This three-part talk explores the key role of discrete distribution of circles in practical applications. Through interconnected themes, we will revisit foundational tools and introduces techniques to analyze, synthesize, and design circle configurations. Applications span across disciplines, with a focus on scenarios where geometric intuition and computational insights converge.
Circles as Weighted Points: Power Distance, Generalized Voronoi, and Beyond
The first part builds on the representation of circles as weighted points and introduces the power distance as a central concept. Generalized Voronoi diagrams, derived from these principles, are presented with applications in triangle mesh optimization, as well as molecular biology, where spatial relationships among circular entities provide valuable insights.
Statistical Analysis and Synthesis of Circle Distributions
This section addresses the statistical analysis of circle distributions, transitioning seamlessly to example-based synthesis methods. We will explore how point patterns inspire the design of circle configurations, supported by computational tools for interactive editing and adaptive refinement. Applications of texture synthesis through light learning for medical data augmentation, specifically for 2D histological data, are discussed as a promising future direction.
Circle Packing and Conformal Geometry: Toward Applications in Medical Imaging
The final part highlights circle packing and its deep connections to conformal geometry, emphasizing the role of tangency configurations. Applications are illustrated across various domains, including medical imaging—for instance, in the characterization and classification of cortical surfaces—or clustering data sets with circular structures in cell biology.