Segmenting dot patterns by voronoi diagram concavity

Area of Science:

• Computational geometry
• Image analysis
• Pattern recognition

Background:

• Voronoi diagrams and Delaunay triangulations are fundamental structures in computational geometry.
• Segmentation of dot patterns is crucial for various applications in image analysis and data visualization.
• Existing methods may face challenges in accurately delineating complex or overlapping patterns.

Purpose of the Study:

• To define and utilize a novel metric, "internal concavity," for analyzing dot patterns.
• To develop and describe an algorithm for segmenting dot patterns based on internal concavity.
• To demonstrate the algorithm's ability to produce meaningful subsets of the Dirichlet tessellation.

Main Methods:

• Definition of a signed distance function termed "internal concavity" applied to Voronoi diagram paths.
• Development of a segmentation algorithm leveraging the internal concavity metric.
• Application of the algorithm to segment dot patterns and their corresponding Dirichlet tessellations.

Main Results:

• Successful definition of the internal concavity metric for dot pattern analysis.
• Implementation of a novel algorithm for dot pattern segmentation.
• Generation of segmented subsets of the Dirichlet tessellation (Delaunay triangulation) based on the algorithm's output.

Conclusions:

• Internal concavity provides a robust measure for segmenting dot patterns.
• The described algorithm offers an effective approach for pattern segmentation and analysis.
• The method successfully links pattern segmentation to the underlying geometric structures of Delaunay triangulations.