Lunes 08/10/2018, 14:30 hs. Aula 15
Título: Compensated convexity, multiscale medial axis maps, and sharp
regularity of the squared distance function
Resumen:
Compensated convex transforms enjoy tight-approximation and locality
properties that can be exploited to develop multiscale parametrized
methods for identifying singularities in functions. When applied to
the squared distance function to a closed subset of Euclidean space,
these ideas yield a new tool for locating and analyzing the medial
axis of geometric objects called the multiscale medial axis map. This
consists of a parametrized family of nonnegative functions that
provides a Hausdorff-stable multiscale representation of the medial
axis, in particular producing a hierarchy of heights between different
parts of the medial axis depending 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-known stability issue that small
perturbations in an object can produce large variations in the
corresponding medial axis. A sharp regularity result for the squared
distance function is obtained as a by-product of the analysis of this
multiscale medial axis map.
This is joint work with Professor Kewei Zhang (The University of
Nottingham, UK) and Professor Elaine Crooks (Swansea University, UK).
Brief Bio
Antonio Orlando is a Professor of the National University of Tucumán,
Argentina, and an Independent Researcher of the National Argentinian
Research Council CONICET-CCT Tucumán. He read Civil Engineering at the
University of Naples Federico II, Italy, and graduated from the
Imperial College, London, with a Master of Science in Earthquake
Engineering and Structural Dynamics. He read his Ph.D. in
Computational Mechanics at
Swansea University, UK, working on a-posteriori error estimation in
the finite element method under the supervision of Djordje Peric.
After his doctorate, he moved for one year at the Department of
Structural Analysis of the University of Naples Federico II as
Postdoctoral Research Assistant, and then three years as Postdoctoral
Research Scientist at the Institut für Mathematik of the
Humboldt-Universität zu Berlin in Germany, working with Carsten
Carstensen and Andreas Griewank. In Berlin, he was also a member of
the Research Center Matheon Mathematics for Key Technologies. In 2006
he
took the position of Lecturer in Land Surveying and Advanced
Computational Methods at Swansea University and started working with
Kewei Zhang, now at The University of Nottingham, and Elaine Crooks.
In 2010 he joined the Research and Development Project for the
Relocation of Argentinean Researchers, Project 2009 PRH 30, and moved
to the
National University of Tucumán where now he teaches Reconstruction of
Medical Images as part of the Master and Ph.D. Course in Engineering.
Antonio Orlando has published in the field of computational mechanics,
material modelling, and numerical analysis. Particular areas of
expertise include use of the calculus of variations in the modelling
of materials, adaptivity/error estimation of finite element methods,
image processing and applications/numerical
implementation of compensated convexity.