A Contrario 2D Point Alignment Detection.

Area of Science:

• Computer Vision
• Computational Geometry
• Pattern Recognition

Background:

• Automatic alignment detection in 2D point sets remains a challenging problem despite various attempts.
• Existing methods often struggle with complex point distributions and require significant parameter tuning.

Purpose of the Study:

• To develop a robust and accurate method for automatic alignment detection in 2D point sets.
• To integrate multiple detection criteria into a unified probabilistic framework.
• To provide a reproducible solution with open-source code and an online demo.

Main Methods:

• A novel alignment detection algorithm based on four interlaced criteria: texture masking, relative bilateral local density, internal regularity, and redundancy reduction.
• Extension of the a contrario detection theory using sophisticated conditional events on random point sets.
• Development of a single probabilistic a contrario model with a user-defined false alarm rate.
• Incorporation of a new formulation of the Gestalt theory's exclusion principle to prevent redundant detections.

Main Results:

• The proposed method demonstrates mathematical consistency through derived bounds for conditional event expectations.
• The algorithm effectively integrates multiple criteria into a unified probabilistic model.
• Experimental comparisons show the method's performance against three state-of-the-art algorithms.
• Successful application to real-world data is discussed, highlighting practical utility.

Conclusions:

• The developed method offers a significant advancement in automatic alignment detection for 2D point sets.
• The probabilistic a contrario model provides a flexible and powerful framework for this task.
• The inclusion of Gestalt principles enhances detection accuracy and reduces redundancy.
• The provided resources promote reproducibility and further research in the field.