracy at high photon flux could enable real-time applications such as autonomous navigation