## 3 Results  
This section reports the validation results and main outcomes for all deep learning models considered in this paper. Table 2 compares the values of the area under the receiver operating characteristics (ROC) curve (area under the ROC curve (AUC)) obtained from a fivefold cross-validation performed on the dataset containing 670 images. In Table 2, we can observe that in terms of mean and deviation of the AUC, the most promising result was achieved by the ResNet-104 architecture using triplet loss with semi-hard negative mining, while the poorest performance was demonstrated by the ResNet-68 architecture without metric learning. Surprisingly, the metric embeddings in the DenseNet architecture led to the increased variation of prediction performance over different folds compared to no metric learning. On the other hand, the overall AUC achieved over different folds is very high for each model. Therefore, it becomes very difficult or even impossible to improve this performance measure. Correspondingly, Table 3 reports the summary of Dice coefficient values achieved during the fivefold cross-validation experiment. As shown in Table 3, the average values of Dice coefficient range from 0.8109 to 0.8461, with the highest result achieved by the Resnet-104 model using triplet loss with semi-hard negative mining. The performance demonstrated by the considered models corresponds with the results illustrated in Table 2. Here, we observe the same tendency, i.e., the use of metrics in the deep learning model enabled it to achieve a better segmentation performance compared to no metric learning. Notably, the variation among folds decreased when using ResNet metric learning, while DenseNet with embedded metrics demonstrated a larger deviation in the values of Dice coefficient. On the whole, cross-validation results give us assurance that the performance of a classifier is stable since the standard deviation is comparatively low. In the following, we compare the segmentation prediction performance of the ResNet-104 architecture using triplet loss with semi-hard negative mining for testing the dataset consisting of 134 images). We relied on the Dice similarity coefficient, which is a preferable performance measure for \begin{table}
\begin{tabular}{l l l l} \hline \hline  & **DenseNet-71** & **ResNet-68** & **ResNet-104** \\ \hline No metric learning & 0.97952 \(\pm\) 0.00198 & 0.97176 \(\pm\) 0.00394 & 0.98312 \(\pm\) 0.00272 \\ Contrastive loss & 0.98703 \(\pm\) 0.00458 & 0.98678 \(\pm\) 0.00351 & 0.98873 \(\pm\) 0.00199 \\ Triplet Loss & 0.98817 \(\pm\) 0.00225 & 0.98902 \(\pm\) 0.00229 & 0.99089 \(\pm\) 0.00150 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Area under the receiver operating characteristics (ROC) curve (AUC): average \(\pm\) standard deviation. \begin{table}
\begin{tabular}{l l l l} \hline \hline  & **DenseNet-71** & **ResNet-68** & **ResNet-104** \\ \hline No metric learning & 0.8118 \(\pm\) 0.0043 & 0.8109 \(\pm\) 0.0057 & 0.8175 \(\pm\) 0.0098 \\ Contrastive loss & 0.8233 \(\pm\) 0.0083 & 0.8327 \(\pm\) 0.0048 & 0.8401 \(\pm\) 0.0027 \\ Triplet Loss & 0.8308 \(\pm\) 0.0065 & 0.8357 \(\pm\) 0.0029 & 0.8461 \(\pm\) 0.0034 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Dice coefficient values: average \(\pm\) standard deviation. the nuclei segmentation task, since it quantifies the similarity between the model output and reference mask. In particular, the Dice similarity coefficient was estimated separately for sample groups drawn up based on the type of image. Recall that the images in the dataset were acquired under a variety of conditions and vary in cell type, cell spatial distribution, magnification, and imaging modality (brightfield vs. fluorescence). The obtained results are summarised in Figure 2.  
From the Figure 2, it is apparent that a 3.12% increase in the average value of Dice similarity coefficients with deep metric learning was achieved as compared to no metric learning.