Axis-level Symmetry Detection with Group-Equivariant Representation
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909846712877056 |
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| author | Yu, Wongyun Seo, Ahyun Cho, Minsu |
| author_facet | Yu, Wongyun Seo, Ahyun Cho, Minsu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_10740 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Axis-level Symmetry Detection with Group-Equivariant Representation Yu, Wongyun Seo, Ahyun Cho, Minsu Computer Vision and Pattern Recognition 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. |
| title | Axis-level Symmetry Detection with Group-Equivariant Representation |
| topic | Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2508.10740 |