Free actions and Grassmanian variety

TL;DR

This paper introduces an algebraic framework connecting representational consistency with free actions, explores the metrizability of shape space quotients, and presents a new algebraic variety with applications in stereo vision.

Contribution

It establishes a novel algebraic notion of representational consistency and links it to free group actions, also addressing metrizability of shape space quotients and introducing a new algebraic variety.

Findings

Proved a theorem relating representational consistency to free actions.

Discussed metrizability of shape space quotients.

Provided a concrete stereo vision example.

Abstract

An algebraic notion of representational consistency is defined. A theorem relating it to free actions is proved. A metrizability problem of the quotient (a shape space) is discussed. This leads to a new algebraic variety with a metrizability result. A concrete example is given from stereo vision.