利用Stein-Weiss解析函数性质的3维血管分割

New 3D vessel segmentation algorithm using the Stein-Weiss analytic function properties

目的针对现有的血管分割方法对血管的分割精度尚有不足,尤其是对噪声等影响下的断裂血管,基于Stein-Weiss函数的解析性提出了一种新的3维血管分割算法,能够分割出更精细更清晰的血管。方法首先,通过图像增强和窗宽窗位调节的预处理来增加血管点与背景的对比度。然后,将Stein-Weiss函数与梯度算子结合起来,把CT体数据的每一个体素都表示为一个Stein-Weiss函数,体素6邻域的灰度值作为Stein-Weiss函数各组成部分的系数。再求出Stein-Weiss函数在x、y、z 3个方向上的梯度值,大于某一个阈值时,便将此体素视为血管边缘上的点。最后,根据提取出血管边缘的2维CT切片重建出3维的血管。结果对肝静脉的造影数据S70进行肝脏血管分割与3维重建的实验结果表明,利用该算法进行血管分割的敏感性和特异性相对于区域生长算法和八元数解析分割算法都较高。尤其是对于血管分割的去噪方面有明显优势,因此能够快速有效地分割出更清晰更精细的血管。结论提出了一种新的血管分割算法,利用Stein-Weiss函数的解析性来提取血管的边缘,实验结果表明,此算法可以有效快速地去除血管噪声并得到更精细的分割结果。由于Stein-Weiss解析的性质可以适合任意维数,所以利用Stein-Weiss解析函数性质可以进行2维或更高维的图像边缘识别。

Objective 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 vascu- lar 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. Method First, the contrast of vascular point and background was increased by pretreatment of image through en-hancement and adjustment to window width and position. Then, we combined the Stein-Weiss function with the gradient op- erator. 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 x, y, and z. 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 re- constructed the 3D blood vessels. Result 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 contin- ue 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. Conclusion 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 muhiple characteristics during the calculation process. Com- pared with the results of a small number of characteristics, the proposed algorithm has evident advantages and wide applica- tion 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.