One of the most commonly encountered tasks in computer vision is the estimation of model parameters from image measurements. This scenario arises in a variety of applications -- for instance, in the estimation of geometric entities, such as camera pose parameters, from feature matches between images. The main challenge in this task is to handle the problem of outliers -- in other words, data points that do not conform to the model being estimated. It is well known that if these outliers are not properly accounted for, even a single outlier in the data can result in arbitrarily bad model estimates. Due to the widespread prevalence of problems of this nature, the field of robust estimation has been well studied over the years, both in the statistics community as well as in computer vision, leading to the development of popular algorithms like Random Sample Consensus (RANSAC). While recent years have seen exciting advances in this area, a number of important issues still remain open. In this dissertation, we aim to address some of these challenges. The main goal of this dissertation is to advance the state of the art in robust estimation techniques by developing algorithms capable of efficiently and accurately delivering model parameter estimates in the face of noise and outliers. To this end, the first contribution of this work is in the development of a coherent framework for the analysis of RANSAC-based robust estimators, which consolidates various improvements made over the years. In turn, this analysis leads naturally to the development of new techniques that combine the strengths of existing methods, and yields high-performance robust estimation algorithms, including for real-time applications. A second contribution of this dissertation is the development of an algorithm that explicitly characterizes the effects of estimation uncertainty in RANSAC. This uncertainty arises from small-scale measurement noise that affects the data points, and consequently, impacts the accuracy of model parameters. We show that knowledge of this measurement noise can be leveraged to develop an inlier classification scheme that is dependent on the model uncertainty, as opposed to a fixed inlier threshold, as in RANSAC. This has the advantage that, given a model with associated uncertainty, we can immediately identify a set of points that support this solution, which in turn leads to an improvement in computational efficiency. Finally, we have also developed an approach to addresses the issue of the inlier threshold, which is a user-supplied parameter that can vary depending on the estimation problem and the data being processed. Our technique is based on the intuition that the residual errors for good models are in some way consistent with each other, while bad models do not exhibit this consistency. In other words, looking at the relationship between \\subsets of models can reveal useful information about the validity of the models themselves. We show that it is possible to efficiently identify this consistent behaviour by exploiting residual ordering information coupled with simple non-parametric statistical tests, which leads to an effective algorithm for threshold-free robust estimation.Doctor of Philosoph
