On a realization of motion and similarity group equivalence classes of labeled points in $\mathbb R^k$ with applications to computer vision

TL;DR

This paper develops a method to realize motion and similarity group equivalence classes of labeled points in Euclidean space as a metric space, facilitating applications in computer vision.

Contribution

It introduces a new realization of equivalence classes of labeled points under motion and similarity groups as a computable metric space.

Findings

Provides a computable metric for equivalence classes

Enables analysis of labeled points in computer vision

Facilitates comparison of point configurations

Abstract

We study a realization of motion and similarity group equivalence classes of $n\geq 1$ labeled points in $\mathbb R^k,\, k\geq 1$ as a metric space with a computable metric. Our study is motivated by applications in computer vision.