The Hitchhiker's guide to the galaxy of mathematical tools for shape analysis

A practical guide for researchers who are exploring the new frontiers of 3D shape analysis and managing the complex mathematical tools that most methods rely on. Many research solutions come from advances in pure and applied mathematics, as well as from re-reading classical mathematical theories. Managing these math tools is critical to understanding and solving current problems in 3D shape analysis. This course is designed to help mathematicians and scientists communicate in a world where boundaries between disciplines are (fortunately) blurred, so they can quickly find the right mathematical tools for a bright intuitive idea and strike a balance between theoretical rigor and computationally feasible solutions. The course presents basic concepts in differential geometry and proceeds to advanced topics in algebraic topology, always keeping an eye on their computational counterparts. It includes examples of applications to shape correspondence, symmetry detection, and shape retrieval that show how these mathematical concepts can be translated into practical solutions.