Hello Muhammad,

according to the paper in your reference, for each point (x,y,z) in your point cloud you should check if the inequation above holds true. If this is the case, you put the point into the set POI ("plane of interest"). Afterwards, the vessel diameter at the corresponding centerline location is computed as twice the average Euclidean distance of the POI points and the corresponding centerline location.

Good luck and best regards

Ralf

This i can understand. My problem is how to implement this equation.

nx(x - xc) + ny(y - yc) + nz(z - zc)

For each point (x,y,z) you have to multiply nx with (x - xc), ny with (y - yc), and nz with (z -zc), then add the three terms and check if the result is lower than T.

I tried to do it, but when i plotted the obtained points on my point cloud, i got strange result... this is the reason ( figure is attached here,), i posted this question. 

Can you explain the details of this image? What are the grey regions, the dark spots, and the red spots? How was the image generated and how did the "original" look like?

I segmented the coronary arteries using the region growing method as proposed by the article attached with this Question. I generated the 3D point cloud by using Isosurface command in MATLAB. Attached image shows a portion of point cloud, in this image,

1. The grey region represents a portion of segmented coronary arterial tree.

2. The black sports, represents centerline points of the segmented coronary tree.

3. The red points are the points for which the following equation holds

                          nx(x - xc) + ny(y - yc) + nz(z - zc)