  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 the 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.
