【Mathathon2】Image comparison and scaling via nonlinear elasticity

Speaker:  Sir John Ball

Heriot-Watt University and Maxwell Institute for Mathematical Sciences, Edinburgh

Abstract

A nonlinear elasticity model for comparing images is formulated and analyzed, in which optimal transformations between images are sought as minimizers of an integral functional. The existence of minimizers in a suitable class of homeomorphisms between image domains is established under natural hypotheses, and the question of whether for linearly related images the minimization algorithm delivers the linear transformation as the unique minimizer is discussed. This is joint work with Chris Horner.

Profile:

Sir John Macleod Ball, FRS, FRSE is a former Sedleian Professor of Natural Philosophy at the University of Oxford. He is currently a Professor of Heriot-Watt University and Maxwell Institute of Mathematical Sciences, Edinburgh. He is a  President of Royal Society of Edinburgh. John Ball was knighted in the New Year Honours list for 2006 "for services to Science". He is a member of the Norwegian Academy of Science and Letters and a fellow of the American Mathematical Society. From 1996 to 1998 he was president of the London Mathematical Society, and from 2003 to 2006 he was president of the International Mathematical Union, IMU. John Ball is a recepient of  Theodore von Kármán Prize in 1999 (along with Stuart Antman). In 2018, he received the King Faisal International Prize in Mathematics. He was a member of the first Abel Prize Committee in 2002, and for the Fields Medal Committee in 1998. 

John Ball's main research areas lie in  the calculus of variations, nonlinear partial differential equations, infinite-dimensional dynamical systems and their applications to nonlinear mechanics. In solid mechanics, he is especially interested in the mathematics of microstructure arising from phase transformations in solids, using models based on nonlinear elasticity, where the problem of predicting microstructure morphology is related to deep unsolved questions of the multi-dimensional calculus of variations such as understanding quasiconvexity. A more recent research interest is in the mathematics of liquid crystals.