Recovering affine features from orientation- and scale-invariant ones

TL;DR

This paper presents a fast, closed-form method to recover affine correspondences from orientation- and scale-invariant features, enabling efficient homography estimation from single correspondences with comparable accuracy to state-of-the-art methods.

Contribution

The authors introduce a novel, rapid closed-form solution for recovering affine parameters from invariant features, allowing single correspondence-based homography estimation.

Findings

The method computes affine parameters in under 1 millisecond.

Using single correspondences, the approach achieves accuracy comparable to multi-point methods.

It significantly speeds up robust estimation processes like RANSAC.

Abstract

An approach is proposed for recovering affine correspondences (ACs) from orientation- and scale-invariant, e.g. SIFT, features. The method calculates the affine parameters consistent with a pre-estimated epipolar geometry from the point coordinates and the scales and rotations which the feature detector obtains. The closed-form solution is given as the roots of a quadratic polynomial equation, thus having two possible real candidates and fast procedure, i.e. <1 millisecond. It is shown, as a possible application, that using the proposed algorithm allows us to estimate a homography for every single correspondence independently. It is validated both in our synthetic environment and on publicly available real world datasets, that the proposed technique leads to accurate ACs. Also, the estimated homographies have similar accuracy to what the state-of-the-art methods obtain, but due to requiring only a single correspondence, the robust estimation, e.g. by locally optimized RANSAC, is an order of magnitude faster.