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.
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 |