To find rotational axis of an incomplete point cloud

Hello All,

I am new to matlab and I am trying to find solution to a very specific problem. I have a point cloud with approx. 10000 points which has a rotational axis, but is incomplete (this means that the centroid does not lie on the rotation axis, because of incomplete nature of data).

My problem is to find the rotational axis of this point cloud. I have attached images below any kind of help would be really appreciated.

These images show different views of same point cloud and also incomplete nature of point cloud can be seen in here.

[Matt J]

What exactly do you mean by a "rotational axis"? Do you mean the cloud are sample points in a shape that is circularly symmetric about that axis?

If so, you have to know something about the shape in order for the solution to be well-defined. For example, if the underlying shape is a sphere, then every axis is an axis of circular symmetry.

[New user]

Yes, I mean that the points are circularly symmetric around an axis.

About the shape, the point cloud is somewhat torriodal in shape

I could have easily calculated the mean and then divided it with all points like in SVD to get the rotational axis, if the point cloud were complete. But here the centroid does not lie on the rotational axis so that method wont work. I am looking for an alternate method to find the rotational axis

[darova]

I think such algorithm will be too complicated (if it exists)

Can't you just manually replace your object to origin and rotate it?

Answer 1

[Image Analyst]

I'd use pca() to find the 3 principal axes. You can then rotate the cloud so that the 3rd principal axis lines up with the z direction if you want.

[New user]

Hello Image analyst,

I went through some of the answers for similar kind of problem on the forum where I found a solution for a problem answered by you.

I tried using the code for my model and found three principal axis. but these axis are not at the rotational axis (which is unknown) and thats why does not my problem.

Please see the below images, where you can see that the incompleteness of point cloud has shifted the axis system to the side where there are more points (i.e away from the rotational axis)

[Matt J]

If PCA is successfully finding the plane of the toroid, project all your points onto that plane and do a 2D circle fit, e.g. using

https://www.mathworks.com/matlabcentral/fileexchange/22642-circle-fit-kasa-method

This will estimate the point where the symmetry axis intersects the plane.

[New user]

Thank you Matt,

I am new to matlab so doing this might take some time for me( I dont really know how to project them, so I will search for it) ,I will try this and let you guys know how it worked

[New user]

I tried to use the function you told to and, I get the coordinates of the centre at this point(black point) which can visually seen is no the centre of the circle. I dont understand why this is happening

[Matt J]

The only thing I can suggest is that you attach a .mat file with your point data so that people can play with it.

[Matt J]

Instead of fitting a circle, you could try minboundcircle from this file exchange submission,

https://www.mathworks.com/matlabcentral/fileexchange/34767-a-suite-of-minimal-bounding-objects

to find the tightest circular envelope around your 2D projected points.. Since your points fill up most of a circle nicely, I'd bet this gives you a much more accurate estimate of the center.

[New user]

Thanks Matt this works perfectly for my cloud