## 3 Results  
### Comparison of Algorithm Performance  
We compared each algorithm to the ground truth in a pairwise fashion. Table 1 shows how the algorithms performed relative to each other, the comparison being based on the ground truth dataset. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sample ID** & **Algorithm 1** & **Algorithm 2** & **Algorithm 3** \\ \hline
1M01 & 0.8159 & 0.8817 & 0.8825 \\
1M02 & 0.8076 & 0.8372 & 0.8440 \\
1M03 & 0.8145 & 0.8270 & 0.8078 \\
1M04 & 0.8468 & 0.8617 & 0.8423 \\
1M06 & 0.8201 & 0.8480 & 0.8530 \\
1M10 & 0.8502 & 0.8618 & 0.8920 \\
1M11 & 0.8279 & 0.8583 & 0.8787 \\
1M12 & 0.8065 & 0.8848 & 0.8718 \\
1M13 & 0.8219 & 0.8488 & 0.8474 \\
1M14 & 0.8041 & 0.8450 & 0.8351 \\
1M15 & 0.6787 & 0.8265 & 0.7748 \\
1M16 & 0.7929 & 0.8217 & 0.8214 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: F1 score for each sample and algorithm, with arithmetic mean and standard deviation over all the samples, calculated in a macroscopic manner. Figure 7: Method of measuring integrated density (ID), a background-compensated intensity sum. The resolution of the system is visible; the objects are only tens of pixels in size. In Figure 8, it can be seen how these algorithms are only slightly influenced by sample density (at least to the extent of this digital slide set). Taking a second glance at Figure 8, sample 1M15 seems to be an outlier, and seemed useful to investigate. Figure 9 shows the main difference to the other samples. We intentionally selected an adjacent sample regarding density for comparison. Both samples are around average density, but most objects are in the groups visible on the image. These clumps are closely packed, and with the relatively high image intensity the objects are harder to separate. Sample intensity is also visibly different. Table 2 shows a comparison of the algorithms based on precision calculated from the confusion matrix. Algorithms 2 and 3 are close, but interestingly Algorithm 1 performs better than both. Table 3 contains data for the sensitivity metric. In this regard, Algorithm 2 performs best of the three algorithms based on our findings. Figure 10 shows the same sample region segmented by all the algorithms for better visibility of differences. See how each algorithm solves the segmentation on this somewhat problematic region. \begin{table}
\begin{tabular}{c c c c} \hline
**Sample ID** & **Algorithm 1** & **Algorithm 2** & **Algorithm 3** \\ \hline
1M17 & 0.8082 & 0.8271 & 0.8110 \\
1M18 & 0.7708 & 0.8771 & 0.8523 \\
1M20 & 0.8422 & 0.8278 & 0.8776 \\ \hline Mean & 0.8072 & 0.8490 * & 0.8461 \\ SD & 0.0397 & 0.0206 * & 0.0314 \\ \hline \end{tabular}  
* Algorithm 2 gave the most accurate result, along with more consistent results over the samples than the other two, but differences to Algorithm 3 are very small.  
\end{table} 
Table 1: _Cont._  
Figure 8: The F1 scores are calculated from the confusion matrices calculated for each algorithm, for each sample. The horizontal axis values are in increasing order of sample density and a normalized value of this is also present on the chart (dashed green, with rectangular data points). F1 score decreases only slightly with increasing density in the case of all three algorithms. Algorithms 2 and 3 are more sensitive to low-intensity nuclei, but produce false positives, due to the nature of the manually generated annotations. To compare the algorithms, we used their geometric data only. The task was to find a segmentation object pair for a reference marker. We executed the same matching algorithm for each of the three algorithms. Algorithm 3 seems to follow object outlines best, resulting in more robust results from the validation point of view (markers are inside the segmentation objects by a greater margin). Clump separation is problematic with all three algorithms, but Algorithm 3 has further options for fine tuning in this regard.