用成核点和晶格点估算体积

IF 0.8 4区计算机科学 Q4 IMAGING SCIENCE & PHOTOGRAPHIC TECHNOLOGY

Image Analysis & Stereology Pub Date : 2019-07-18 DOI:10.5566/IAS.2012

Domingo Gómez-Pérez, Javier González-Villa, Florian Pausinger

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引用次数: 0

摘要

核子是一种估计粒子体积的方法，即一个紧子集，在立体学中得到了广泛的应用。它基于几何抽样，并且是无偏的。然而，该估计量的方差预测是非平凡的，并且依赖于底层抽样方案。我们从拟蒙特卡罗积分中提出了完善的工具来解决这个问题。特别是，我们展示了如何将再现核希尔伯特空间的理论用于方差预测，以及如何使用格点(或类格点)减少基于核子思想的估计量的方差。我们用不同的例子来说明和测试我们的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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ESTIMATION OF VOLUME USING THE NUCLEATOR AND LATTICE POINTS

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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来源期刊

Image Analysis & Stereology MATERIALS SCIENCE, MULTIDISCIPLINARY-MATHEMATICS, APPLIED

CiteScore

2.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Image Analysis and Stereology is the official journal of the International Society for Stereology & Image Analysis. It promotes the exchange of scientific, technical, organizational and other information on the quantitative analysis of data having a geometrical structure, including stereology, differential geometry, image analysis, image processing, mathematical morphology, stochastic geometry, statistics, pattern recognition, and related topics. The fields of application are not restricted and range from biomedicine, materials sciences and physics to geology and geography.