Axis-level Symmetry Detection with Group-Equivariant Representation

• URL: http://arxiv.org/abs/2508.10740v2
• Date: Wed, 15 Oct 2025 04:58:20 GMT
• Title: Axis-level Symmetry Detection with Group-Equivariant Representation
• Authors: Wongyun Yu, Ahyun Seo, Minsu Cho,
• Abstract summary: Recent heatmap-based approaches can localize potential regions of symmetry axes but often lack precision in identifying individual axes.<n>We propose a novel framework for axis-level detection of the two most common symmetry types-reflection and rotation.<n>Our method achieves state-of-the-art performance, outperforming existing approaches.
• Score: 48.813587457507786
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Symmetry is a fundamental concept that has been extensively studied, yet detecting it in complex scenes remains a significant challenge in computer vision. Recent heatmap-based approaches can localize potential regions of symmetry axes but often lack precision in identifying individual axes. In this work, we propose a novel framework for axis-level detection of the two most common symmetry types-reflection and rotation-by representing them as explicit geometric primitives, i.e. lines and points. Our method employs a dual-branch architecture that is equivariant to the dihedral group, with each branch specialized to exploit the structure of dihedral group-equivariant features for its respective symmetry type. For reflection symmetry, we introduce orientational anchors, aligned with group components, to enable orientation-specific detection, and a reflectional matching that measures similarity between patterns and their mirrored counterparts across candidate axes. For rotational symmetry, we propose a rotational matching that compares patterns at fixed angular intervals to identify rotational centers. Extensive experiments demonstrate that our method achieves state-of-the-art performance, outperforming existing approaches.

Related papers

• Global Symmetry and Orthogonal Transformations from Geometrical Moment $n$-tuples [0.304585143845864]
  This paper employs geometrical moments to identify symmetries and estimate transformations, including rotations and mirror transformations, for objects centered at the frame origin.<n>A comprehensive methodology is developed to obtain these functions in n-dimensional space, specifically moment ( n )-tuples.<n> Extensive validation tests are conducted on both 2D and 3D objects to ensure the robustness and reliability of the proposed approach.
  arXiv  Detail & Related papers  (2026-02-08T00:07:11Z)
• Generalized Linear Mode Connectivity for Transformers [87.32299363530996]
  A striking phenomenon is linear mode connectivity (LMC), where independently trained models can be connected by low- or zero-loss paths.<n>Prior work has predominantly focused on neuron re-ordering through permutations, but such approaches are limited in scope.<n>We introduce a unified framework that captures four symmetry classes: permutations, semi-permutations, transformations, and general invertible maps.<n>This generalization enables, for the first time, the discovery of low- and zero-barrier linear paths between independently trained Vision Transformers and GPT-2 models.
  arXiv  Detail & Related papers  (2025-06-28T01:46:36Z)
• Relative Representations: Topological and Geometric Perspectives [53.88896255693922]
  Relative representations are an established approach to zero-shot model stitching.<n>We introduce a normalization procedure in the relative transformation, resulting in invariance to non-isotropic rescalings and permutations.<n>Second, we propose to deploy topological densification when fine-tuning relative representations, a topological regularization loss encouraging clustering within classes.
  arXiv  Detail & Related papers  (2024-09-17T08:09:22Z)
• R2Det: Exploring Relaxed Rotation Equivariance in 2D object detection [26.05910177212846]
  Group Equivariant Convolution (GConv) empowers models to explore underlying symmetry in data, improving performance.<n>We introduce a novel Relaxed Rotation-Equivariant GConv (R2GConv) with only a minimal increase of $4n$ parameters compared to GConv.<n>Based on R2GConv, we propose a Relaxed Rotation-Equivariant Network (R2Net) as the backbone and develop a Relaxed Rotation-Equivariant Object Detector (R2Det) for 2D object detection.
  arXiv  Detail & Related papers  (2024-08-21T16:32:03Z)
• Partial Symmetry Detection for 3D Geometry using Contrastive Learning with Geodesic Point Cloud Patches [10.48309709793733]
  We propose to learn rotation, reflection, translation and scale invariant local shape features for geodesic point cloud patches. We show that our approach is able to extract multiple valid solutions for this ambiguous problem. We incorporate the detected symmetries together with a region growing algorithm to demonstrate a downstream task.
  arXiv  Detail & Related papers  (2023-12-13T15:48:50Z)
• Oracle-Preserving Latent Flows [58.720142291102135]
  We develop a methodology for the simultaneous discovery of multiple nontrivial continuous symmetries across an entire labelled dataset. The symmetry transformations and the corresponding generators are modeled with fully connected neural networks trained with a specially constructed loss function. The two new elements in this work are the use of a reduced-dimensionality latent space and the generalization to transformations invariant with respect to high-dimensional oracles.
  arXiv  Detail & Related papers  (2023-02-02T00:13:32Z)
• Deep Learning Symmetries and Their Lie Groups, Algebras, and Subalgebras from First Principles [55.41644538483948]
  We design a deep-learning algorithm for the discovery and identification of the continuous group of symmetries present in a labeled dataset. We use fully connected neural networks to model the transformations symmetry and the corresponding generators. Our study also opens the door for using a machine learning approach in the mathematical study of Lie groups and their properties.
  arXiv  Detail & Related papers  (2023-01-13T16:25:25Z)
• Reflection and Rotation Symmetry Detection via Equivariant Learning [40.61825212385055]
  We introduce a group-equivariant convolutional network for symmetry detection, dubbed EquiSym. We present a new dataset, DENse and DIverse symmetry (DENDI), which mitigates limitations of existing benchmarks for reflection and rotation symmetry detection. Experiments show that our method achieves the state of the arts in symmetry detection on LDRS and DENDI datasets.
  arXiv  Detail & Related papers  (2022-03-31T04:18:33Z)
• Using Machine Learning to Detect Rotational Symmetries from Reflectional Symmetries in 2D Images [0.0]
  This paper focuses on aiding the latter by comparing different state-of-the-art automated symmetry detection algorithms. We propose post-processing improvements to find localised symmetries in images, improve the selection of detected symmetries and identify another symmetry type (rotational) We demonstrate and analyze the performance of the extended algorithm to detect localised symmetries and the machine learning model to classify rotational symmetries.
  arXiv  Detail & Related papers  (2022-01-17T19:14:58Z)
• Learning to Discover Reflection Symmetry via Polar Matching Convolution [33.77926792753373]
  We introduce a new convolutional technique, dubbed the polar matching convolution, which leverages a polar feature pooling, a self-similarity encoding, and a kernel design for axes of different angles. The proposed high-dimensional kernel convolution network effectively learns to discover symmetry patterns from real-world images. Experiments demonstrate that our method outperforms state-of-the-art methods in terms of accuracy and robustness.
  arXiv  Detail & Related papers  (2021-08-30T01:50:51Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.