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