Seminars at the Faculty of Informatics

Approximation of set-valued functions, with applications to reconstruction from cross-sections

The Faculty of Informatics is pleased to announce a guest lecture given by Nira Dyn

DATE: Monday, May 9th 2011
PLACE: USI Università della Svizzera italiana, room SI-13, Informatics building (Via G. Buffi 13)
TIME: 08.30

ABSTRACT:
The talk presents approximation methods for set-valued functions, based on adaptation of sample-based approximation operators for real-valued functions. The adaptation is done by replacing operations between numbers by operations between sets. First we discuss approximation methods in the case that the error is measured in the Hausdorff metric, and give error estimates in terms of the regularity properties of the approximated set-valued function.
Then we present the interpolatory  4-point subdivision scheme, adapted to sets, using a new binary average between sets, designed for the case that the approximation error is measured in the symmetric-difference metric. The application of the latter method to the reconstruction of 3D objects from parallel 2D cross-sections is demonstrated by examples, which indicate the quality of this method.

BIO:
Nira Dyn received the B.Sc. degree in applied mathematics from the Technion and the M.Sc. and Ph.D. degrees in applied mathematics from the Weizmann Institute. She currently is a Professor of applied mathematics at Tel-Aviv University. Her main fields of activity are Geometric Modeling and Approximation Theory. She has authored more than 150 papers and has participated actively in more than 80 conferences and workshops. Prof. Dyn serves on the editorial boards of: Journal of Approximation Theory, Computer Aided Geometric Design, SIAM Journal on Imaging Sciences and is on the advisory board of the journal Foundations of Computational Mathematics.

HOST: Prof. Kai Hormann

URL 1: http://www.inf.usi.ch