Fig. 4

Estimation of σ values of the tubeness filters and the optimal lower thresholds of hysteresis thresholding. a Results of the tubeness filter on a hypothetical root of a diameter \({d}_{r}\) obtained for different \(q\) values. The dashed blue lines show the original root outline whereas the solid yellow lines show the position of the transects used to plot the GV along the root diameter axis. b Plot of GV along the root diameter axis for some of the \(q\) values shown in a. The colored dots at the intersection between the root outline and the GV parabola correspond to \({t}_{hys}^{opt}\) for a given \(q\) value. c Line of best fit imposed on the couple of points \(q\) and \({t}_{hys}^{opt}\). In this study, we calculated \({t}_{hys}^{opt}\) corresponding to = \(q\)0.5 using the model regression. The calculated value is indicated by the dashed line (i.e., \({t}_{hys}^{opt}=79)\)