On the Problem of Detecting When Two Implicit Plane Algebraic Curves Are Similar

TL;DR

This paper presents a deterministic algorithm using complex implicit representations to determine if two algebraic curves are similar, with practical implementation and promising results in pattern recognition and computer vision.

Contribution

It introduces a novel algorithm leveraging complex implicit forms to detect curve similarity, implemented in Maple 2015.

Findings

Algorithm successfully identifies curve similarities in various examples

Practical implementation demonstrates good performance

Applicable to pattern recognition and computer vision tasks

Abstract

We make use of the complex implicit representation in order to provide a deterministic algorithm for checking whether or not two implicit algebraic curves are related by a similarity, a central question in Pattern Recognition and Computer Vision. The algorithm has been implemented in the computer algebra system Maple 2015. Examples and evidence of the good practical performance of the algorithm are given.