Stereological determination of the second moment of mean curvature

Abstract

In this note smooth surface processes and their sections with planes are considered. A formula is given which enables the determination of the second moment M² of the mean curvature in a “typical” surface point by using the second moment k² of curvature in a “typical” fibre point in the section plane and the mean Gaussian curvature G. It is a generalisation of a formula given by SALTYKOV Methods for the statistical estimation of k² are suggested

AMS 1980 subject classification:

• Primary 60D05
• secondary 52A15

Keywords:

• Stereology
• mean curvature
• second–order moment