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

arXiv: https://arxiv.org/abs/1704.06392 · HTML: https://mlsanity.com/paper/1704.06392/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Apr 2017.

## Built on by (most cited first, 2 of 2)

- [Learning to Discover Reflection Symmetry via Polar Matching Convolution](https://mlsanity.com/paper/2108.12952/) (2021)
- [ARD-REFSM: Enhancing Reflection Symmetry Detection with Asymmetric Denoising and Rotation Equivariance](https://mlsanity.com/paper/2607.27927/) (2026)

## Abstract (arXiv)

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.