Figure 1: Example outputs of the proposed classical polygonal approximation (left) and unconstrained polygonal fitting (right) for N = 4 vertices.

This work presents 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. 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. 

This is the first work to define and solve the UPF problem.  In a low-dimensional search space, that is true for low number of vertices, the proposed  method clearly outperforms baselines of classical PA, since even the optimal solutions of  the classical PA problem usually fail to obtain high performance results due to the limited search space (shape boundary) of PA problem.

Related Publications

[1]  C. Panagiotakis, PSO based Polygonal Fitting of 2D Shapes, Agorithms, 2024 (under revision).

[2]  Panagiotakis, C. PSO based Unconstrained Polygonal Fitting of 2D Shapes. Preprints 2023, 2023120933. https://doi.org/10.20944/preprints202312.0933.v1