# Homography from two orientation- and scale-covariant features

## TL;DR

This paper introduces a novel homography estimation method leveraging orientation- and scale-covariant features like SIFT, deriving new constraints that enable minimal two-point estimation, reducing computational effort and improving stability.

## Contribution

It presents new geometric constraints on scales and rotations, leading to a minimal two-point homography solver that enhances efficiency and robustness in geometric estimation tasks.

## Key findings

- Requires only two feature correspondences for homography estimation
- Reduces RANSAC iterations significantly compared to four-point methods
- Demonstrates effectiveness on synthetic and real-world datasets

## Abstract

This paper proposes a geometric interpretation of the angles and scales which the orientation- and scale-covariant feature detectors, e.g. SIFT, provide. Two new general constraints are derived on the scales and rotations which can be used in any geometric model estimation tasks. Using these formulas, two new constraints on homography estimation are introduced. Exploiting the derived equations, a solver for estimating the homography from the minimal number of two correspondences is proposed. Also, it is shown how the normalization of the point correspondences affects the rotation and scale parameters, thus achieving numerically stable results. Due to requiring merely two feature pairs, robust estimators, e.g. RANSAC, do significantly fewer iterations than by using the four-point algorithm. When using covariant features, e.g. SIFT, the information about the scale and orientation is given at no cost. The proposed homography estimation method is tested in a synthetic environment and on publicly available real-world datasets.