# Potential of Deep Learning Methods for Deep Level Particle Characterization in Crystallization
## 4 Results
### Mask-RCNN Applied to Three-Class Task
Since there is a high semantic similarity of single crystals and primary crystals in agglomerates, false positive primary crystals can be identified and deleted. This additional post-processing step added to the two-network variant M3_2 constitutes the third variant M3_2 PP. Evaluation of the third variant shows that post-processing of the results within M3_2 PP does not yield a further improvement in numbers over the variant without post-processing (M3_2). In fact, it is mostly on par (except \(AP^{pc_{\text{ag}}}=39.1\)). That means, that for \(AP\) the false positives are not strongly decisive; however, the \(\overline{pc/ag}\) decreases to 2.73, indicating that there are false positives. Since the intersections of pc\({}_{\text{ag}}\) and ag are needed for later calculation in Section 4.2, the post processing is kept. Common to all variants is the dependence of accuracy on particle size. This is reflected in the class-specific values, which are high for agglomerates, i.e., larger particles on average, and lower for pc\({}_{\text{ag}}\) and sc. Even more specifically, it also confirmed by size-specific metrics as shown in Figure 4. The larger the particle, the better the shape and further details can be reproduced, which facilitates the classification. It is essential to mention that all training and evaluation is performed for the original image size (\(2048\times 2048\) px). This is in contrast to Mask-RCNN/Detectron2 default settings, which result in a down-scaling of image size, which is usually set to \(800\times 800\) px. As to be expected, down-scaling of the input images results in a significant drop of detection accuracy (\(AP=37.9\); \(AP^{pc_{\text{ag}}}=29.1\); \(AP^{ag}=65.0\); \(AP^{sc}=19.6\)). Especially the small \begin{table}
\begin{tabular}{l c c} \hline \hline  & \(Ag\) & \(\overline{pc/ag}\) \\ \hline Annotations & 0.27 & 3.08 \\ Mask-RCNN M3\_1 & 0.28 & 2.42 \\ Mask-RCNN M3\_2 & 0.28 & 2.91 \\ Mask-RCNN M3\_2 PP & 0.28 & 2.73 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Agglomeration degree (\(Ag\)) and number of primary crystals per agglomerate (\(\overline{pc/ag}\)) for the test set; manual annotations compared to the results of different Mask-RCNN approaches. crystals are detected worse due to resizing, since they do not consist of enough pixels to reflect shape accurately. By ISO-13322-1 [56] for the original image size the minimal equivalent diameter must be larger than 25.4 \(\upmu\)m (\(d_{eq,1}\)) for compliant detection. For the resized images, this would be accordingly less. In order to improve the results the size threshold of 25.4 \(\upmu\)m (\(d_{eq,1}\)) is investigated. Additionally a second threshold based on annotated unknown objects is defined. All particles the annotators were not certain whether they were a crystal, dirt or even artifact are subsumed under _unknown_. By a size analysis of the unknown objects shown in Figure 5, it is highlighted that with 90% of the unknown objects are smaller than the size class of 50.8 \(\upmu\)m. To avoid the influence of particles of an uncertain class, a second size threshold of \(d_{eq,2}=50.8\)\(\upmu\)m is chosen. Figure 6 shows results for M3_2 PP with the different area thresholds applied. Excluding objects below the chosen threshold further increases detection accuracy, which, for the principal \(AP\)-measure, rises from 51.6 without any threshold to 53.4 and 59.3, for \(d_{eq,1}\) and \(d_{eq,2}\), respectively. Whereas the annotators do not identify many crystals below \(d_{eq,1}\) manually (see Table A1), an increased accuracy for \(d_{eq,2}\) is achieved because fewer artifacts and poorly depicted objects are analyzed. Examples for the final results are given in Figure 7. For the exemplary image in Figure 1 the detection of single crystals and agglomerates (see Figure 7a) as well as primary crystals in agglomerates (see Figure 7b) are presented. It can be seen that the differentiation between single crystals and agglomerates is successfully implemented and also the primary crystals can be depicted by segmentation masks.