## 4 Results
From Figure 10, we can notice that the precision and recall were about 10.00% and 95.15%, respectively, under the default threshold (the default value of the minimum number of adjacent rectangles in which the target was detected was three). Besides, we show the comparison of the detection results on synapses in Figure 10 to illustrate the effectiveness of our algorithm for assigning a 3D serial number to synapses on the serial image stack and the algorithm for deleting pseudo-synapses and locating missed synapses. In total, we detected 13,036 synapses on the serial image stack. We found that there were 2027 synapses that only appeared on one section, which were considered as pseudo-synapses. With the algorithm for deleting pseudo-synapses and locating missed synapses, we removed these pseudo-synapses and located 445 missed synapses. As shown in Figure 10, the recall rate was increased from 97.15%-97.64%, and the accuracy rate was increased from 54.30%-62.12%. For the comparison of synapse segmentation results, the morphology-based method and a variational model-based method [34; 35; 36] were selected. As shown in Figure 11, the mask R-CNN was superior to the other two methods in maintaining the basic shape and edge smoothness and was basically consistent with the manually-annotated ground truth. The Jaccard similarity of the  
Figure 10: Comparison of the detection results on synapses. segmentation results of synapses is shown in Table 1. For the comparison of the segmentation results of neurons, the neuronal membrane prediction results of ResNet50 [37] are shown in Figure 12. Obviously, our approach was superior to ResNet50 in maintaining the neuronal membrane. The _Pixel-error_ and _Rand-error_[32] of the segmentation results of neurons are shown in Table 2. In this way, the accuracy of the segmentation was guaranteed when the neurons were segmented based on the probability map of the neuronal membrane. We list the number of misdetected MSBs and missed MSBs in 10 images in Table 3, where the first image is from the training set and the others images are from the test set. Figure 13 shows the identification results of MSBs on the 121 th image. There were six MSBs identified, in which one MSB was missed (Figure 13A) and two MSBs were misidentified (Figure 13C). Figure 13B shows one of the four correctly-identified MSBs. The identified results on the whole image stack are available on the website mentioned above. According to our statistics, each section of a size of 12 \(\upmu\)m \(\times\) 11.3 \(\upmu\)m from mouse cortex had about 5.1 MSBs. The precision and recall of our method on MSBs' identification were 68.57% and 94.12%, respectively. \[Recall=\frac{\text{True Positives}}{\text{True Positives}+\text{False Negatives}}. \tag{13}\]0 The comparison of neuronal membrane prediction (Row 1: raw images; Row 2: the ground truth; Row 3: prediction results of ResNet50 [37]; Row 4: prediction results of Mask R-CNN). \[Recall=\frac{\text{True Positives}}{\text{True Positives}+\text{False Negatives}}. \tag{13}\]1 Detection results of MSBs on the 121 th image. (**A**) A missed MSB; (**B**) a correctly-detected MSB; (**C**) a misdetected MSB. In Figure 14, we show three types of MSBs: Type A, one bouton to two synapses; Type B, one bouton to three synapses; and Type C, one bouton to four synapses. From left to right are raw images, bouton segmentations, synapse segmentations and the superimposed images of synapse segmentations and the manually-labeled ground truth of synapses. In the superimposed images, the yellow area is the overlapping area of segmentations and the manually-labeled ground truth, containing correctly-predicted pixels. The red area and green area consist of misclassified pixels and missing pixels, respectively.