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Table 3 Correlation and regression expression between shape parameters values and the Krumbein’s visual images

From: New parameter of roundness R: circularity corrected by aspect ratio

Shape parameters Correlation coefficient     Regression expressions References
Individual valuesa (n = 81) Adjusted coefficient of determination of individual values (n = 81) Mean values (n = 9) Adjusted coefficient of determination of mean values (n = 9)   
D 0.778b 0.549b D = 1.0541 − 0.0335·R K Vallejo and Zhou (1995)
R K  = 19.255 − 18.079·D c
Mi 0.940 Mi = 28.38 − 46.18 R K  + 21.71 R K 2 Itabashi et al. (2004)
FD 0.939 FD = 1.03655 − 0.05799·R K  + 0.02698·R K 2 Itabashi et al. (2004)
FU d 0.857 FU = 0.0736 + 0.264·R K Itabashi et al. (2004)
rW 0.919 0.992   Roussillon et al. (2009)
R 0.937 0.874 0.995 0.987 R K  = 6.9940 − 20.575·R + 15.349·R 2 This study
  1. aThe shape factor for each group is the average of nine shape factors corresponding to the nine particles forming each group in Krumbein’s pebble images
  2. bThis parameter is recalculated values to the third decimal place by the author
  3. cThis expression is recalculated by the author
  4. dThis parameter is the same definition as circularity on ImageJ