## 4 Discussion  
Conventional U-net is a commonly used deep learning network that displays good performance in various kinds of studies. It is used for segmentation of organs and cancers in various types of medical images [28; 29; 30], and it is also used for object segmentation of optical images [31]. Figure 8: Segmentation results. (**a**) Input MR spine image. (**b**) Boundary segmentation result from U-net. (**c**) Boundary segmentation result from cascaded U-net. (**d**) Boundary segmentation result from BSU-net. White pixels correspond to boundary pixels that were perfectly matched with true boundary labels. BSU-net preserved more boundaries than other models. Figure 7: Segmentation results of the networks overlaid on the input image. (**a**) The input magnetic resonance (MR) image. (**b**) The input MR image with U-net segmentation result. (**c**) The input MR image with the result from the modified U-net which is U-net whose convolutional and pooling layers are replaced with BSU-layers. (**d**) The input MR image with BSU-net result. Figure 9: Segmentation results from all networks illustrating the outlier case of cascaded U-net. Brown area, yellow area, and blue area denote correctly segmented area, under-segmented area, and over segmented area, respectively. (**a**) Input image with label. (**b**) U-net result. (**c**) Cascaded U-net result. (**d**) BSU-net result. However, conventional U-net has limited ability for detailed boundary segmentation [10] due to the structural limitations of a max-pooling layer that plays a key role in feature extraction process. It is not suitable for segmentation of objects with complex boundaries, such as intervertebral discs. The purpose of our proposed network, BSU-net, is to improve the pooling layer of conventional U-net. In this paper, BSU-net showed a better performance than conventional U-net for intervertebral disc segmentation in MR spine images. This indicates that BSU-net can perform more precise and fine-grain segmentation than conventional U-net. BSU-net will be of value in MR studies where quantitative MR values of disc need to be determined. As shown in Tables 1 and 2 and Figure 5, dilated U-net performed better than conventional U-net and BSU-net showed better performance than dilated U-net. In most accuracy measurements, dilated U-net showed statistically significant performance improvement, but the improvement in MHD measurement was quite small. MHD indicates the accuracy of boundaries because it is based on the distances between obtained boundaries and reference boundaries. This indicates that the results of dilated U-net have many incorrectly segmented areas. Figure 10 shows the results of dilated U-net and BSU-net. There are some incorrectly segmented areas in the results of dilated U-net while the results of BSU-net have no incorrectly segmented areas. This is because the feature extraction process of dilated U-net did not remove unnecessary information compared to BSU-net. The number of trainable parameters used in BSU-net is 53,740,674 which is approximately 22% lower than dilated U-net (69,048,584) and approximately 14% lower than conventional U-net (62,803,650). This indicates that BSU-net performed successful fine-grain segmentation efficiently. The components of the BSU-net are the BSU-pooling layer and residual block, and cascaded network. As shown in Table 3, the application of each component contributed to performance enhancement. The performance improvement of applying residual blocks is much smaller than those of applying other components. However, the number of trainable parameters were approximately 12% decreased. Therefore, the application of residual blocks brought efficiency to the entire learning. When BSU-layers were applied to U-net, the result of DSC measurement 1 was only 0.74% higher than conventional U-net.