The Medial Axis - Image Analysis, Homological Simplification, Gerrymandering

Explore the diverse applications of the medial axis in a comprehensive lecture covering image segmentation, shape simplification, and gerrymandering detection. Delve into three distinct research areas: learn about a novel method for segmenting objects in natural images by extracting and combining medial axis fragments; discover a geometrically satisfying approach to the homological simplification problem for shapes using the medial axis; and examine a new measure for identifying gerrymandered congressional districts based on shape depth defined on the medial axis. Gain insights into collaborative research efforts and cutting-edge applications of algebraic topology in image analysis, shape processing, and political geography.