Estimating the surface area of nonconvex particles from central planar sections

• Published in: Journal of microscopy (Oxford) Vol. 255; no. 1; pp. 49 - 64
• Main Authors: THÓRISDÓTTIR, Ó., RAFATI, A.H., KIDERLEN, M.
• Format: Journal Article
• Language: English
• Published: England Wiley Subscription Services, Inc 01.07.2014
• Subjects: Area tangent count; Atoms & subatomic particles; Estimating; Estimators; invariator principle; local stereology; Microscopy; Morse‐type surface area estimator; Planes; Sampling; Stereology; Surface area; Three dimensional; surface area; invariator principle; Morse-type surface area estimator; local stereology; Area tangent count
• ISSN: 0022-2720; 1365-2818
• DOI: 10.1111/jmi.12136

Summary In this paper, we present a new surface area estimator in local stereology. This new estimator is called the ‘Morse‐type surface area estimator’ and is obtained using a two‐stage sampling procedure. First a plane section through a fixed reference point of a three‐dimensional structure is taken. In this section plane, a modification of the area tangent count method is used. The Morse‐type estimator generalizes Cruz‐Orive's pivotal estimator for convex objects to nonconvex objects. The advantages of the Morse‐type estimator over existing local surface area estimators are illustrated in a simulation study. The Morse‐type estimator is well suited for computer‐assisted confocal microscopy and we demonstrate its practicability in a biological application: the surface area estimation of the nuclei of giant‐cell glioblastoma from microscopy images. We also present an interactive software that allows the user to efficiently obtain the estimator.