Shai Kels (School of mathematical sciences, Applied math, Tel Aviv Univ.)
Sunday, 27.12.2009, 13:00
We introduce a new geometric definition of affine combinations of two
compact subsets of R^n.
The 4-point interpolatory subdivision schemes for points is adapted to
sets, by first expressing the insertion rule in terms of repeated binary
averages, and then replacing these affine
combinations of pairs of points by the new affine combinations of sets.
This subdivision scheme is applied to the reconstruction of
objects from cross-sections.
We address the questions of convergence and approximation order of this new
set-valued subdivision scheme and present several computational examples.