Computing optimal homotopies

Erin Wolf Chambers, Saint Louis University

Date and time: 2pm (New York time), Tuesday, December 8, 2020

Place: On Zoom (details provided on the seminar mailing list)

The question of how to measure similarity between curves in various settings has received much attention recently, motivated by applications in GIS data analysis, medical imaging, and computer graphics. Geometric measures such as Hausdorff and Fr├ęchet distance have efficient algorithms, but often are not desirable since they do force any deformation based on them to move continuously in the ambient space. In this talk, we'll consider measures that instead are based on a homotopy between the two curves. Such deformations will generally look to minimize some quantity associated with the homotopy, such as total area swept or longest intermediate curve. We will survey several measures based on homotopy which have been introduced and studied in recent years, examining structural properties as well as considering the complexity of the problem or known algorithms to compute it. We will also give an overview of the many remaining open questions connected to this area.