Robust Self-Calibration and Fundamental Matrix Estimation in 3D Computer Vision - Rastgar, Houman (Université d'Ottawa / University of Ottawa, 2013)
The recent advances in the field of computer vision have brought many of the laboratory algorithms into the realm of industry. However, one problem that still remains open in the field of 3D vision is the problem of noise. The challenging problem of 3D structure recovery from images is highly sensitive to the presence of input data that are contaminated by errors that do not conform to ideal assumptions. Tackling the problem of extreme data, or outliers has led to many robust methods in the field that are able to handle moderate levels of outliers and still provide accurate outputs. However, this problem remains open, especially for higher noise levels and so it has been the goal of this thesis to address the issue of robustness with respect to two central problems in 3D computer vision. The two problems are highly related and they have been presented together within a Structure from Motion (SfM) context. The first, is the problem of robustly estimating the fundamental matrix from images whose correspondences contain high outlier levels. Even though this area has been extensively studied, two algorithms have been proposed that significantly speed up the computation of the fundamental matrix and achieve accurate results in scenarios containing more than 50% outliers. The presented algorithms rely on ideas from the field of robust statistics in order to develop guided sampling techniques that rely on information inferred from residual analysis. The second, problem addressed in this thesis is the robust estimation of camera intrinsic parameters from fundamental matrices, or self-calibration. Self-calibration algorithms are notoriously unreliable for general cases and it is shown that the existing methods are highly sensitive to noise. In spite of this, robustness in self-calibration has received little attention in the literature. Through experimental results, it is shown that it is essential for a real-world self-calibration algorithm to be robust. In order to introduce robustness to the existing methods, three robust algorithms have been proposed that utilize existing constraints for self-calibration from the fundamental matrix. However, the resulting algorithms are less affected by noise than existing algorithms based on these constraints. This is an important milestone since self-calibration offers many possibilities by providing estimates of camera parameters without requiring access to the image acquisition device. The proposed algorithms rely on perturbation theory, guided sampling methods and a robust root finding method for systems of higher order polynomials. By adding robustness to self-calibration it is hoped that this idea is one step closer to being a practical method of camera calibration rather than merely a theoretical possibility.
Keywords: computer vision; 3D reconstruction; Structure from Motion; robust estimation; self-calibration; autocalibration; fundamental matrix