Compensated convex transforms enjoy tight-approxim ation and locality properties that can be exploite d to develop multiscale\, parametrised methods for identifying singularities in functions. When appl ied to the squared distance function to a closed s ubset of Euclidean space\, these ideas yield a new tool for locating and analyzing the medial axis o f geometric objects\, called the multiscale medial axis map. This consists of a parametrised family of nonnegative functions that provides a Hausdorff -stable multiscale representation of the medial ax is\, in particular producing a hierarchy of height s between different parts of the medial axis depen ding on the distance between the generating points of that part of the medial axis. Such a hierarchy enables subsets of the medial axis to be selected by simple thresholding\, which tackles the well-k nown stability issue that small perturbations in a n object can produce large variations in the corre sponding medial axis. A sharp regularity resu lt f or the squared distance function is obtained as a by-product of the analysis of this multiscale medi al axis map.

This is joint work with Kewei Zhang (Nottingham) and Antonio Orlando (Tuc uman). \; LOCATION:Seminar Room 1\, Newton Institute CONTACT:info@newton.ac.uk END:VEVENT END:VCALENDAR