Leveraging 3D Geometric Priors in 2D Rotation Symmetry Detection

2025-03-26

AI Summary

This paper addresses the problem that rotation symmetry detection in 2D images suffers from viewpoint distortion, leading to 3D geometric inconsistency. To tackle this, we propose the first end-to-end differentiable framework explicitly embedding 3D geometric priors—namely, equal edge lengths and equal interior angles. Our method models symmetry via 3D vertex regression followed by orthogonal projection, explicitly enforcing structural consistency of both the rotation center and supporting vertices in 3D space. A geometry-aware loss function jointly optimizes these constraints. Unlike purely 2D modeling approaches, our framework ensures geometric integrity from the outset. On the DENDI dataset, our method achieves a substantial improvement in rotation axis detection average precision (AP) over state-of-the-art methods. Ablation studies quantify the contribution of the 3D geometric priors at +12.7% AP, demonstrating their effectiveness in mitigating performance degradation induced by viewpoint distortion.

Technology Category

• Computer Vision: 3D Computer Vision
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Machine Learning: Learning with Manifolds

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Data transparency and provenance
• Responsible Web: Consent frameworks and practices on the web

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.

Problem

• Detect 2D rotation symmetry using 3D geometric priors
• Improve accuracy in identifying rotation centers and vertices
• Address viewpoint distortions in symmetry detection models

Innovation

• Predicts 3D rotation centers and vertices
• Projects 3D results to 2D preserving integrity
• Enforces 3D geometric priors for accuracy