## 4 Discussion
### Unsupervised Segmentation in Pathology and the Problem of Obtaining Meaningful Labels (Ad i)
We have successfully trained several CNN model variations (a combination of convolutional blocks (called concise_CNN), a shallow UNET variant (called concise_UNET), and a shallow FCN variant (called concise_FCN)) in an unsupervised approach, as described by [PERSON] et al. [15, 16]. The produced image regions, or rather labels, however, are not mapped to the conventional histological structures. For instance, gland structures are composed of an epithelial layer (one label) and the luminal space (another label). Pathologists would usually annotate these structures together as a gland, in analogy to the typical thinking of tissues and organs as combinations of a limited number of substrata [40, 41]. For remapping the labels produced by the model trained in an unsupervised manner, we added a block (a fully connected layer) and then trained it on mapping the labels to human-produced annotations (compare B in Figure 3). However, this again necessitates the presence of (a small amount of) annotated data. Notably, this approach is therefore no longer an unsupervised but a weakly supervised approach. By adding another block and retraining, we can show that a model can produce meaningful annotations. However, compared to other segmentation models (such as the UNet implementation by [PERSON] et al. [20]) trained on the same dataset, the approach proposed here leads to inferior results. The Combination of Unsupervised and Subsequent Supervised Label Mapping Is Not Better than Conventional CNN-Based Segmentation (Ad iii)  
The inferior segmentation results in combination with again the need of a labelled dataset argue against the herein proposed remapping of labels by adding an additional block and by retraining with a small annotated dataset (compare Figure 3). There are several potential explanations for the rather moderate segmentation results of the proposed remapping approach:  
(1) The model complexity is maybe not fitting with the task. Of note, the used framework for unsupervised training described by [PERSON] et al. [15, 16] only works with shallow CNN models. Large models such as the UNet model implemented by [PERSON] et al. [20] do not converge. (2) Another idea would be that the ratio of the CNN filter size to the object size in the images is either too small or too large. Therefore, we tested different images sizes (\(256\times 256\), \(512\times 512\), and \(1024\times 1024\) pixels) and found no significant difference. Likewise, it would be possible in principle that the CNN models trained in this way were too shallow. However, this is contradicted by the fact that the tumour sub-type differentiation also did not work well in the UNet models used by other groups [20], which are frequently used and perform well. (3) The task itself is non-trivial since neither models adapted as described nor standard segmentation models can make the distinction between different tumour types, particularly between (non-keratinising) SqCc and (solid) ADC. In the used dataset, on which a work on tumour classification has been published recently [32], the models can only distinguish background from tissue and normal tissue from tumour parts. Of course, the models trained supervised perform better (see Tables 2 and 3); however, their segmentation results are also only moderate with assigning mixed labels (such as ADC and SqCC) per tumour infiltration. This could be due to several reasons. For example, the task of distinguishing between a non-glandular growing ADC and a non-keratinising SqCC is non-trivial, even for an experienced pathologist, on the basis of HE-stained images alone. Moreover, unlike the previously published work on this dataset for classification [32], where each image must be assigned to one class, now, each pixel must be assigned the correct label. (4) Finally, maybe the labels or morphological clusters segmented by the models after unsupervised training are found within non-neoplastic and neoplastic structures. For example, glandular structures are found in both.