# Multiple Reflection Symmetry Detection via Linear-Directional Kernel Density Estimation

## TL;DR

This paper introduces a new voting method using weighted linear-directional kernel density estimation for detecting multiple symmetries in images, improving accuracy over existing methods especially in complex real-world scenarios.

## Contribution

It presents a novel voting representation that enhances symmetry detection by efficiently identifying multiple axes using linear-directional kernel density estimation.

## Key findings

- Outperforms existing symmetry detection methods on public datasets.
- Effectively detects multiple symmetry axes in complex images.
- Demonstrates robustness on real-world and synthetic images.

## Abstract

Symmetry is an important composition feature by investigating similar sides inside an image plane. It has a crucial effect to recognize man-made or nature objects within the universe. Recent symmetry detection approaches used a smoothing kernel over different voting maps in the polar coordinate system to detect symmetry peaks, which split the regions of symmetry axis candidates in inefficient way. We propose a reliable voting representation based on weighted linear-directional kernel density estimation, to detect multiple symmetries over challenging real-world and synthetic images. Experimental evaluation on two public datasets demonstrates the superior performance of the proposed algorithm to detect global symmetry axes respect to the major image shapes.