## 2 Related Work
### Machine-Learning-Based Counting Methods  
As shown in Table 1, the machine-learning-based microorganism counting approaches consist of machine-learning- and deep-learning-based methods. The classical machine-learning-based approaches contain Principal Component Analysis (PCA) [61] and Support Vector Machine (SVM) [62]. Deep-learning methods are usually based on CNN [63], Back Propagation Neural Network (BPNN) [64] and Artificial Neural Network (ANN) [65] algorithms.  
The works [48; 49; 50; 51] used classical machine learning for microorganism counting. In [48], PCA was applied for separation the bacteria with other debris. After that, the nearest neighbor searching algorithm was applied for clustered colony separation. In [49], the shape features were extracted for training, then the SVM was applied for microorganism classification and counting after Otsu thresholding.  
In [50], the histogram local equalization was applied to enhance the contours of protozoa images. Then, morphological erosion and reconstruction were used to eliminate the flocs of the protozoa silhouette. Finally, PCA was applied to classify different protozoa, and the number of the various species of protozoa was counted. In [51], local auto-correlational masks were used for image enhancement, and PCA was applied for plankton counting.  
The works [52; 53; 54; 55] used deep learning for microorganism classification and counting. In [52], the Marr-Hildreth operator and thresholding were applied for edge detection and binarization of bacteria images. Then, ANN was designed for classification and counting. In [53], the contrast-limited adaptive histogram equalization was applied for bacteria image segmentation, then four convolutional and one fully connected was trained for classification and counting. In [54], contrast limited adaptive histogram equalization was used for image enhancement.  
Then, CNN was applied for bacteria classification, and the watershed algorithm was applied for colony separation and counting. In [55], a classification-type convolutional neural network (cCNN) was proposed for automatic bacteria classification and counting. First, the original images were segmented with an adaptive binary thresholding method, and images with individual cells or cell clusters were cropped. Then, the images were classified using cCNN. The network can output the number of bacteria in given clusters, and the total count can be calculated.  
By reviewing all related works of microorganism counting, we found that deep learning technologies are widely applied for microorganism classification; however, few machine-learning-based image segmentation methods are applied. Since the development of deep learning and computer vision technologies, CNN-based image segmentation approaches have be applied for accurate microorganism segmentation, such as SegNet [33], U-Net [34], Attention U-Net [66], Trans U-Net [67] and Swin U-Net [68]. Though the methods above have not been applied for microorganism-counting tasks, they have enough potential to extract the microorganism before counting, which can be inferred with better performance.  
Since the yeast images in our dataset range from 1 to 256 yeast cells in each image, and the boundaries of the cells are not clear, it can be inferred that the classical segmentation methods may show poor performance in this counting task. Therefore, we propose an encoder-decoder model that concentrates on the dense and tiny object counting task.