BibTeX entry

@PHDTHESIS{200703Sergio_Hernandez-Marin,
  AUTHOR={Sergio Hernandez-Marin},
  TITLE={Bayesian analysis of lidar signals using reversible jump
    Markov chain Monte Carlo algorithms},
  SCHOOL={Heriot-Watt University},
  MONTH=Mar,
  YEAR=2007,
  URL={http://www.bmva.org/theses/2007/2007-hernandezmarin.pdf},
}

Abstract

Standard 3D ranging and imaging systems process only one return from an assumed single opaque surface. However, there are many situations when the laser return consists of multiple peaks, due for example to the footprint of the beam impinging on a target with surfaces distributed in depth, or on a target with semi-transparent surfaces. In this thesis, we present a unified theory of pixel processing based on a Bayesian framework, applicable to pulsed laser ranging and depth imaging systems, which allows for a careful and thorough treatment of all types of uncertainties associated with the data. We use reversible jump Markov chain Monte Carlo (RJMCMC) techniques to evaluate the posterior distribution of the parameters and to explore spaces with different dimensionality. Further, we use a delayed rejection step to allow the generated Markov chain to mix better through the use of different proposal distributions. Finally, for full 3D image data, we incorporate spatial constraints on the number of peaks through a particular Markov random field, the Potts prior model. This allows uncertainty about the underlying spatial process. To palliate some inherent deficiencies of this prior model, we also introduce two proposal distributions, one based on spatial mode jumping, the other on a spatial birth/death process. The methods we employ are demonstrated on simulated and real data, showing that the laser return parameters can be estimated to a high degree of accuracy. We show practical examples from both near and far range depth imaging. Two techniques of particular relevance for this work are Time-Correlated Single Photon Counting (TCSPC) and Burst Illumination Laser (BIL) imaging. In each case, the goal is a complete characterisation of the 3D surfaces viewed by the particular laser imaging system. For TCSPC data, we determine the number, positions and amplitudes of returns from a histogram, or histograms, of photon counts. For BIL data, we determine the same parameters from integrated intensities as a range gate is moved through an image sequence. In either case, a more informative multi-layered 3D image can be created through the spatial analysis.