Simple macro to illustrate how historically common descriptions such as area equivalent diameter and fiber thickness as well as new geometries can be added to an ImageJ Results table.
The additional measurements in this version are:
Interfacial density (assuming each interface is shared by two objects - e.g. grain boundary density).
Area equivalent diameter (AKA Heywood diameter): The "diameter" of an object obtained from the area assuming a circular geometry.
Perimeter equivalent diameter: The "diameter" calculated from the perimeter assuming a circular geometry.
Spherical equivalent diameter: The "diameter" calculated from the volume of a sphere (Russ page 182) but using the mean projected Feret diameters to calculate the volume.
Roundnesss_cAR: Circularity corrected by aspect ratio, from Y. Takashimizu and M. Iiyoshi, "New parameter of roundness R: circularity corrected by aspect ratio," Progress in Earth and Planetary Science, vol. 3, no. 1, p. 2, Jan. 2016. DOI: 10.1186/s40645-015-0078-x
Round end ribbon thickness ("snake") from repeating half-annulus (Lee & Jablonski LTSW'94).
Two calculated fiber widths obtained from the fiber length from John C. Russ, Computer Assisted Microscopy, page 189.
Fiber length from fiber width (Lee and Jablonski LTSW'94; modified from the formula in John C. Russ, Image Processing Handbook 7th Ed. Page 612).
Two estimates of fiber length and two examples of volumetric estimates from projections obtained from the formulae in John C. Russ, Computer Assisted Microscopy page, 189.
Additional shape factors: "Compactness" (using Feret diameter as maximum diameter), "Convexity" (using the calculated elliptical fit to obtain a convex perimeter), "Thinnes ratio", "Extent ratio", Curl etc.
Square geometries appropriate to HV (hardness) indents:
Sqr_Diag_A = √(2Area) for a NSEW square this length should match the bounding box height and width
Like circularity the following "squarity" values should approach 1 for a perfect square:
Squarity_AP = 1-|1-(16Area)/Perimeter2| (perhaps too sensitive to perimeter error)
Squarity_AF = 1-|1-Feret/(A*√2)|
Squarity_Ff = 1-|1-√2/Feret_AR|
Hexagonal geometries more appropriate to close-packed structures than ellipses:
HexSide = √((2Area)/(3√3))
HexPerimeter = 6 * HexSide
Hexagonal Factor from Behndig et al. and Collin and Grabsch (1982)
Hexagonal Shape Factor Ratio "HSFR" = abs(13.856/(P²/Area)): as above but expressed as a ratio like circularity, with 1 being an ideal hexagon.
HexPerimeter = 6 * HexSide
Hexagonality = 6 * HexSide/Perimeter
Full Feret coordinate listing using new Roi.getFeretPoints macro function added in ImageJ 1.52m.
Preferences are automatically saved and retrieved from the IJ_prefs file so that favorite geometries can be retained. Help button provides more information on each measurement.
These macros have been developed to demonstrate the power of the ImageJ macro language and we assume no responsibility whatsoever for its use by other parties, and make no guarantees, expressed or implied, about its quality, reliability, or any other characteristic. On the other hand we hope you do have fun with them without causing harm.
The macros are continually being tweaked and new features and options are frequently added, meaning that not all of these are fully tested. Please contact me if you have any problems, questions or requests for new modifications.