  Light detection and ranging (Lidar) data can be used to capture the depth and
intensity profile of a 3D scene. This modality relies on constructing, for each
pixel, a histogram of time delays between emitted light pulses and detected
photon arrivals. In a general setting, more than one surface can be observed in
a single pixel. The problem of estimating the number of 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). This paper presents a new approach to 3D
reconstruction using single-photon, single-wavelength Lidar data, which is
capable of identifying multiple surfaces in each pixel. Adopting a Bayesian
approach, the 3D structure to be recovered is modelled as a marked point
process and reversible jump Markov chain Monte Carlo (RJ-MCMC) moves are
proposed to sample the posterior distribution of interest. In order to promote
spatial correlation between points belonging to the same surface, we propose a
prior that combines an area interaction process and a Strauss process. New
RJ-MCMC dilation and erosion updates are presented to achieve an efficient
exploration of the configuration space. To further reduce the computational
load, we adopt a multiresolution approach, processing the data from a coarse to
the finest scale. The experiments performed with synthetic and real data show
that the algorithm obtains better reconstructions than other recently published
optimization algorithms for lower execution times.
