Learning-Based Intrinsic Reflectional Symmetry Detection

Area of Science:

• Computer Vision
• Computational Geometry
• Machine Learning

Background:

• Reflectional symmetry is prevalent in natural objects.
• Existing symmetry detection methods are computationally expensive and prone to randomness.

Purpose of the Study:

• To develop a faster and more robust learning-based approach for intrinsic reflectional symmetry detection.
• To overcome the limitations of voting and sampling in symmetry detection.

Main Methods:

• Parametrizing symmetry using a functional map matrix derived from Laplacian eigenfunction signs.
• Training a neural network to predict eigenfunction signs for symmetry.
• Converting the manifold-based problem to the functional domain for global property learning.

Main Results:

• The proposed method achieves over 20x speed improvement compared to state-of-the-art techniques.
• Demonstrated robustness on shapes with complex topologies and holes.
• Achieved higher correspondence accuracy, outperforming existing methods.

Conclusions:

• The learning-based functional map approach offers a significant advancement in intrinsic reflectional symmetry detection.
• The method generalizes well to new shapes and is invariant to eigenfunction perturbations.
• This approach provides a robust and efficient solution for identifying symmetry in challenging 3D shapes.