Abstract
We introduce a modification of the classic notion of intrinsic volume using persistence moments of height functions. Evaluating the modified first intrinsic volume on digital approximations of a compact body with smoothly embedded boundary in Rn, we prove convergence to the first intrinsic volume of the body as the resolution of the approximation improves. We have weaker results for the other modified intrinsic volumes, proving they converge to the corresponding intrinsic volumes of the n-dimensional unit ball.
Original language | English |
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Pages (from-to) | 674-703 |
Journal | Advances in Mathematics |
Volume | 287 |
Early online date | 20 Nov 2015 |
DOIs | |
Publication status | Early online date - 20 Nov 2015 |
Externally published | Yes |
Keywords
- Crofton formula
- Digital image processing
- Distorted normals
- Intrinsic volume
- Persistent homology
ASJC Scopus subject areas
- General Mathematics
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Florian Pausinger
- School of Mathematics and Physics - Visiting Scholar
- Mathematical Sciences Research Centre
Person: Academic