On Making SIFT Features Affine Covariant

An approach is proposed for recovering affine correspondences (ACs) from orientation- and scale-covariant, e.g., SIFT, features exploiting pre-estimated epipolar geometry. The method calculates the affine parameters consistent with the epipolar geometry from the point coordinates and the scales and rotations which the feature detector obtains. The proposed closed-form solver returns a single solution and is extremely fast, i.e., 0.5 μ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\upmu $$\end{document} seconds on average. Possible applications include estimating the homography from a single upgraded correspondence and, also, estimating the surface normal for each correspondence found in a pre-calibrated image pair (e.g., stereo rig). As the second contribution, we propose a minimal solver that estimates the relative pose of a vehicle-mounted camera from a single SIFT correspondence with the corresponding surface normal obtained from, e.g., upgraded ACs. The proposed algorithms are tested both on synthetic data and on a number of publicly available real-world datasets. Using the upgraded features and the proposed solvers leads to a significant speed-up in the homography, multi-homography and relative pose estimation problems with better or comparable accuracy to the state-of-the-art methods.