ESTIMATION OF VOLUME USING THE NUCLEATOR AND LATTICE POINTS

Authors

  • Domingo Gomez-Perez University of Cantabria
  • Javier Gonzalez-Villa University of Cantabria
  • Florian Pausinger Queen's University Belfast

DOI:

https://doi.org/10.5566/ias.2012

Keywords:

nucleator, Quasi-Monte Carlo integration, stereology, variance prediction

Abstract

The nucleator is a method to estimate the volume of a particle, i.e. a compact subset of ℝ3, which is widely used in Stereology. It is based on geometric sampling and known to be unbiased. However, the prediction of the variance of this estimator is non-trivial and depends on the underlying sampling scheme.

We propose well established tools from quasi-Monte Carlo integration to address this problem. In particular, we show how the theory of reproducing kernel Hilbert spaces can be used for variance prediction and how the variance of estimators based on the nucleator idea can be reduced using lattice (or lattice-like) points. We illustrate and test our results on various examples.

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Published

2019-07-18

How to Cite

Gomez-Perez, D., Gonzalez-Villa, J., & Pausinger, F. (2019). ESTIMATION OF VOLUME USING THE NUCLEATOR AND LATTICE POINTS. Image Analysis and Stereology, 38(2), 141–150. https://doi.org/10.5566/ias.2012

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Original Research Paper

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