# Negentropic Planar Symmetry Detector

## TL;DR

This paper introduces an information-theoretic method for detecting reflectional and rotational symmetries in greyscale images, demonstrating high precision and superior performance over existing methods through rigorous experiments.

## Contribution

It presents a novel symmetry detection approach based on negentropy functions, linking 2D symmetry detection to 1D negentropy analysis, advancing robustness and accuracy.

## Key findings

- Method achieves high precision in symmetry detection.
- Outperforms existing symmetry detection techniques.
- Validated through rigorous experimental verification.

## Abstract

In this paper we observe that information theoretical concepts are valuable tools for extracting information from images and, in particular, information on image symmetries. It is shown that the problem of detecting reflectional and rotational symmetries in a two-dimensional image can be reduced to the problem of detecting point-symmetry and periodicity in one-dimensional negentropy functions. Based on these findings a detector of reflectional and rotational global symmetries in greyscale images is constructed. We discuss the importance of high precision in symmetry detection in applications arising from quality control and illustrate how the proposed method satisfies this requirement. Finally, a superior performance of our method to other existing methods, demonstrated by the results of a rigorous experimental verification, is an indication that our approach rooted in information theory is a promising direction in a development of a robust and widely applicable symmetry detector.