Accurate and precise vessel segmentation is the key technology of medical image three-dimensional(3D) reconstruction and visualization. However

the existing methods of vascular segmentation still have shortcomings. According to the correlation between adjacent layers of computed tomography(CT) images and multiple directions of vascular distribution

this study proposes a new 3D vessel segmentation algorithm based on the Stein-Weiss analytic function. The algorithm can delineate more precise and clearer blood vessels

particularly in the case of noise and other effects of broken vessels. First

the contrast of vascular point and background was increased by pretreatment of image through enhancement and adjustment to window width and position. Then

we combined the Stein-Weiss function with the gradient operator. Each voxel of the CT volume data was expressed as a Stein-Weiss function. We also used the gray value of the six neighborhoods of the voxel as coefficients of the Stein-Weiss functions. Then

we determined the gradient values of the Stein-Weiss function in the three directions of

and . When the values were larger than the threshold

the voxel was considered a point of the vascular edge. Finally

according to the CT slices extracted from the edge of the vessels

we reconstructed the 3D blood vessels. In the experimental part

we used our proposed algorithm

the octonion analytic function

and the region-growing algorithm to segment blood vessels. Given that the region-growing algorithm cannot continue to grow in the region of the breakpoint of the vascular region

the first two methods can delineate more abundant blood vessel branches. As the Stein-Weiss analytic function has better analytic properties than the octonion analytic function

the segmentation of blood vessels using our proposed algorithm is clearer and has lesser noise than the segmentation using the octonion analytic function. The experimental results of liver blood vessel segmentation and 3D reconstruction show that the sensitivity and specificity of the proposed algorithm are relatively high compared with that of the region-growing algorithm and the octonion analytic segmentation algorithm. In particular

the algorithm has evident advantages in the denoising of vessel segmentation and can rapidly and efficiently segment clearer and more refined vessels. In this study

a new algorithm for vessel segmentation is proposed. We used the Stein-Weiss function of high-dimensional mathematical tools to extract vessel edge. The proposed algorithm can consider multiple characteristics during the calculation process. Compared with the results of a small number of characteristics

the proposed algorithm has evident advantages and wide application prospects.Because the nature of Stein-Weiss parsing can be suitable for arbitrary dimension

we can use the Stein-Weiss analytic function to identify the image edge of 2D or higher dimension.