Leveraging 3D Geometric Priors in 2D Rotation Symmetry Detection

TL;DR

This work tackles rotation symmetry detection under perspective distortion by introducing a 3D-aware framework that predicts rotation centers, seed vertices, and rotation axes directly in 3D space and then projects them to 2D. A vertex reconstruction module enforces geometric priors (e.g., equal edge lengths and angles) to maintain structural consistency, improving robustness over 2D-only approaches. The method employs camera-centric queries, cross-attention, and a Transformer encoder, trained with set-based RCM and RVM losses in a DETR-like paradigm. Experiments on the DENDI dataset demonstrate state-of-the-art performance for rotation center and vertex detection, with ablations confirming the value of 3D priors. The work suggests that explicit 3D geometry consideration enhances symmetry analysis and has practical implications for 3D-aware scene understanding and object recognition.

Abstract

Symmetry plays a vital role in understanding structural patterns, aiding object recognition and scene interpretation. This paper focuses on rotation symmetry, where objects remain unchanged when rotated around a central axis, requiring detection of rotation centers and supporting vertices. Traditional methods relied on hand-crafted feature matching, while recent segmentation models based on convolutional neural networks detect rotation centers but struggle with 3D geometric consistency due to viewpoint distortions. To overcome this, we propose a model that directly predicts rotation centers and vertices in 3D space and projects the results back to 2D while preserving structural integrity. By incorporating a vertex reconstruction stage enforcing 3D geometric priors -- such as equal side lengths and interior angles -- our model enhances robustness and accuracy. Experiments on the DENDI dataset show superior performance in rotation axis detection and validate the impact of 3D priors through ablation studies.

Figures (11)

• Figure 1: Rotation symmetry detection models and results. (a) 3D detection baseline model without geometric priors, and (b) its qualitative results. (c) Our 3D detection model with geometric priors, and (d) its corresponding qualitative results. The results highlight the benefits of incorporating 3D geometric constraints.
• Figure 2: Overall pipeline. The input image is processed through a backbone and transformer encoder with camera queries. The detection head predicts the 3D rotation center, seed vertex, rotation axis, and symmetry group. The seed vertex is then duplicated according to the predicted symmetry group before the 3D coordinates are projected to 2D.
• Figure 3: Camera Cross Attention. The 3D reference point grids in camera coordinates are projected onto image coordinates to query the backbone image features.
• Figure 4: Overview of the training pipeline. The model employs a two-step bipartite matching process: first, rotation center matching aligns the centers of predictions with ground truth centers, followed by matching the rotation vertices after vertex reconstruction.
• Figure 5: Class distribution of rotational symmetry groups in the DENDI dataset, shown as object counts (log scale) per group. The x-axis shows rotation groups, and the y-axis shows object frequency. Train, validation, and test splits are shown side-by-side.