ArchSym: Detecting 3D-Grounded Architectural Symmetries in the Wild
Authors: Hanyu Chen, Ruojin Cai, Steve Marschner, Noah Snavely
Organizations: Cornell University · Kempner Institute, Harvard University
Abstract
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.
Detecting partial extrinsic symmetry in 3D geometry is a fundamental yet persistent challenge in computer vision and graphics, critical for tasks ranging from shape completion to procedural generation. Classical transformation-space voting methods rely on pairwise matching, scaling as O(n^2) and struggling to resolve coherent multi-instance groups. Recent learning approaches advance global symmetry detection but restrict the solution space to reflection planes, failing to capture rotational or translational repetitions such as the legs of a chair or the steps of a staircase. We propose SymCL, a self-supervised contrastive learning framework that detects partial symmetries across rotation, translation, and reflection (with scale-invariant features) and requires no ground truth annotations. By mapping local geodesic patches to a latent space invariant to the Euclidean group, we reformulate symmetry detection as a density-based clustering problem, enabling the simultaneous discovery of multi-instance symmetric relationships in a single forward pass. We evaluate quantitatively on SymPartNet, a new benchmark annotating all PartNet categories with partial symmetry relations, and demonstrate class-agnostic generalization qualitatively on everyday objects outside the training distribution.
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.
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.