Ph.D. course on the Functional Maps framework and its use in the problem of shape correspondence.

Course Abstract

This PhD course is organised as a series of seminars focused on modern approaches to geometric data processing and shape analysis, with an emphasis on spectral methods and learning-based solutions. Beginning with an introduction to the fundamentals of geometric data and spectral geometry, the course will explore the challenges of shape matching and registration, particularly through the lens of the functional maps framework, a powerful paradigm that has transformed how correspondences between 3D shapes are estimated. Subsequent lectures will delve into deep functional maps and data-driven techniques that leverage modern machine learning architectures to enhance shape understanding and registration. Finally, broader applications of functional map-based methods in areas such as graph analysis and exploration of maps between embedding spaces highlight open problems and research directions in this evolving field.