BibTeX entry

@PHDTHESIS{200707Gary_Atkinson,
  AUTHOR={Gary Atkinson},
  TITLE={Surface Shape and Reflectance Analysis Using Polarisation},
  SCHOOL={University of York},
  MONTH=Jul,
  YEAR=2007,
  URL={http://www.bmva.org/theses/2007/2007-atkinson.pdf},
}

Abstract

When unpolarised light is reflected from a smooth dielectric surface, it becomes partially polarised. This is due to the orientation of dipoles induced in the reflecting medium and applies to both specular and diffuse reflection. This thesis aims to exploit the polarising properties of surface reflection for computer vision applications. Most importantly, the thesis proposes novel shape and reflectance function estimation techniques. The methods presented rely on polarisation data acquired using a standard digital camera and a linear polariser. Fresnel theory lies at the heart of the thesis and is used to process the polarisation data in order to estimate the surface normals of target objects. Chapter 2 surveys the related literature in the fields of polarisation vision, shape-fromshading, stereo techniques, and reflectance function analysis. Chapter 3 commences by presenting the underlying physics of polarisation by reflection, starting with the Fresnel equations. The outcome of this theory is a means to ambiguously estimate surface normals from polarisation data, given a rough estimate of the material refractive index. The first novel technique is then presented, which is a simple single-view approach to shape reconstruction. In this case, efficiency is given priority over accuracy. Chapter 3 ends with a description of a device for measuring refractive indices. Chapter 4 is concerned with image-based reflectance function estimation. Firstly, the special case of retro-reflection is assumed. An algorithm is described that constructs a histogram of surface zenith angles and pixel intensities. Probability density functions are then robustly fitted to this histogram to obtain a one-dimensional “slice” of the material BRDF. A second algorithm is then presented, which is designed for more general illumination conditions. This uses a three-dimensional histogram that includes the surface azimuth angles, in addition to the zenith angles and pixel intensities. Simulated annealing optimisation is then used to fit surfaces to the histogram, thus estimating a two-dimensional slice of the BRDF. Chapter 4 also contains a method for photometric stereo, which is used by the above two-dimensional BRDF technique to fully constrain the previously ambiguous surface normal estimates. i The most sophisticated and accurate shape reconstruction technique is presented in Chapter 5. The reflectance function algorithm described previously is first applied to enhance the surface normal estimates obtained from the raw polarisation data. This is done for two views. An new algorithm is then described that solves the stereo correspondence problem using the refined surface normals. To do this, a set of patches are extracted from each view and are aligned by minimizing an energy functional based on the surface normal estimates and local topographic properties. The optimum alignment parameters for different patch pairs then gives a matching energy. The combination of pairings that minimises the total matching energy for all patches relates to the correct correspondences. In solving the correspondence problem in this way, two fields of accurate and unambiguous surface normals are acquired which can subsequently be converted into depth. Our techniques are most suited to smooth, non-metallic surfaces. The multi-view method complements existing stereo algorithms since it does not require salient surface features to obtain correspondence. The use of shading information is shown to significantly improve the accuracy of the reconstructions compared to most previous polarisation-based methods. A set of experiments, yielding reconstructed objects and reflectance functions, are presented and compared to ground truth. The experiments involve a variety of materials and object geometries. The work provides the foundation for the development of a novel sensor that can non-intrusively recover depth information using two cameras. Suggestions for such a device are outlined in Chapter 6.