Combining Probabilistic Shape-from-Shading & Statistical Facial Shape Models

In this thesis we present an approach to combine a probabilistic Shape-from-Shading algorithm with statistical models of facial shapes. Thesis presents how Fisher-Bingham (FB8) distributions are sampled using Gibbs sampling to give normal distributions on the tangent plane. These normal distributions are in turn combined with normal distributions arising from statistical models of facial shapes. Chapter 2 gives a brief review of Shape-from-Shading and statistical shape models. In Chapter 3 we formulate the problem under consideration and give an outline of our approach. In Chapter 4 we describe the probabilistic Shape-from-Shading algorithm based on Directional Statistics, Markov Random Fields and Belief Propagation. We describe the statistical facial shape models for needle maps and surface height in the same chapter based on the concepts of dimension reduction e.g. Principal Component Analysis, Principal Geodesic Analysis and tools of cartography e.g. Azimuthal Equidistant Projection. Chapter 5 details sampling of Fisher-Bingham distributions using a slice sampling approach of the Gibbs sampler. In Chapter 6 we discuss the actual algorithm of combining the two types of surface normals using multivariate Gaussian distributions on the tangent plane. This chapter also details how the statistical surface height model is used to recover surface heights from surface normals. The Fisher criterion and smoothing are used to deal with outliers arising from the regions of shadow and specular reflectance. Chaper7 lists our experiment results for synthetic and real images. The Iterative Closest Point algorithm is used to calculate the error di�fference between the groundtruth and recovered normals and surface heights. The results of experiments in this thesis have shown improvements in probabilistic shape-from-shading when statistical shape models are used