Statistical Approaches to Inferring Object Shape from Single Images

Depth inference is a fundamental problem of computer vision with a broad range of potential applications. Monocular depth inference techniques, particularly shape from shading dates back to as early as the 40's when it was first used to study the shape of the lunar surface. Since then there has been ample research to develop depth inference algorithms using monocular cues. Most of these are based on physical models of image formation and rely on a number of simplifying assumptions that do not hold for real world and natural imagery. Very few make use of the rich statistical information contained in real world images and their 3D information. There have been a few notable exceptions though. The study of statistics of natural scenes has been concentrated on outdoor scenes which are cluttered. Statistics of scenes of single objects has been less studied, but is an essential part of daily human interaction with the environment. Inferring shape of single objects is a very important computer vision problem which has captured the interest of many researchers over the past few decades and has applications in object recognition, robotic grasping, fault detection and Content Based Image Retrieval (CBIR). This thesis focuses on studying the statistical properties of single objects and their range images which can benefit shape inference techniques. I acquired two databases: Single Object Range and HDR (SORH) and the Eton Myers Database of single objects, including laser-acquired depth, binocular stereo, photometric stereo and High Dynamic Range (HDR) photography. I took a data driven approach and studied the statistics of color and range images of real scenes of single objects along with whole 3D objects and uncovered some interesting trends in the data. The fractal structure of natural images was previously well known, and thought to be a universal property. However, my research showed that the fractal structure of single objects and surfaces is governed by a wholly different set of rules. Classical computer vision problems of binocular and multi-view stereo, photometric stereo, shape from shading, structure from motion, and others, all rely on accurate and complete models of which 3D shapes and textures are plausible in nature, to avoid producing unlikely outputs. Bayesian approaches are common for these problems, and hopefully the findings on the statistics of the shape of single objects from this work and others will both inform new and more accurate Bayesian priors on shape, and also enable more efficient probabilistic inference procedures

Improving Face Recognition Performance Using a Hierarchical Bayesian Model

Over the past two decades, face recognition research has shot to the forefront due to its increased demand in security and commercial applications. Many facial feature extraction techniques for the purpose of recognition have been developed, some of which have also been successfully installed and used. Principal Component Analysis (PCA), also popularly called as Eigenfaces has been used successfully and also is a de facto standard. Linear generative models such as Principal Component Analysis (PCA) and Independent Component Analysis (ICA) find a set of basis images and represent the faces as a linear combination of these basis functions. These models make certain assumptions about the data which limit the type of structure they can capture. This thesis is mainly based on the hierarchical Bayesian model developed by Yan Karklin of Carnegie Mellon University. His research was mainly focused on natural signals like natural images and speech signals in which he showed that for such signals, latent variables exhibit residual dependencies and non-stationary statistics. He built his model atop ICA and this hierarchical model could capture more abstract and invariant properties of the data. We apply the same hierarchical model on facial images to extract features which can result in an improved recognition performance over already existing baseline approaches. We use Kernelized Fisher Discriminant Analysis (KFLD) as our baseline as it is superior to PCA in a way that it produces well separated classes even under variations in facial expression and lighting. We conducted extensive experiments on the GreyFERET database and tested the performance on test sets with varying facial expressions. The results demonstrate the increase in performance that was expected