How to quantify angle of a 3-dimensional cylinder

Dear MATlab help community,

I am working on a project that involves quantifying angle/tortuosity of cylinder beams segmented from optic nerve. Is there a simple MATlab function that will allow me to quantify (does not have to be absolute angle, since relative comparison will be carried out) angle or tortuosity of 3D cylinder beams? The cylinders are segmented from AMIRA (FEI Visualization Science Group).

See attached sample image.

Many Thanks,

Please email your answers or comments to: [e-mail]

John Xie

[Walter Roberson]

Are the images each 2D ? And the circle should be considered to be a plane and the angle of the piles should be measured relative to that? If so then are you looking for an angle pair (left-right and forward-back) or do you want the center of the base of each pile to be used to calculate a single angle relative to the center projected perpendicular to the plane?

[John Xie]

Dear Walter, Thank you so much for your speedy response. To answer your question, I am interested in quantifying the tortuosity/curviness of the a line linking the center of the 2D discs in 3 dimensional space. I am mostly interested in the relative curviness between any two / or groups of cylinders, so I can say the average curviness of the nerve fibers in one quadrants of the nerve is more than the other quadrant.

Thank You !

John Xie

[Image Analyst]

That's what I figured and why I answered below like I did. So, what do you need help with if anything? Do you have the centroids of all the blobs? Do you know how to use the Pythagorean theorem between slices and between the first and last slice?

[Walter Roberson]

It looks to me as if the discs that make up each stack are not all the same size. If that is correct, I am not certain that you will be able to get the 3-space distances instead of the 2-space distances.

Normally some 3-space information can be derived from shadowing, but the shadowing on those piles is inconsistent with the hypothesis of single illumination point, it appears to me.

[John Xie]

Dear Image Analyst,

    Yes the discs are of different size, but I am only interested in the tortuosity of the stack of discs as a whole. I can skeletonize the discs to a line going through the center of each discs. Does MATLAB offer a tool box function or GUI that allows me point to each segmented segment and calculate the tortuosity? Does bwdistgeodesic function able to analyze 3D curves or only 2D curves?
Thanks,

John

Answer 1

[Image Analyst]

No. There is no simple MATLAB function to do that, that I'm aware of. You can measure the curl of the path through the centers of the discs at each plane. Also see this. It's also called tortuosity. It's basically the ratio of the the actual curvy path distance to the straight line, Euclidean distance (or the inverse).