Computing Optimal Homotopies

Explore the concept of measuring curve similarity through optimal homotopies in this 47-minute lecture. Delve into geometric measures like Hausdorff and Fr\'echet distance, and discover why homotopy-based deformations are often preferred in applications such as GIS data analysis, medical imaging, and computer graphics. Survey various homotopy-based measures, examining their structural properties and computational complexities. Gain insights into recent algorithms and open questions in this field, covering topics such as topology, discrete homotopy, combinatorial problems, graph height, and homotopy height. Learn about the challenges and potential applications of computing optimal homotopies in diverse scientific domains.