# Vertebral Center Points Locating and Cobb Angle Measurement Based on Deep Learning
## 3 Materials and Methods  
### Network Structure  
The network structure for detecting vertebral center points consists of three parts, with a lightweight network MobileNetV3 [19] as the Backbone for feature extraction. This Backbone network can generate five feature layers with different resolutions and a different number of convolution kernels which contain the information on different scales of the input X-ray image.  
The middle part of the network is U-Net [20], which is specially designed for medical datasets with large resolution and small size. The left half of the network is a shrinking network for extracting information, where the size of the feature image is constantly decreasing. It consists of four blocks with the same structure, each containing several convolution layers and a Max Pool layer. The 4 blocks are downsampled by the convolution kernel to obtain a feature layer respectively. In this paper, MobileNetV3 is employed to generate the four feature layers. The right half of U-Net is an expansion path that is symmetrical to the left. The expansion path block is firstly sampled from the previous feature layer to the size of the corresponding feature layer in the shrinking network, and then copied and spliced with the feature layer in the channel number dimension. After convolution, the number of channels is made the same as the number of channels in the feature layer. During the information extraction process, the contraction path will  
Figure 1: Definition of Cobb angle.  
continuously reduce the resolution of the feature layer. In contrast, the expansion path can retain high-level abstract semantic information in the upsampling process and concatenate feature maps corresponding to the contraction path, thus making it essential for more accurate localization.  
The final prediction module of the network utilizes the idea of CenterNet [21], employs a \(3\times 3\) convolution layer to transform the feature map to the desired dimension, and adopts the \(1\times 1\) convolution to generate a heat map of vertebral center points and center offset. The center offset can accurately detect the vertebral center points based on the heatmap.  
The human spine consists of seven cervical vertebrae, twelve thoracic vertebrae, five lumbar vertebrae, one sacrum, and one cocyx. To distinguish the cervical vertebrae, which generate 85% of the noise with similar features to the thoracic and lumbar vertebrae, a parallel network is established to detect four anchor points. These anchor points are located at the first group of the clavicle and hip bone, respectively. As shown in Figure 2, the network structure is designed to accurately predict the center points of the vertebrae.  
The network structure parameters are few, and the low-semantic information in the spine X-ray can be extracted through the Backbone of the model. The contraction and expansion paths of the U-Net structure in the middle of the network are also the encoding and decoding processes which extract more features of the image in the encoding process and gradually restore the spatial dimension in the decoding process, fusing the previously extracted features to achieve accurate target positioning. The network's structural characteristics and the transfer learning method enable the model to be trained and converged on a custom dataset of spine X-rays with only a few hundred images.