Stable length estimates of tube-like shapes

H. Edelsbrunner, F. Pausinger, Journal of Mathematical Imaging and Vision 50 (2014) 164–177.

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Journal Article | Published | English
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Abstract
Motivated by applications in biology, we present an algorithm for estimating the length of tube-like shapes in 3-dimensional Euclidean space. In a first step, we combine the tube formula of Weyl with integral geometric methods to obtain an integral representation of the length, which we approximate using a variant of the Koksma-Hlawka Theorem. In a second step, we use tools from computational topology to decrease the dependence on small perturbations of the shape. We present computational experiments that shed light on the stability and the convergence rate of our algorithm.
Publishing Year
Date Published
2014-09-01
Journal Title
Journal of Mathematical Imaging and Vision
Volume
50
Issue
1
Page
164 - 177
ISSN
IST-REx-ID

Cite this

Edelsbrunner H, Pausinger F. Stable length estimates of tube-like shapes. Journal of Mathematical Imaging and Vision. 2014;50(1):164-177. doi:10.1007/s10851-013-0468-x
Edelsbrunner, H., & Pausinger, F. (2014). Stable length estimates of tube-like shapes. Journal of Mathematical Imaging and Vision, 50(1), 164–177. https://doi.org/10.1007/s10851-013-0468-x
Edelsbrunner, Herbert, and Florian Pausinger. “Stable Length Estimates of Tube-like Shapes.” Journal of Mathematical Imaging and Vision 50, no. 1 (2014): 164–77. https://doi.org/10.1007/s10851-013-0468-x.
H. Edelsbrunner and F. Pausinger, “Stable length estimates of tube-like shapes,” Journal of Mathematical Imaging and Vision, vol. 50, no. 1, pp. 164–177, 2014.
Edelsbrunner H, Pausinger F. 2014. Stable length estimates of tube-like shapes. Journal of Mathematical Imaging and Vision. 50(1), 164–177.
Edelsbrunner, Herbert, and Florian Pausinger. “Stable Length Estimates of Tube-like Shapes.” Journal of Mathematical Imaging and Vision, vol. 50, no. 1, Springer, 2014, pp. 164–77, doi:10.1007/s10851-013-0468-x.
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