Modelling curvature of a bent paper leaf

TL;DR

This paper explores how algebraic geometry tools can model and straighten curved paper-like objects, proposing it as a fast alternative to neural networks for feature recognition on manifolds.

Contribution

It demonstrates the potential of algebraic geometry to serve as an efficient alternative to neural networks in vision and machine learning tasks involving curved objects.

Findings

Algebraic geometry can model bent paper as elastica curves.

Proposes algebraic geometry as a fast alternative to neural networks.

Shows potential for algebraic geometry in feature extraction on manifolds.

Abstract

In this article, we briefly describe various tools and approaches that algebraic geometry has to offer to straighten bent objects. Throughout this article we will consider a specific example of a bent or curved piece of paper which in our case acts very much like an elastica curve. We conclude this article with a suggestion to algebraic geometry as a viable and fast performance alternative of neural networks in vision and machine learning. The purpose of this article is not to build a full blown framework but to show possibility of using algebraic geometry as an alternative to neural networks for recognizing or extracting features on manifolds.