## 2 Methods and Materials
### Construction of 3D Model of Human Tibia  
A 29-year-old male volunteer weighing 65 kg and standing 175 cm tall was selected for this study to construct a 3D model of the human tibia, as his tibia was considered representative of those in the population. CT scans were performed on the lower limbs of volunteers, with a slice thickness of X, an increment of 0.625 mm, a pixel size of 0.5 \(\times\) 0.5 mm, and an image size of 512 \(\times\) 512. There were a total of 787 images, and the image output format was DICOM 3.0. The CT image of the volunteer's tibia is shown in Figure 1.  
Interpolation processing was required when constructing a tibial model using CT images before 3D modeling to generate new tomographic images due to the slice increment of the CT scanning being larger than the pixel size. The one-way linear interpolation method was used. This method placed each 2D fault image in the same 2D coordinate system based on spatial location parameters and then arranged them in order in space to form a 3D data field. Vertical parameters were weighted and averaged using one-way linear interpolation for each adjacent fault [10; 11]. The equation for calculating the grayscale value of the inserted layer is shown in Equation (1). Figure 1: CT image of the tibia of a volunteer. \[H_{d}(i,j)=\left(1-\frac{l_{k}}{l_{k}+l_{k+1}}\right)H_{k}(i,j)+\frac{l_{k}}{l_{k}+ l_{k+1}}\times H_{k+1}(i,j) \tag{1}\]  
\(H_{d}(i,j)\) is the grayscale value of pixel \((i,j)\) in the new tomographic image. \(l_{k}\) and \(l_{k+1}\) are the distances between the new fault and the images of the \(k\)th and \(k+1\)th layers, respectively. \(H_{k}(i,j)\) and \(H_{k+1}(i,j)\) are the grayscale values of pixel \((i,j)\) in the \(k\)th and \(k+1\)th layers of the image, respectively. Although the interpolation of CT images can improve modeling accuracy, the new tomographic image must be sharpened due to the large clarity differences between the new and original images. The Laplace operator is selected as the sharpening method, which is calculated as shown in Equation (2). \[\
abla^{2}f=4f(x,y)-f(x-1,y)-f(x,y+1)-f(x+1,y)-f(x,y-1) \tag{2}\]  
In Equation (2), \(\
abla^{2}f\) is the Laplace operator, \(f(. )\) is a 2D function, and \((x,y)\) is the Cartesian coordinate. Equation (3) is obtained using a template to represent. \[L_{0}= \begin{bmatrix}0&-1&0\\ -1&4&-1\\ 0&-1&0\end{bmatrix}  \tag{3}\]  
In Equation (3), \(L_{0}\) represents the grayscale variation in the orthogonal direction. The grayscale changes in the diagonal direction are introduced because the above equation only considers the grayscale value changes in the orthogonal direction, as shown in Equation (4). \[\left\{\begin{array}{c}L_{1}=\left[ \begin{array}{ccc}-1&-1&-1\\ -1&8&-1\\ -1&-1&-1\\ L_{2}=\left[\begin{array}{ccc}1&-2&1\\ -2&4&-2\\ 1&-2&1\end{array}\right]\end{array} \right.\right. \tag{4}\]  
In Equation (4), \(L_{1}\) and \(L_{2}\) are the grayscale changes in the diagonal direction. The sharpened image is overlaid with the original CT image to obtain the final image, as shown in Equation (5). \[g(x,y)=h(x,y)+\
abla^{2}h(x,y) \tag{5}\]  
In Equation (5), \(g(x,y)\) is the final image. \(h(x,y)\) is the original image. The image can be visualized after the CT image processing is completed. The selected visualization processing software is MIMICS 21.0. First, the CT data were imported into the software, and six display orientations were set, including up, down, left, right, front, and back. The reconstructed coronal and sagittal images were obtained after processing. Second, graphic segmentation was performed to obtain the tibial images. Segmentation based on grayscale values was an appropriate choice due to wide differences in the grayscale values among the tissues in the human body. The ability to accurately and completely extract relevant organizations depended on whether the threshold segmentation range was reasonable. If the threshold segmentation range was set too large, it would result in many irrelevant tissues in the final extraction result.