Relative Pose from SIFT Features

TL;DR

This paper introduces a novel linear constraint linking SIFT feature properties with epipolar geometry, enabling faster and often more accurate fundamental matrix estimation from fewer correspondences.

Contribution

A new linear constraint relating SIFT features to epipolar geometry, reducing the number of required correspondences for fundamental matrix estimation and improving computational efficiency.

Findings

Fewer correspondences needed for accurate estimation.

Faster RANSAC-like robust estimation.

Superior performance on real-world datasets.

Abstract

This paper proposes the geometric relationship of epipolar geometry and orientation- and scale-covariant, e.g., SIFT, features. We derive a new linear constraint relating the unknown elements of the fundamental matrix and the orientation and scale. This equation can be used together with the well-known epipolar constraint to, e.g., estimate the fundamental matrix from four SIFT correspondences, essential matrix from three, and to solve the semi-calibrated case from three correspondences. Requiring fewer correspondences than the well-known point-based approaches (e.g., 5PT, 6PT and 7PT solvers) for epipolar geometry estimation makes RANSAC-like randomized robust estimation significantly faster. The proposed constraint is tested on a number of problems in a synthetic environment and on publicly available real-world datasets on more than 80000 image pairs. It is superior to the state-of-the-art in terms of processing time while often leading to more accurate results.