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SUMMARY:Compensated convexity\, multiscale medial axis maps\, and sharp re
 gularity of the squared distance function - Elaine Crooks (Swansea Univers
 ity)
DTSTART:20171215T100000Z
DTEND:20171215T110000Z
UID:TALK96667@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:<span>Co-authors: Kewei Zhang		(University of Nottingham\, UK)
 \, Antonio Orlando		(Universidad Nacional de Tucuman\, Argentina)        <
 br></span><br>Compensated convex transforms enjoy tight-approximation and 
 locality properties that can be exploited to develop multiscale\, parametr
 ised methods for identifying singularities in functions. When applied to t
 he squared distance function to a closed subset of Euclidean space\, these
  ideas yield a new tool for locating and analyzing the medial axis of geom
 etric objects\, called the multiscale medial axis map. This consists of a 
 parametrised family of nonnegative functions that provides a Hausdorff-sta
 ble multiscale representation of the medial axis\, in particular producing
  a hierarchy of heights between different parts of the medial axis dependi
 ng on the distance between the generating points of that part of the media
 l axis. Such a hierarchy enables subsets of the medial axis to be selected
  by simple thresholding\, which tackles the well-known stability issue tha
 t small perturbations in an object can produce large variations in the cor
 responding medial axis. A sharp regularity resu lt for the squared distanc
 e function is obtained as a by-product of the analysis of this multiscale 
 medial axis map. <br><span><br>This is joint work with Kewei Zhang (Nottin
 gham) and Antonio Orlando (Tucuman).&nbsp\;</span>
LOCATION:Seminar Room 1\, Newton Institute
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