Surface shape and reflectance analysis using polarisation

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.