基于切片图像的血管三维重建方法

The Method of Three-dimensional Reconstruction of Blood Vessels Based on Images of Slices

研究了基于血管切片投影图像的血管三维重建问题.通过对所给血管切片图像格式的转换,利用细化方法和轮廓边缘检测的Kirsch算法,构建了切片图像的骨架(中心线)和轮廓线;提出了最小距离最大半径法,得到了切片图像最大内含圆的圆心和半径.对于球心坐标及其在XY,YZ,ZX坐标面上投影的散点图,利用非均匀有理B样条(NURBS)技术、三次样条插值方法对散点数据进行拟合,分别得到了三坐标面的投影图及空间中轴线的方程.进而建立圆柱螺线模型,利用最小二乘原理对散点数据再拟合,得到结果如下:中轴线为圆柱螺线,半径为30,在3个坐标面XY,YZ,ZX上的投影分别为:半圆弧曲线、正弦曲线、余弦曲线,并给出了相应的算法.最后,利用得到血管的中轴线方程及半径,建立了血管的管状曲面模型,对血管进行了三维重建.

The problem of three\|dimensional reconstruction of blood vessel based on projecting image of slices of blood vessel is studied. The format of the given image of slices of blood vessel is transformed. The methods of thinning and the operator of Kirsch are used and the media\|axis and contour line of image of slices are obtained. The method of the least distance and the biggest semidiameter is given. The coordinate center of a circle and semidiameter of the biggest inner\|contained circle is computed, i.e. the point of intersection of parallel slices and media\|axis of blood vessel is obtained. The method of non\|uniform rational B\|spline (NURBS) and cubic spline is used respectively. The scattered points of the coordinate center of ball and its projection on the axes of XY, YZ, ZX are fitted and the equation of space media\|axis and its projecting figure are obtained. The NURBS representation of the media\|axis is actually a cylindrical helix. The model of cylindrical helix is established and the scattered points are fitted again by use of the method of least squares. The result is that the semidiameter is 30, its projective image is semicircular curve, sinusoid and cosine respectively. Then the pipe surface of blood vessel is built and the three\|dimensional image is reconstructed.