TY - JOUR
AU - Janacek, Jiri
AU - Jirak, Daniel
PY - 2019/12/13
Y2 - 2024/06/13
TI - Variance of the Isotropic Uniform Systematic Sampling
JF - Image Analysis and Stereology
JA - Image Anal Stereol
VL - 38
IS - 3
SE - Original Research Paper
DO - 10.5566/ias.2218
UR - https://ias-iss.org/ojs/IAS/article/view/2218
SP - 261-267
AB - <p>The integral of a smooth function with bounded support over a set with finite perimeter in Euclidean space ℝ<sup><em>d</em></sup> 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 <em>d</em>+1. Our result generalizes the Kendall-Hlawka-Matheron formula for the variance of the isotropic uniform systematic estimator of volume.</p>
ER -