# A linear method for camera pair self-calibration and multi-view reconstruction with geometrically verified correspondences

## TL;DR

This paper presents a linear self-calibration method for camera pairs that improves 3D reconstruction accuracy by verifying correspondences and integrating multiple pair reconstructions into a robust pipeline.

## Contribution

A novel linear self-calibration approach for camera pairs with unknown focal lengths, including a correspondence verification method and an integrated 3D reconstruction pipeline.

## Key findings

- Performs comparably to Kruppa equations in rotation error
- Improves point correspondence robustness in architectural scenes
- Introduces a method to average focal length estimates across camera pairs

## Abstract

We examine 3D reconstruction of architectural scenes in unordered sets of uncalibrated images. We introduce a linear method to self-calibrate and find the metric reconstruction of a camera pair. We assume unknown and different focal lengths but otherwise known internal camera parameters and a known projective reconstruction of the camera pair. We recover two possible camera configurations in space and use the Cheirality condition, that all 3D scene points are in front of both cameras, to disambiguate the solution. We show in two Theorems, first that the two solutions are in mirror positions and then the relations between their viewing directions. Our new method performs on par (median rotation error $\Delta R = 3.49^{\circ}$) with the standard approach of Kruppa equations ($\Delta R = 3.77^{\circ}$) for self-calibration and 5-Point algorithm for calibrated metric reconstruction of a camera pair. We reject erroneous image correspondences by introducing a method to examine whether point correspondences appear in the same order along $x, y$ image axes in image pairs. We evaluate this method by its precision and recall and show that it improves the robustness of point matches in architectural and general scenes. Finally, we integrate all the introduced methods to a 3D reconstruction pipeline. We utilize the numerous camera pair metric recontructions using rotation-averaging algorithms and a novel method to average focal length estimates.