Detecting Cocircular Subsets of a Spherical Set of Points

Area of Science:

• Computational geometry
• Computer vision
• Geographic information systems

Background:

• Detecting circular patterns in spherical data is challenging due to unique geometric constraints.
• Existing methods may not adequately address the complexities of spherical parameter spaces.

Purpose of the Study:

• To develop and evaluate algorithms for detecting cocircular points on a sphere.
• To distinguish between great circles and small circles in spherical datasets.
• To address parameter-space quantization issues inherent in spherical geometry.

Main Methods:

• Extension of the Hough transform for spherical data analysis.
• Development of novel quantization schemes to handle spherical parameter space.
• Evaluation of quantization-induced errors.

Main Results:

• Successful detection of cocircularities for both great and small circles on a spherical surface.
• Demonstration of algorithms using real-world data, such as cities and airports on Earth.
• Quantification and analysis of errors associated with spherical quantization.

Conclusions:

• The proposed algorithms provide an effective solution for detecting cocircularities in spherical images.
• The methods are applicable to various fields, including geographic data analysis and computer vision.
• This work advances the understanding and computational treatment of circular features in spherical geometry.