管道切片的三维重建

3D Reconstruction of Pipeline Slice

文中证明了所有切片含有过轴心的大圆 ,该大圆直径一定与切片边界相交。通过构造连续型模型和离散型模型 ,从0 .BMP中定出轴心为 (0 ,16 0 )和半径为 30的最大圆 ,并相继在其它切片中运用最大圆必包含在切片中的先决条件 ,找出相应切片中所有可能的轴心坐标 ,进一步对每一切片待选的轴心坐标 ,根据其球体必在上 2 9～下 2 9层切片中存在相应半径的圆 (在上下 2 9层中存在半径为 7.6 8,在 2 4层存在半径为 18的该球体的相应的截面圆 )的特征 ,筛选上述待选轴心坐标 ,比较准确地定出了 0到 70层的轴心坐标。对于 71至 99层由于上 2 9层的信息不全 ,还存在不少待选点 ,再应用切片尖端特性 (在 70层左下角的点只能由半径较小的圆包络而成 ,由此定出 99层的轴心坐标 )确定其余切片的轴心坐标。绘制出的三维图形和各坐标面的投影图是光滑流畅的。最后文中用所得轴心坐标重新构造各切片 ,与原切片比较 ,相异象素点误差不足 3% ,结果令人满意。

This article proves that there exists the biggest circle on each slice, whose center is on the pipeline center curve. By constructing the continuous model and the discrete one, we are able to determine the biggest circle on 0.bmp slice, of which radius is 30 and center coordinate is (0,160). Using the predetermined condition that the biggest circle should be contained in each slice, we find out all possible coordinates of the pipeline center curve on corresponding slices. For each slice, basing on the principle that a slice which lies on over 29～under 29 layers of the slice must contain a corresponding section of the sphere of radius 30, we filtrate the coordinates of the pipeline center curve and determine the more precise one. However, there are still some coordinates of the pipeline center curve left to be filtrated, such as slices from 71 to 99, due to the information is not enough. Further, we use the pointed end property to determine the coordinates of the pipeline center curve on other slices. The projecting figures on each coordinate plane are smooth and fluent. In the end, by using the coordinates to reconstruct all the slices and comparing the slices with the original ones, we found that the error of different pixels is less than 3%. The result is satisfied.