A dyadic solution of relative pose problems

TL;DR

This paper introduces a p-adic encoding approach for solving relative pose problems in computer vision, leveraging hierarchical interval subdivision and Hensel's lifting to enhance robustness in linear and nonlinear equations.

Contribution

It presents a novel p-adic encoding method combined with Hensel's lifting for solving relative pose problems, improving robustness over traditional techniques.

Findings

Effective in solving linear and nonlinear pose equations

Applicable to 5, 7, and 8 point correspondences

Demonstrates inherent robustness of the method

Abstract

A hierarchical interval subdivision is shown to lead to a $p$-adic encoding of image data. This allows in the case of the relative pose problem in computer vision and photogrammetry to derive equations having 2-adic numbers as coefficients, and to use Hensel's lifting method to their solution. This method is applied to the linear and non-linear equations coming from eight, seven or five point correspondences. An inherent property of the method is its robustness.