## 4 Results  
To demonstrate the effectiveness of the proposed algorithm, we counted the number of detected MSBs from our dataset and compared the results with the manually-labeled ground truth. The measurements we selected to evaluate the results of synapse detection were _Precision_ and _Recall_.. _Precision_, also referred to as the positive predictive value, is the fraction of relevant instances among the retrieved instances, while _Recall_ is the fraction of relevant instances that have been retrieved over the total amount of relevant instances:  
\[Precision=\frac{\text{True Positives}}{\text{True Positives}+\text{False Positives}}, \tag{12}\]  
\[Recall=\frac{\text{True Positives}}{\text{True Positives}+\text{False Negatives}}. \tag{13}\]  
This study adopted the _Jaccard similarity_[31] as the evaluation measurement for segmentation, which is defined as the size of the intersection divided by the union of the two segmentation results in the field of image processing:  
\[J(S_{i},S_{j})=\frac{|S_{i}\cap S_{j}|}{|S_{i}\cup S_{j}|}, \tag{14}\]  
where \(S_{i}\) and \(S_{j}\) represent the ground truth and segmentation, respectively. _Pixel-error_ and _Rand-error_[32] were used for evaluating the segmentation results of neurons. _Pixel-error_ is the ratio of the number of misclassified pixels to the total number of pixels. _Rand-error_ is the difference between one and the _Rand-index_. The _Rand-index_ is a similarity evaluation method for two clusters that can be used to measure segmentation due to the fact that segmentation can be regarded as a cluster of pixels. \[\text{{Pixel-error}}=\frac{\text{Number of False Positive Pixels + Number of False Negative Pixels}}{\text{Number of Pixels}}, \tag{15}\]  
\[\text{{Rand-error}}=1-\text{{Rand-index}}=1-\frac{N_{1}+N_{2}}{C_{n}^{2}}, \tag{16}\]  
where \(n\) is the number of pixels, \(N_{1}\) is the number of pairs of pixels that are in the same connected object in the ground truth and in the same connected object in the segmentation results, and \(N_{2}\) is the number of pairs of pixels that are in the different connected objects in the ground truth and in the different connected objects in the segmentation results  
Due to the limitation of computer memory, we split each original image of size 6004 pixels \(\times\) 5174 pixels into nine sub-images with a size of 2048 \(\times\) 2048 in the experiment for training the Mask  
Figure 9: The workflow of MSB identification. **(A)** Mask of synapses; **(B)** segmentation of neurons; **(C)** mask of synapses superimposed on the segmentation of neurons. R-CNN. The overlapping pixels between adjacent sub-images in the x and y directions were 485 and 78, respectively. For the 1602 sub-images, 630 sub-images were for training, while 270 sub-images were for verification, and the other 702 sub-images were for testing. The neuronal membrane of the former five images was manually annotated. The images with a size of 6004 pixels \(\times\) 5174 pixels were split into sub-images with a size of 1024 pixels \(\times\) 1024 pixels, each of which was further split into four images with a size of 512 pixels \(\times\) 512 pixels. In total, 720 sub-images with a size of 512 pixels \(\times\) 512 pixels were obtained, 450 sub-images for training, 150 sub-images for validation, and 120 sub-images for testing. To improve the robustness of the networks, we enlarged the training dataset by means of data augmentation, including rotation and flipping. In addition, reliability issues arise when the distribution of input training data differs from the distribution of the evaluation model [33]. Therefore, we randomly added Gaussian noise to the raw image (mean = 0, variance = 0.1) to make the model more robust during the training phase. The training and testing tasks were conducted on a server equipped with an Intel i7 CPU with 512 GB of main memory and a Tesla K40 GPU. To illustrate the effectiveness of Mask R-CNN in the detection of synapses, we show the detection results of synapses using AdaBoost.