Approximation and Convergence of the First Intrinsic Volume

The Steiner polynomial of a solid body in $R^n$ is of degree $n$ and describes the volume as a function of the thickening parameter (parallel body). The coefficient of the degree-$i$ term is used to define the $(n-i)$-th intrinsic volume. Using an integral geometric approach, we modify the Crofton formula using persistent moments to get a measure for approximating bodies that converges to the intrinsic volume of the solid body. We have a proof of convergence for $n-i = 1$.

Work with Florian Pausinger.

Presentation Slides: PDF

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