Affine Correspondences and their Applications for Model Estimation

Abstract

Department of Algorithms And Their Applications Doctor of Philosophy Affine Correspondences and their Applications for Model Estimationby Dániel BARÁTH This work aims to solve sub-problems of two major fields in computer vision: minimal problems in two-or multi-view geometric model estimation and robust model fitting. Minimal solvers, i.e. algorithms solving estimation problems from a minimal sample of data points, are involved in most of the vision pipelines as an the engine of the applied robust method, e.g. RANSAC [1] and its recent variants. Vision pipelines, including calibration, structure-from-motion, image matching and retrieval, benefits from efficient minimal solvers which improve their performance upon. Given a minimal point correspondence set in two views, state-ofthe-art solvers, with a few exceptions, use them solely through their coordinates. Nevertheless, as it will be demonstrated in this thesis, exploiting affine correspondences which encode higher-order geometric information leads to methods superior to the state-of-the-art in terms of stability and the number of data points required. Methods will be proposed for surface normal, homography, epipolar geometry, and focal length estimation.The second major part of this work focuses on robust model fitting which is also a significant part of vision tasks. The base problem is to fit a single or more model instances, e.g. planes to a 3D point cloud or fundamental matrix to point correspondences, interpreting the input whilst it is contaminated by noise and contains outliers. We consider outliers as points not belonging to any desired model instance. First, a method is proposed to distinguish inliers and outliers in a set of correspondences without necessarily assuming an underlying model. Then a new local optimization step is proposed for locally optimized RANSAC (LO-RANSAC) outperforming its state-of-the-art variants. Finally, we focus on multi-homography, then general multi-class multi-instance, fitting -the problem of interpreting the input data as a mixture of noisy observations originating from multiple instances of multiple classes. The methods proposed in this work were validated both on synthesized and publicly available real world datasets.