Computing Optimal Homotopies

Explore the concept of measuring similarity between curves in various settings through this 59-minute lecture by Erin Chambers. Delve into the motivations behind this topic, including applications in GIS data analysis, medical imaging, and computer graphics. Examine geometric measures like Hausdorff and Fréchet distance, and understand their limitations in continuous deformation. Investigate homotopy-based measures that minimize quantities such as total area swept or longest intermediate curve. Survey various geometric and topological measures introduced in recent years, analyzing their structural properties and computational complexity. Gain insights into known algorithms for computing these measures and discover the numerous open questions remaining in this field of study.