A $p$-adic RanSaC algorithm for stereo vision using Hensel lifting

TL;DR

This paper introduces a novel $p$-adic RanSaC algorithm for stereo vision that uses Hensel lifting and hierarchical classification to solve the relative pose problem efficiently.

Contribution

It develops a $p$-adic variation of the RanSaC method incorporating Hensel lifting and hierarchical clustering for improved stereo vision pose estimation.

Findings

Successfully classifies solutions using $p$-adic hierarchical clustering.

Determines the true solution cluster through cluster ranking.

Employs Hensel lifting to solve essential matrix equations from $p$-adic encoded images.

Abstract

A $p$-adic variation of the Ran(dom) Sa(mple) C(onsensus) method for solving the relative pose problem in stereo vision is developped. From two 2-adically encoded images a random sample of five pairs of corresponding points is taken, and the equations for the essential matrix are solved by lifting solutions modulo 2 to the 2-adic integers. A recently devised $p$-adic hierarchical classification algorithm imitating the known LBG quantisation method classifies the solutions for all the samples after having determined the number of clusters using the known intra-inter validity of clusterings. In the successful case, a cluster ranking will determine the cluster containing a 2-adic approximation to the "true" solution of the problem.