A unifying approach to moment-based shape orientation and symmetry classification

Area of Science:

• Computer Vision
• Image Analysis
• Pattern Recognition

Background:

• Traditional moment-based methods for shape analysis face limitations, particularly with accurate shape centroid estimation.
• Existing geometric moment functions require generalization for robust orientation and symmetry classification.

Purpose of the Study:

• To jointly address shape orientation and symmetry classification using a generalized moment-based approach.
• To develop a robust frequency domain method for feature extraction, overcoming spatial domain limitations.

Main Methods:

• Generalization and modification of state-of-the-art geometric moment-based functions.
• Fourier series analysis to investigate function properties and derive closed-form solutions.
• Frequency domain analysis using polar Fourier representation of image complex gradients and subspace analysis for periodicity detection.

Main Results:

• A unifying framework for shape orientation and symmetry detection is established.
• A novel frequency domain approach provides robust moment-based feature sets.
• The proposed method eliminates the need for precise shape centroid estimation, a key limitation of prior work.

Conclusions:

• The developed framework offers a significant advancement in shape analysis, unifying orientation and symmetry detection.
• The frequency domain method demonstrates improved performance and robustness compared to existing state-of-the-art techniques.