ARD-REFSM: Enhancing Reflection Symmetry Detection with Asymmetric Denoising and Rotation Equivariance
Authors: Dongfu Yin, Rourou Su, Cong Zhao, Fei Yu
Organizations: Guangdong Laboratory of Artificial Intelligence and Digital Economy(SZ), Shenzhen, China · College of Computer Science and Software Engineering, Shenzhen University, China · Department of Biomedical Engineering, Southern University of Science and Technology, China · School of Information Technology, Carleton University, Canada
Reflection symmetry detection remains challenging due to interference from asymmetric regions and arbitrary orientations of symmetric patterns. Asymmetric regions introduce background clutter that disrupts symmetric pattern matching, whereas conventional convolutional neural networks lack rotation equivariance, leading to inconsistent feature representations under rotational transformations. To address these issues, we propose an Asymmetric Region Denoising (ARD) module and a Rotation Equivariant Feature Similarity Matching (REFSM) module. The ARD module suppresses asymmetric interference to refine symmetric patterns, while the REFSM module enhances rotation equivariance through feature similarity matching between original and rotated images. Specifically, our dual-input REFSM framework leverages rotation loss to maximize consistency between the score maps of original and rotated images, thereby enabling precise prediction of rotation-equivariant symmetry axes. Furthermore, we introduce GMSYM, a new benchmark dataset that categorizes images into diverse scenarios and incorporates various interferences to address the limitations of existing reflection symmetry detection benchmarks. Extensive experiments on four standard datasets (DENDI, NYU, LDRS, SDRW) and our proposed GMSYM dataset demonstrate that our method achieves state-of-the-art performance in both accuracy and robustness.
Symmetry detection is a fundamental problem in computer vision, and symmetries serve as powerful priors for downstream tasks. However, existing learning-based methods for detecting 3D symmetries from single images have been almost exclusively trained and evaluated on object-centric or synthetic datasets, and thus fail to generalize to real-world scenes. Furthermore, due to the inherent scale ambiguity of monocular inputs, which makes localizing the 3D plane an ill-posed problem, many existing works only predict the plane's orientation. In this paper, we address these limitations by presenting the first framework for detecting 3D-grounded reflectional symmetries from single, in-the-wild RGB images, focusing on architectural landmarks. We introduce two key innovations: (1) a scalable data annotation pipeline to automatically curate a large-scale dataset of architectural symmetries, ArchSym, from SfM reconstructions by leveraging cross-view image matching; and building on the dataset, (2) a single-view symmetry detector that accurately localizes symmetries in 3D by parameterizing them as signed distance maps defined relative to predicted scene geometry. We validate our symmetry annotation pipeline against geometry-based alternatives and demonstrate that our symmetry detector significantly outperforms state-of-the-art baselines on our new benchmark.
Reflections of water pose a significant challenge for computer vision systems, as standard deep learning models frequently confuse objects with their mirror images, producing spurious false positives and negatives in tasks such as object detection and semantic segmentation. As a result, detecting reflection axes in natural-water scenes is pivotal for reliable object detection and scene understanding. To mitigate this issue, we leverage the intrinsic imperfect reflective symmetry of water and introduce a Symmetry-Aware Water Reflection Detection Network, namely, SAWRD-Net, that couples dihedral group-equivariant convolutions with a matrix-decomposition decoder in an end-to-end framework. First, dihedral group convolutional layers extract geometry-consistent feature maps that explicitly encode both rotational and mirror symmetries. A Multi-scale Reflection Equivariant block then aggregates features across scales and employs a symmetric-attention mechanism to highlight reflection-relevant regions. The proposed matrix-decomposition decoder factorizes high-dimensional features into compact low-rank parameter and confidence spaces, after which the network directly regresses keypoints on the reflection axis. Then a robust principal component analysis fits the final axis. Evaluated on the largest available water reflection scene data set, SAWRD-Net achieves a true-positive rate of 0.890 against human annotations, outperforming all existing water reflection detectors.
Quantifying how mirror-symmetric an image is about a given axis (symmetry scoring) underpins applications from visual aesthetics to medical imaging, yet proposed scoring methods have never been compared on a common, statistically grounded protocol. We benchmark 13 scoring methods (nine collected from literature, four introduced here) spanning from classical features to frozen deep features, across four single-axis and five multi-axis datasets under a reflection-exact protocol with a chance-anchored, significance-tested discrimination skill. Deep backbones perform best on single-axis and harder multi-axis protocols. However, a classical histogram-of-oriented-gradients (HOG) descriptor trails the best frozen-network readout by a small (but significant) margin, is not statistically separable from the runner-up (a CNN-filter measure), and runs ~300x faster on CPU. Our results show that discrimination concentrates in mid-scale oriented features, where deep backbones peak at a low or mid stage, and HOG peaks at a mid cell size. Among existing methods, frozen deep features thus offer little over a tuned classical descriptor for measuring symmetry; whether task-trained deep scorers can do better remains open. We release the scorers and harness in imgsym, an open toolkit for image symmetry detection and measurement.