The Ellipsoid Factor for Quantification of Rods, Plates, and Intermediate Forms in 3D Geometries - Doube, Michael (Frontiers in Endocrinology, 2015)
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 which fits inside the structure and which 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 a ≤ b ≤ c, 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 utilises an ellipsoid optimisation algorithm which assumes that maximal ellipsoids are centred on the medial axis, then dilates, rotates and translates slightly each ellipsoid until it cannot increase in volume any further. Ellipsoid Factor successfully identifies rods, plates and intermediate structures within trabecular bone, and summarises the distribution of geometries with an overall EF mean and standard deviation, EF histogram and Flinn diagram displaying a/b versus b/c. Ellipsoid Factor is released to the community for testing, use, and improvement.