## 2 Materials and Methods
### Voxel Patch Generation by Image Reduction and Slice Selection  
In this section, a VP composed of limited slices was created by reducing the input image and selecting 56 slices. A VP is a voxel set that summarizes information about the body axis. Generally, a deep convolutional neural network (DCNN) requires a large number of training images, but it is challenging to create a large number of training images for skeletal muscles, especially for surface muscles, which have substantial individual differences. Therefore, we propose a VP-based method. In training, one VP is generated for each case. In the test, multiple VPs are created according to the number of slices in the test case. Then, segmentation is performed for each VP, and finally, the results of each VP are merged. The details of how to generate training and test VPs are described below.  
The input images were resized from \(512\times 512\) pixels to \(256\times 256\) pixels in an axial cross-section with nearest-neighbor interpolation. Next, 56 slices were selected at equal intervals from each of the whole-body slices. Our GPU environment is four Tesla V100 (32 GB), and is not necessarily poor, but the VP size that can be generated depends on the total GPU memory capacity (128 GB). In this study, the VP size was set to maintain the resolution of the cross-section while maintaining the number of slices in the body axis direction in the whole-body CT images. When using the original image size (\(512\times 512\) pixels) without resizing, the number of images in the body axis direction for which a VP can be constructed is only 14 slices. In a whole-body CT image consisting of approximately 1500 images per case, it is thought that the number of images will be too small for training. Therefore, we defined the VP size as \(256\times 256\times 56\) voxels.  
Figure 1: Schematic diagram of the proposed method. The proposed method consists of three steps. First, a voxel patch is created by image reduction and slice selection. Next, a three-dimensional U-Net is used to segment the surface muscle in each test voxel patch. Finally, slices are combined from each test voxel patch, and the image is enlarged in order to obtain the original size of the surface muscle segmentation results. VP, voxel path; 3D, three-dimensional.  
The VP for training used 56 slices selected at equal intervals from the first slice in the axial direction of the whole-body CT image; one VP per case was used for training. The selected slices vary in anatomical spatial position between training cases, so the effect of increasing the variation in training is expected.  
In our method, the above-mentioned training VP consisted of 56 slices per case. Similarly, the test VP was also constructed with 56 slices per VP, so using VPs of N sets gives a segmentation result for all slices in a test case (Figure 1). The test VPs consisted of 56 slices selected at equal intervals in the same manner as the training VPs. Moreover, N sets of VPs were created by selecting the first slice without consecutive duplication from the axial cross-section in the whole-body CT-image. However, this slice selection method has a problem; the test VP cannot be constructed when the number of slices is not a multiple of 56. At that time, the slices used in other test VP sets could be selected at equal intervals from the head again, and the test VP is composed of 56 slices. Note that the slices are rearranged craniocaudally in one VP set. As described above, all slices can be covered by combining all test VPs; therefore, surface muscle segmentation can be performed.