Fitting a plane through a 3D point data

For example, i have 3d point cloud data [xi, yi, zi] as the attachment .txt file. I want to fit a plane to a set of 3D point data. What kind of method to do that?

[Matt J]

How does one know that M and L are different planes and not just noise? Is there a known upper bound on the noise? A known lower bound on the separation distance between M and L?

Answer 1

[Matt J]

You will probably have to implement a RANSAC plane fitting routine.

[ha ha]

I also think that I need to use RANSAC approach. Do you have a matlab code to do it?

[Matt J]

No, I do not.

[Matt J]

However, you may be able to modify this RANSAC line fitting routine

https://www.mathworks.com/matlabcentral/fileexchange/40873-ransac-algorithm

[ha ha]

Thanks.

[Matt J]

One approach you might consider is to take planar cross sections of your data. This will give 2D data for a line, with outliers. Then you can apply a ready-made RANSAC line-fitter, like the one I linked you to. From line fits in two or more cross-secting planes you should be able to construct the desired plane K.

Answer 2

[Walter Roberson]

data = load('1.txt');
coeffs = [data(:,1:2), ones(size(data,1),1)]\data(:,3);

The equation of the plane is then coeffs(1)*x + coeffs(2)*y - coeffs(3) = z

[ha ha]

From your answer, I plot the surface as below image. But That plane is not same as my expected plane. If we use the formulas as your proposed method, the plane is fitting through all points & will be slightly different with my expected plane K(=plane M)

Answer 3

[Matt J]

   xyz=load('1.txt');
    xyz(xyz(:,2)>40, :)=[];

   mu=mean(xyz,1);

   [~,~,V]=svd(xyz-mu,0);

   normal=V(:,end).';
   d=normal*mu';

The equation of the plane is then xyz*normal.' = d

[ha ha]

Why you delete my data by using below syntax:

xyz(xyz(:,2)>40, :)=[];

In general, how can you know the value of Y coordinate which is larger than 40 will be deleted????

[ha ha]

In my question: Plane M contains a large number of point data when compared with plane L(i.e., 90%). I wanna find the plane can cover large number points as plane M. Example: in the general, there are some outlier(or noise) points. So, the result will be affected significantly. Because you are using "least square regression method" as I guessed

[Matt J]

How does one know that M and L are different planes and not just noise? Is there a known upper bound on the noise? A known lower bound on the separation distance between M and L?