Table 1 Notation of shape parameters and respective morphometric systems analysed by DendroScan. Shape parameters which are mathematically equivalent and therefore would provide redundant information, are omitted by default for DendroScan analyses, but could nevertheless be activated by the user. Definitions for each shape parameter are provided in the second column, with p particle perimeter, A projected particle area, w short side of the minimum area bounding rectangle, b long side of the minimum area bounding rectangle, c perimeter of the circle with area A, a maximum intercept, m mean intercept perpendicular to a, Lb maximum length of all possible lines from one point of the perimeter to another point on the perimeter projected on the major axis of the particle, Wb maximum of all possible lines from one point of the perimeter to another point on the perimeter, projected on the minor particle axis, pcp perimeter of smallest convex polygon around particle, Acp area of smallest convex polygon around particle, ece perimeter the smallest area ellipse that encloses, but does not intersect the particle, Lmaj major axis of best fit ellipse, Lmin minor axis of best fit ellipse, dBC diameter of circle that encloses, but not intersects particle, lF minimum Feret length, wF Feret length perpendicular to lF and dF maximum Feret distance. For further details see Table 1 in Dürig et al. 32.

From: DendroScan: an open source tool to conduct comparative statistical tests and dendrogrammatic analyses on particle morphometry

Notation

Definition

Shape parameter

Used by default

Remark

Morphometric system by

Circ_DL

\(p/c\)

Circularity

Yes

 

Dellino and La Volpe2

Rec_DL

\(p/\left( {2b + 2w} \right)\)

Rectangularity

Yes

 

Com_DL

\(A/\left( {b \cdot w} \right)\)

Compactness

Yes

 

Elo_DL

\(a/m\)

Elongation

Yes

 

Circ_CI

4 \(\pi A/p^{2}\)

Circularity

Yes

 

Cioni et al.29

AR_CI

\(L_{maj} /L_{min}\)

Aspect ratio

Yes

 

Con_CI

\(e_{ce} /p\)

Convexity

Yes

 

Sol_CI

\(A/A_{CP}\)

Solidity

Yes

 

Circ_LL

\(c/p\)

Circularity

Yes

 

Leibrandt and Le Pennec28

Elo_LL

\(1 - W_{b} /L_{b}\)

Elongation

Yes

 

AR_LL

\(W_{b} /L_{b}\)

Aspect ratio

Yes

 

Con_LL

\(p_{CP} /p\)

Convexity

Yes

 

Sol_LL

\(A/A_{CP}\)

Solidity

No

Identical to Sol_CI

FF

4 \(\pi A/p^{2}\)

Form factor

No

Identical to Circ_CI

Liu et al. 31

AR_LI

\(L_{min} /L_{maj}\)

Aspect ratio

Yes

 

Con_LI

\(p_{CP} /p\)

Convexity

No

Identical to Con_LL

Sol_LI

\(A/A_{CP}\)

Solidity

No

Identical to Sol_CI

Circ_SC

\(4A/\pi d_{BC}^{2}\)

Circularity

Yes

 

Schmith et al. 30

Rec_SC

\(A/\left( {b \cdot w} \right)\)

Rectangularity

No

Identical to Com_DL

FF_1

4 \(\pi A/p^{2}\)

Form factor

No

Identical to Circ_CI

AR_F

\(l_{F} /w_{F}\)

Feret aspect ratio

Yes

 

AR_SC

\(w_{F} /l_{F}\)

Reciprocal aspect ratio

Yes

 

Reg

\(16A^{3} /\left( {b \cdot w \cdot p^{2 \cdot } d_{BC}^{2} } \right)\)

Regularity

Yes