Stereological estimation of integral mixed curvature with application

This article addresses a bounded system of compact smooth surfaces in three-dimensional space. Recently, an unbiased estimator of the integral mixed curvature of the given system based on a vertical sampling design has been proposed. The aims of the present paper are: (i) to show that the proposed estimator may have an infinite variance; (ii) to suggest a modification that has better statistical properties; (iii) to extend the point estimator to a function that monitors the curvature along the gradient microstructures; (iv) to present an application of the method to real microscopic images.