# A New Approach to Border Irregularity Assessment with Application in Skin Pathology
## 3 Results
### Performance  
In total, the dataset consisted of 992 manually segmented retes, whereas our method detected 894 retes--825 were detected correctly (83%), 147 manually segmented retes were not detected, in 20 cases either one manually segmented rete was assigned multiple automatically segmented retes or vice versa (automatically segmented retes should be split or merged), and 42 detected retes were actually false positives. Figure 25 shows the distribution of retes as well as individual error types with respect to rete's length and width. Most \"should split or merge\" errors are confined to micro-retes: 62% of all \"should split or merge\" retes had the width of less than 140 px and the length of less than 90 px whereas only 15% of all retes had such dimensions. \begin{table}
\begin{tabular}{l l l l l l} \hline \hline
**Set** & **Mag.** & **\(\upmu\)m/px** & **Image Format** & **Device** & **Laboratory** \\ \hline
1 & 20\(\times\) & 0.345 & TIFF & Olympus BX51+ Pike F505C VC50 & Jagiellonian Univ. MC \\
2 & 10\(\times\) & 0.44 & TIFF & Axio Scan.Z1 & Jagiellonian Univ. MC \\
3 & 40\(\times\) & 0.25 & JPEG2000 q70 & Aperio AT2 & Univ. of Michigan [43] \\
4 & 40\(\times\) & 0.25 & JPEG q30 & Aperio ScanScope CS2 & Univ. of British Columbia [44] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: WSI datasets used to evaluate the specimen segmentation method. Each dataset consisted of 3 images. Figure 24: A section of epidermis: (**a**) two boundary details are definitely retes (“+”), one might be a rete (“?”), and one is definitely not a rete (“-”); (**b**) the \(U\) difference field (see [40]) for the two central boundary details; (**c**) the skeleton obtained by thresholding the \(U\) difference field with \(t=100\). Figure 26 shows a histogram of incorrectly detected retes w.r.t. the rete length. It can be noted, that the proportion of misdetections rapidly decreases with the length of a rete and stabilize at 10-17% for retes longer than 90 px (which make 77% of all retes). The highest shares of errors were among retes shorter than 80 px, where up to 65% of retes were not detected. A high number of false positives for retes longer than 200 px (15 cases) is caused by skin appendages (mainly hair follicles) misclassified as retes. Both retes and hairs have similar morphometry, yet their tissue structure differs (Figure 27). However, to the best of our knowledge, no automatic method for the segmentation of skin appendages in histopathological images has been proposed so far. Figure 28 shows boxplots of Jaccard indexes computed on the set of \(n=25\) of images. The median and interquartile range (IQR) for \(J_{\mathrm{strict}}\) were 0.80 and 0.10, whereas for \(J_{\mathrm{relaxed}}\) they equaled 0.81  
Figure 26: A histogram of the share of incorrectly detected retes with respect to the rete length (the first bin also includes all retes shorter than 50 px and the last bin also includes all retes longer than 410 px). Figure 27: Morphometric similarity between skin appendages (e.g., hair follicles) and fused rete ridges. Figure 25: Scatter plots of the distribution of retes wrt. to their length and width. The marker scale for all error plots is the same, yet (for clarity) it differs from the marker scale for the “all retes” plot. and 0.11, respectively. The lower adjacent value was nearly 0.70 for both the strict and the relaxed version. The Jaccard indexes computed for the aggregated data (from all slides) were \(J_{\text{strict}}=0.798\) and \(J_{\text{relaxed}}=0.817\). Figure 29a,b shows histograms of relative errors for estimating rate width and length, respectively. The mean absolute value of relative errors (\(|\delta x|\)) was 20% for the width and 16% for the length. Both distributions of relative errors were right-skewed, with skewness equals to 0.79 for width errors (moderate skewness) and 3.42 for length errors (high skewness), which means that our method tends to overestimate both width and length of retes rather than to underestimate them.