detect the centerline of 3D data points

Hello, everyone. I am trying to detect the centerline of a set of 3D points. These 3D points are plotted and the figure is attached.

Does anybody know how to detect the centerline of these 3D data points. The equation of this centerline may be z = k1*x+k2*y+b; The coordinates of the 3D points are stored in X, Y, Z.

[Matt J]

The equation of this centerline may be z = k1*x+k2*y+b

That's the equation of a plane, not a line.

[Matt J]

Do the points lie on the surface of a circular cylinder, or some more general surface?

[Penny]

Yes, the points lie on the surface of a circular cylinder. But not a regular cylinder

Answer 1

[Matt J]

If the parametric equations for the line is L(t)=m+t*d, the following should give a good estimate of m and d, as long as the sampling of the surface is uniformly distributed,

A=[X(:),Y(:),Z(:)];
 m=mean(A,1).';
 A=A-m.';

   [~,~,V]=svd(A,0);

    d=V(:,1);

[Penny]

Hi Matt. Thanks for your answer. I got the red line by using this code. How could I do if I want to get the green line.

[Matt J]

Whoops, that should be

   d=V(:,1);

I've edited my original answer.

[Penny]

Got it. It works well. Thank you very much.

[ng]

Hi,

Did you get a chance to check if the resulting centreline was correct? I did the same as above to get the centreline. I noticed that the line was parallel to the axis (assuming the axis of the cylinder is parallel to the Z-axis) when you look at it in one plane( say Y-Z plane) but is at an angle to the supposed axis when you look at it in the perpendicular plane (that is X-Z plane).

See attached pictures for reference.

[Matt J]

What was the result for d?

[ng]

I got d=[0.8670; -0.0605; 0.4946].

I've attached here the .mat file with the variables.

I am beginning to think it could be because the top and bottom edges of the cylinder are not perpendicular to the expected axis which is why there is the slight angle.

Edit: Just to clarify the pictures in the previous comment were obtained after rotating the point cloud to make the centreline vertical. The attached data is the original, unrotated version.

[Matt J]

I am beginning to think it could be because the top and bottom edges of the cylinder are not perpendicular to the expected axis which is why there is the slight angle.

That would definitely contribute, but even more generally than that, we don't expect exact results when fitting noisy data.

[ng]

That is a fair point. Thank you for taking a look.