Approximation and Convergence of the First Intrinsic Volume

Tuesday, March 4, 2014 - 10:15am - 11:05am
Keller 3-180
Herbert Edelsbrunner (Institute of Science and Technology Austria (IST))
The Steiner polynomial of a solid body in R^d is of degree d
and describes the volume as a function of the thickening parameter
(parallel body). There are d+1 coefficients which are used to define
the d+1 intrinsic volumes of the solid body. In d=2 dimensions,
the first intrinsic volume is the length, and in d=3 dimensions,
it is the total mean curvature of the boundary. Using an integral
geometric approach, we modify the formula using persistent moments
to get a measure for approximating bodies that converges to the first
intrinsic volume of the solid body.
MSC Code: