TY - JOUR
AU - van der Jagt, Thomas
AU - Jongbloed, Geurt
AU - Vittorietti, Martina
PY - 2023/10/27
Y2 - 2024/06/25
TI - Existence and Approximation of Densities of Chord Length- and Cross Section Area Distributions
JF - Image Analysis and Stereology
JA - Image Anal Stereol
VL - 42
IS - 3
SE - Original Research Paper
DO - 10.5566/ias.2923
UR - https://www.ias-iss.org/ojs/IAS/article/view/2923
SP - 171-184
AB - <p>In various stereological problems a <em>n</em>-dimensional convex body is intersected with an (<em>n−</em>1)-dimensional Isotropic Uniformly Random (IUR) hyperplane. In this paper the cumulative distribution function associated with the (<em>n−</em>1)-dimensional volume of such a random section is studied. This distribution is also known as chord length distribution and cross section area distribution in the planar and spatial case respectively. For various classes of convex bodies it is shown that these distribution functions are absolutely continuous with respect to Lebesgue measure. A Monte Carlo simulation scheme is proposed for approximating the corresponding probability density functions.</p>
ER -