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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Reconstruction of a 3D object from a finite number
of its 1D parallel cross-sections - Nira Dyn (T
el Aviv University)
DTSTART;TZID=Europe/London:20190509T140000
DTEND;TZID=Europe/London:20190509T150000
UID:TALK124909AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/124909
DESCRIPTION:The problem of reconstruction of a 3D object
from its parallel 2D cross sections has been
considered by many researchers. In some previous w
orks we suggested to regard the problem as an appr
oximation of a set-valued function from a finite n
umber of its samples\, which are 2D sets. We used
approximation methods for single-valued functions
by applying operations between sets instead of ope
rations between numbers.
Since 2D sets are muc
h more complicated than 1D sets\, we suggest here
to regard 3D objects as bivariate  \;functions
 \;with 1D sets as samples\, and to use the a
nalogue of piecewise linear interpolation on a tri
angulation as the approximation method.
In thi
s talk we present our method\, and discuss the pro
perties of the resulting interpolants\, including
continuity and approximation rates. Few examples w
ill be presented.
LOCATION:Seminar Room 2\, Newton Institute
CONTACT:INI IT
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