A Minimal Solution for Two-view Focal-length Estimation using Two Affine Correspondences

TL;DR

This paper introduces a minimal 2-point method to estimate focal length and fundamental matrix between two semi-calibrated cameras, extending point correspondence techniques with affine constraints and robust root selection.

Contribution

It presents the first minimal solution for joint focal length and fundamental matrix estimation using only two affine correspondences, with an efficient polynomial solver and noise-robust root selection.

Findings

Validated on synthetic and real data with high accuracy.

Outperforms recent methods in noisy conditions.

Includes a practical Matlab implementation.

Abstract

A minimal solution using two affine correspondences is presented to estimate the common focal length and the fundamental matrix between two semi-calibrated cameras - known intrinsic parameters except a common focal length. To the best of our knowledge, this problem is unsolved. The proposed approach extends point correspondence-based techniques with linear constraints derived from local affine transformations. The obtained multivariate polynomial system is efficiently solved by the hidden-variable technique. Observing the geometry of local affinities, we introduce novel conditions eliminating invalid roots. To select the best one out of the remaining candidates, a root selection technique is proposed outperforming the recent ones especially in case of high-level noise. The proposed 2-point algorithm is validated on both synthetic data and 104 publicly available real image pairs. A Matlab implementation of the proposed solution is included in the paper.