Fig 1.
Illustration of the method used to identify the optimal tolerance τb.
On the interval [τs, τf], the proportion of selected pixels χ (solid black) is non-decreasing and reaches the maximum value 1 for τ ≥ τu. The best binary image occurs at the tolerance τb, which occurs just before the rapid increase in χ. For each τm ∈ [τs + 1, τc − 1], a piecewise linear function pm (purple) is fit to χ on the intervals [τs, τm] and [τm + 1, τc], for some critical value τc such that χ(τc) is close to unity. The point τb is taken to be the threshold that minimises the mean error between χ and the piecewise linear interpolant.
Table 1.
Summary of the datasets produced by Binder et al. [7].
Shown are the species, nutrient level (ammonium sulfate), number of samples, number of observation times, and the mean percentage difference between the TAMMiCol and manual images, along with the corresponding mean percentage differences
,
and
when using Otsu’s method [13], k-means++ clustering [16, 38] and the Ridler–Calvard method [14], respectively.
Fig 2.
Example of image processing by TAMMiCol.
(a) Colony 5 after 233 hours of growth and (b) with the selected area overlaid in green. (c) The proportions χ (blue) and error δ (red) are plotted against τ. Marked on this plot are the selected level τb and the critical value τc. TAMMiCol is able to separate the colony from the background with a high degree of accuracy.
Fig 3.
Comparison of images produced by TAMMiCol and images produced manually.
The percentage difference d between binary images produced by TAMMiCol and binary images created manually for the (a) AWRI 796 50 μM, (b) AWRI 796 500 μM and (c) AWRI R2 50 μM datasets. The original images feature colonies of S. cerevisiae produced by Binder et al. [7] and are described in Table 1. The differences are plotted against the sample number s and observation time t. All plots are shown with the same colour scale. The difference is typically less than 10%, and many samples have disagreement values of around 5% or lower, indicating a close agreement between the automated and manual images.
Fig 4.
Comparison of indices computed from TAMMiCol images and manual images.
The spatial indices (a) Ir, (b) IΘ and (c) ICSR computed from both the TAMMiCol images (solid lines) and the manual images produced by Binder et al. [7] (dashed lines). Shown are AWRI 796 50 μM (blue), AWRI 796 500 μM (red), and AWRI R2 50 μM (yellow). The bars represent the standard error. The automated and manual images generally agree on the relative order of the statistics for each of the datasets.
Table 2.
Summary of new data showing the species, nutrient level (ammonium sulfate), number of samples and number of observation times.
Fig 5.
Indices for the new datasets computed using TAMMiCol.
Shown are the indices (a) Ir, (b) IΘ and (c) ICSR for AWRI 796 grown with ammonium sulfate concentrations of 50 μM, 100 μM, 200 μM, 350 μM and 500 μM. The bars represent the standard error. In general, the indices increase with decreasing concentration, indicating greater filamentous growth.
Fig 6.
Examples of other colony types processed by TAMMiCol.
Shown are (a) an S. cerevisiae biofilm and (c) a B. subtilis colony, along with the colony shown in green as identified by TAMMiCol (b and d, respectively). In each case, the colony is identified with a high degree of accuracy, demonstrating the versatility of the software. Fig. 6(a and b) was produced by Tam et al. [34]. Fig. 6(c and d) is reprinted from the Journal of the Physical Society of Japan, 58(11), Hiroshi Fujikawa and Mitsugu Matsushita, Fractal Growth of Bacillus subtilis on Agar Plates, 3875–3879, 1989 and is reproduced under a Creative Commons Attribution licence (CC BY 4.0).