## 4 Experiments
### Evaluation Metrics  
In the task of dense tiny object counting, the evaluation of image segmentation is the most significant part. Hence, the widely applied segmentation evaluation metrics Accuracy, Dice, Jaccard and Precision are employed here to evaluate the performance of microorganism segmentation. Furthermore, the Hausdorff distance is applied to evaluate the shape similarity between the predicted image and GT. Finally, the counting accuracy is calculated to quantify the counting performance of the models.  
Accuracy is applied to calculate the proportion of pixels that are correctly classified. The Dice coefficient [79] is applied to measure the similarity of the predicted image and GT. The similarity can be quantified range from 0 to 1 (1 means the predicted result coincides exactly with the GT). Jaccard [80], also named the intersection over union (IoU), is applied to compare the similarity and differences between the predicted image and GT image, focusing on whether the samples' common characteristics are consistent. Precision is defined as the proportion of positive pixels in the pixels, which are classified as positive.  
The Hausdorff distance [81] is applied to measure the Euclidean distance between the predicted and GT images with the unit of pixels in per image. In contrast with Dice, the Hausdorff distance focuses on the boundary distance of two objects to measure the shape similarity; however, the Dice majors in the inner similarity. An example of the Hausdorff distance between GT and predicted image is shown in Figure 6. The Hausdorff is the maximum of the shortest distance between a pixel in a image and another image [82].  
In the task of microorganism counting, the Hausdorff distance can be applied to measure the shape similarity between the GT and segmentation result, showing the performance of segmentation models. Finally, the performance of counting is measured using counting accuracy, which is defined as the proportion of the predicted number and GT number of yeast cell images.  
The definitions of the proposed evaluation metrics are summarized in Table 2. The TP (True Positive), TN (True Negative), FP (False Positive) and FN (False Negative) are basic evaluation metrics, which can be applied to measure the performance of segmentation in general. An example of a yeast cell image with its TP, TN, FP and FN is illustrated in Figure 7 for intuitive understanding. \(V_{pred}\) is the foreground after segmentation by using the model, \(V_{GT}\) is the foreground of the GT image. Furthermore, \(N_{pred}\) means the number of connected regions in the predicted image, \(N_{GT}\) means the number of connected regions in the GT image, which indicates the number of yeast cells. In the definition of the Hausdorff distance, \(sup\) is the supremum, and \(inf\) is the infimum.  
Figure 6: The visualization result of the Hausdorff distance between the GT and predicted image.  
The proposed evaluation metrics, containing the Accuracy, Dice, Jaccard and Precision, are proportional to the segmentation performance of models. The Hausdorff distance has an inverse correlation with the segmentation performance. Counting accuracy can evaluate the final counting results of different models.