VARIANCE OF THE ISOTROPIC UNIFORM SYSTEMATIC SAMPLING

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

Image Analysis & Stereology Pub Date : 2019-12-13 DOI:10.5566/ias.2218

J. Janáček, D. Jirák

引用次数: 1

Abstract

The integral of a smooth function with bounded support over a set with finite perimeter in Euclidean space ℝ d is estimated using a periodic grid in an isotropic uniform random position. Extension term in the estimator variance is proportional to the integral of the squared modulus of the function over the object boundary and to the grid scaling factor raised to the power of d +1. Our result generalizes the Kendall-Hlawka-Matheron formula for the variance of the isotropic uniform systematic estimator of volume.

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各向同性均匀系统抽样的方差

利用周期网格在各向同性均匀随机位置上估计了欧几里德空间中有限周长集合上具有有界支持的光滑函数的积分。估计量方差中的扩展项与函数在目标边界上的平方模量的积分和网格缩放因子的d +1次方成正比。我们的结果推广了体积各向同性均匀系统估计量方差的Kendall-Hlawka-Matheron公式。

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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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.