Article
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PSO based Unconstrained Polygonal Fitting of 2D Shapes
Version 1
: Received: 11 December 2023 / Approved: 13 December 2023 / Online: 13 December 2023 (04:49:03 CET)
A peer-reviewed article of this Preprint also exists.
Panagiotakis, C. Particle Swarm Optimization-Based Unconstrained Polygonal Fitting of 2D Shapes. Algorithms 2024, 17, 25. Panagiotakis, C. Particle Swarm Optimization-Based Unconstrained Polygonal Fitting of 2D Shapes. Algorithms 2024, 17, 25.
Abstract
In this paper, we present a general version of polygonal fitting problem called Unconstrained Polygonal Fitting (UPF). Our goal is to represent a given 2D shape S with an N-vertex polygonal curve P with a known number of vertices, so that the Intersection over Union (IoU) metric between S and P is maximized without any assumption or prior knowledge of the object structure and the location of the N-vertices of P that can be placed anywhere in the 2D space. The search space of the UPF problem is a superset of the classical polygonal approximation (PA) problem, where the vertices are constrained to belong in the boundary of the given 2D shape. Therefore, the resulting solutions of the UPF may better approximate the given curve than the solutions of the PA problem. For a given number of vertices N, a Particle Swarm Optimization (PSO) method is used to maximize the IoU metric, which yields almost optimal solutions. Furthermore, the proposed method has also been implemented under the equal area principle so that the total area covered by P is equal to the area of the original 2D shape to measure how this constraint affects IoU metric. The quantitative results obtained on more than 2,800 2D shapes included in two standard datasets quantify the performance of the proposed methods and illustrate that their solutions outperform baselines from the literature.
Keywords
Polygonal fitting; Polygonal approximation; PSO; Shape analysis; IoU; Segmentation
Subject
Computer Science and Mathematics, Computer Vision and Graphics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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