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.


  1. Bayesian inference
  2. 3D reconstruction
  3. Lidar
  4. low-photon imaging
  5. Poisson noise

MSC codes

  1. 62F15
  2. 62H12
  3. 62H35
  4. 62P30
  5. 62P12
  6. 65C40

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Supplementary Material

Index of Supplementary Materials

Title of paper: Bayesian 3D Reconstruction of Complex Scenes from Single-Photon Lidar Data

Authors: J. Tachella, Y. Altmann, X. Ren, A. McCarthy, G. S. Buller, S. McLaughlin, and J.-Y. Tourneret

File: M118397_01.pdf

Type: PDF

Contents: Complete RJ-MCMC acceptance rate formulas, details of some mathematical derivations used in the article and election of the impulse response in real Lidar data.


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Information & Authors


Published In

cover image SIAM Journal on Imaging Sciences
SIAM Journal on Imaging Sciences
Pages: 521 - 550
ISSN (online): 1936-4954


Submitted: 30 April 2018
Accepted: 27 December 2018
Published online: 14 March 2019


  1. Bayesian inference
  2. 3D reconstruction
  3. Lidar
  4. low-photon imaging
  5. Poisson noise

MSC codes

  1. 62F15
  2. 62H12
  3. 62H35
  4. 62P30
  5. 62P12
  6. 65C40



Funding Information

STIC-AmSud Project HyperMed
Centre National de la Recherche Scientifique https://doi.org/10.13039/501100004794
QuantIC https://doi.org/10.13039/100012927
Engineering and Physical Sciences Research Council https://doi.org/10.13039/501100000266 : EP/N003446/1, EP/M01326X/1, EP/K015338/1
Royal Academy of Engineering https://doi.org/10.13039/501100000287 : RF201617/16/31

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