# 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.

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:

28A33

Keywords: