The ellipsoid factor for quantification of rods, plates, and intermediate forms in 3D geometries

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal

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Original languageEnglish
Article number15
Journal / PublicationFrontiers in Endocrinology
Online published16 Feb 2015
Publication statusPublished - Feb 2015
Externally publishedYes



The ellipsoid factor (EF) is a method for the local determination of the rod- or plate-like nature of porous or spongy continua. EF at a point within a 3D structure is defined as the difference in axis ratios of the greatest ellipsoid that fits inside the structure and that contains the point of interest, and ranges from -1 for strongly oblate (discus-shaped) ellipsoids, to +1 for strongly prolate (javelin-shaped) ellipsoids. For an ellipsoid with axes abc, EF = a/b - b/c. Here, EF is demonstrated in a Java plugin, "Ellipsoid Factor" for ImageJ, distributed in the BoneJ plugin collection. Ellipsoid Factor utilizes an ellipsoid optimization algorithm, which assumes that maximal ellipsoids are centered on the medial axis, then dilates, rotates, and translates slightly each ellipsoid until it cannot increase in volume any further. EF successfully identifies rods, plates, and intermediate structures within trabecular bone, and summarizes the distribution of geometries with an overall EF mean and SD, EF histogram, and Flinn diagram displaying a/b versus b/c. EF is released to the community for testing, use, and improvement.

Research Area(s)

  • Maximally inscribed ellipsoid, Optimization, Plate, Rod, Segmentation, Tb.EF

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