## 2 Methodology
### Multi-Scale Path  
In the basic U-Net architecture, there are skip pathways between the respective layers of the encoding and decoding side, and shortcut paths before the max-pooling layers in the encoder side and after the deconvolution layers in the decoder side. Often, spatial information gets lost during the max-pooling operation, and the skip connections help the network to propagate information from the encoder side to the decoder side. However, the skip pathways often come up with a problem of a semantic gap during the feature fusion because the first layer of the encoder, which extracts the low-level features, is connected to the terminal layer of the decoder, which deals with more high-level features. Additionally, because of the added complexities of variabilities in sizes, shapes, and positions of bony features, both the low and high level features would have to be retained for detailed segmentation.  
To reduce the discrepancy between the encoder-decoder features and enhance the feature fusion, a multi-scale skip path was proposed in this paper. A multi-scale inception [41] module was incorporated between the encoder and decoder layers to enhance the low-level features extracted in the encoder side. Through this connection, the low-level features will undergo further processing before merging with the high-level features on the decoder side. Moreover, instead of the usual convolutional layers, multi-scale inception layers are used. They improve the utilization rate of computing resources by increasing the depth and width of the network while keeping the computational budget constant [57].  
Inception modules have been proven to be very promising in enlarging receptive fields and capturing more context information [58]. It enhances the depiction capability of low-level features. The inception module adopts multiple branches with different kernel sizes to capture multi-scale information. This methodology is key to dealing with the problem of handling the high variability of shapes, sizes, and positions of bony features in ultrasound images of the spine. However, as the inception module is very computationally demanding, the normal convolution operation in the traditional inception module is replaced by the depthwise convolution in this proposed model.  
Figure 6: Proposed light dense block.  
In the proposed light dense block, a sequence of two \(3\times 3\) depthwise convolutional layers is used to carry out feature extraction. In the skip path, a sequence of \(3\times 3\) convolution blocks is used, as shown in Figure 7, instead of bigger \(5\times 5\) and \(7\times 7\) blocks. Therefore, the outputs from the three \(3\times 3\) convolution blocks are concatenated to enhance the receptive field and reduce the semantic gap between the encoder and the decoder. A residual connection of a \(1\times 1\) convolution block is also presented in the skip path to make the learning procedure stable.  
In the proposed inception module, the technique to control the number of filters of the convolution layers inside the block was adapted [41]. A parameter \(P\) was assigned to control the number of filters as given by Equation (4),  
\[P=\lambda\times F \tag{4}\]  
where \(F\) is the number of filters in the corresponding layers like the basic U-Net, and \(\lambda\) is a scaler coefficient. The number of filters was set to \(F\) = [32, 64, 128, 256, 512], along with the five layers of the LDS U-Net architecture, respectively, and \(\lambda\) was chosen as 1.67 to ensure that the model structure was similar to the basic U-Net. The numbers of filters were set to \(\frac{P}{\xi}\), \(\frac{P}{3}\), and \(\frac{P}{2}\) in the three corresponding convolutional layers for extracting multiscale features.