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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 generalize this model to various shapes of paper which are stretched and bent and then finally implement it on a standard 80mg paper and see how the folds on paper can be completely removed using python and sage-math code. We conclude this article with a suggestion to algebraic geometry as a viable and fast performer 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 evidence or possibility of using algebraic geometry as an alternative to recognizing or extracting features on manifolds.
It uses techniques of spline theory and mechanical engineering to model bent objects and flatten them to improve surface readability like in the case of scanned documents. This is a better approach than existing techniques as they involve heavy use of supervised learning and Computation intensive neural networks to solve the same problem.