PARAMETERS : 79 Weight factors: 6 Parameter Number Volume Equivalent Volume Other name Projection area Surface area Area of the convex hull Symbol V
A S Definition The volume of the particle volume model.
The volume of the sphere having the same projection area of the particle. The projection area of the particle. The external surface area of the particle volume model. The area of the smallest convex hull that contains the projection of the particle Formula Definition
The length of the particle perimeter. The length of the particle perimeter computed by Cauchy‐Crofton formula. The perimeter length of the convex hull (envelope) that bounding the particle. The diameter of a sphere having the same volume as the particle. Formula
Size parameters: 27 Parameter Perimeter Cauchy‐Crofton perimeter Symbol
P Pcc Perimeter of the convex hull PC Volume‐equivalent diameter xV Area‐equivalent diameter Other name
Equivalent circle diameter, ECD xA The diameter of a sphere having the same projection area as particle. OCCHIO USA WHITE STONE VA 22578 TEL(866) 244-1578
www.occhio-usa.com
6
4
Surface‐equivalent diameter xs Perimeter‐equivalent diameter XP Cauchy‐Crofton perimeter‐
equivalent diameter Inner Diameter XPcc Correlates to sieve analysis
results
Legendre ellipse maximum Maximum inscribed circle diameter xLMax Legendre ellipse minimum xLMin Feret diameter maximum Length of particle xFMax Feret diameter minimum Breadth of particle xFMin Feret conjugate Feret length Angle‐average Feret diameter Geodesic length Thickness Minimum circumscribed circle diameter Erosion number ̅F
xLG
xE
dcmin ω1 dimax xLF The diameter of a sphere having the same surface area as the particle. The diameter of a circle having the same perimeter as the projection area of the particle. The diameter of a circle having the same Cauchy‐Crofton perimeter as the projection area of the particle. The biggest circle inscribed into the projection area of the particle. The major axis of an ellipse with its center at the particle’s centroid and with the same geometrical moments, up to the second order, as the projection area of the particle. The minor axis of an ellipse with its center at the particle’s centroid and with the same geometrical moments, up to the second order, as the projection area of the particle. The maximum distance between parallel tangents to the projection area of the particle. The minimum distance between parallel tangents to the projection area of the particle. The Feret diameter (i.e. the distance between parallel tangents to the projection area of the particle) perpendicular to Feret diameter minimum. The mean Feret diameter. A better approximation of the particle length and width for very long and concave particle (fibers) The smallest circle containing the projection area of the particle. The number of erosions necessary to make the projection area of the particle disappears completely. OCCHIO USA WHITE STONE VA 22578 TEL(866) 244-1578
www.occhio-usa.com
A = xE .xLG P = 2(xE +xLG) Convex erosion number ω2
Fractal dimension DF Mean diameter Inertia box width Inertia box height Skeleton length Specific Area Inner threshold area The number of erosions necessary to make the area of the convex hull of the projection area of the particle disappears completely. The relationship between the length of the perimeter [P(λ)] and the length of the step [λ] is considered as linear on log‐log plot. The fractal dimension provides the slope of this linear relationship. The double of the mean distance between gravity center of the projection of the particle and each point of the outline of the projection of the particle. The width of the smallest box that contains the projection of particle with the same principal directions that the projection of the particle. The height of the smallest box that contains the projection of particle with the same principal directions that the projection of the particle. The length of the convex hull outline minus the biggest convex hull segment. The ratio between the external surface of the particle volume model and the volume of this model The area of the inner part of the projection area that are segmented by inner threshold parameters Log
1
log
log Shape parameters: 46 Parameter Ellipse ratio Other name Elliptical shape factor Symbol Definition The ratio of Legendre ellipse minimum to Legendre ellipse maximum. OCCHIO USA WHITE STONE VA 22578 TEL(866) 244-1578
www.occhio-usa.com
Formula Aspect ratio The ratio of Feret minimum to Feret maximum.
Elongation Eccentricity
The ratio of thickness to geodesic length.
Straightness The ratio of Feret maximum to geodesic length.
Curl The ratio of geodesic length to Feret maximum.
Irregularity Modification ratio
Compactness Roundness Rn The ratio of maximum inscribed circle diameter to minimum circumscribed circle diameter. The degree to which the projection area of the particle is similar to a circle. The ration of the area‐equivalent diameter to Feret diameter maximum. Similar to compactness but less robust (see ISO9276‐6) Extent Bulkiness Box ratio Wadell’s sphericity Ψ
Form factor FF Circularity C Crofton Circularity Solidity Global surface concavity index CI
The ratio of projection area to the product of Feret diameter maximum by Feret diameter minimum. The ratio of projection area to the Feret box area. Where the Feret box area is the product of Feret diameter minimum by Feret diameter conjugate. 4
The degree to which the projection area of the particle is similar to a circle, considering the smoothness of the perimeter. It’s the circularity computed with Crofton correction
A measure of the overall concavity of the projection area of the particle. A measure of the overall concavity of the projection area of the particle. OCCHIO USA WHITE STONE VA 22578 TEL(866) 244-1578
www.occhio-usa.com
Concavity Convexity Crofton Convexity Average concavity ΨFP It’s the convexity computed with Crofton correction
Particle robustness Ω1 2
√
2
Largest concavity index A measure of the overall concavity of the projection area of the particle. Ω2 ̅
√
Concavity/robustness ratio Ω3
The ratio of particle robustness to the Largest concavity index. Occhio bluntness CORRELATES TO
T335 FRACTURED FACE TEST
Occhio abrasivity Occhio elongation One minus the ratio Inertia box width to Inertia box CORRELATES TO ELONGATION TEST D4791
height Occhio roughness xx% The ratio of smooth reference to the particle projection area. The smooth reference is define by inscribed circles tangent to each point of the particle projection outline with a radius greater than XX% of the maximum inscribed circle. Mean luminance Mean value of the luminance of pixel inside the projection area of the particle RSD luminance Mean value of the luminance of pixel inside the projection area of the particle Mean red Mean value of the red channel of pixel inside the projection area of the particle RSD red RSD value of the red channel of pixel inside the projection area of the particle Mean green Mean value of the green channel of pixel inside the projection area of the particle RSD green RSD value of the green channel of pixel inside the OCCHIO USA WHITE STONE VA 22578 TEL(866) 244-1578
www.occhio-usa.com
Mean blue RSD blue Mean inner red Mean inner green Mean inner blue projection area of the particle Mean value of the blue channel of pixel inside the projection area of the particle RSD value of the blue channel of pixel inside the projection area of the particle Mean value of the red channel of pixel inside the projection area of the particle that are segmented by inner threshold parameters Mean value of the green channel of pixel inside the projection area of the particle that are segmented by inner threshold parameters Mean value of the blue channel of pixel inside the projection area of the particle that are segmented by inner threshold parameters OCCHIO USA WHITE STONE VA 22578 TEL(866) 244-1578
www.occhio-usa.com