2D plane fitting , ransac, matlab, link

Question

I have set of 3D points.

Points_[x,y,z]% n*3 where n is number of points

I want to fit a plane (it is floor) and check height of plane. I think it is 2D problem .

z=bo+b1x+b2y;

I can't find a link for 2D ransac plane fitting . Can someone please give this link or file.

Secondly, Some softwares (commercial)gives height value of plane. It is mean or some complex value.

Regards,

Answer 1

If you form the following "A" matrix

A = [ones(numel(Points_X),1), Points_X(:), Points_Y(:)]; 

where the (:) is to give you column vectors (in case they were not to begin with)

Then you can write your equation as the classic linear system of equations:

A*b = Points_Z(:);

where b = [b0; b1; b2] -- a column vector of the parameters you are trying to determine. This has the canonical solution

b=A\Points_Z(:)

or b=pinv(A)*Points_Z(:)

See help on mldivide and pinv.

You must have 3 or more points which don't all lie on a line. For an overdetermined system like this, pinv and \\ will basically produce the same results. If they are nearly colinear, there may be some advantage using .

The 3 parameters in b are basically the height of the plane above the origin, the x slope, and the y slope of the plane. If you think about it, the "height" of a plane IS your z term. You can talk about height above some point (like the origin). Now, if you want height at the center of mass of the sampled points, you would then do

z_mean = [1 mean(Points_X(:) ) mean( Points_Y(:) )] * b

which is probably just equivalent to mean( Points_Z(:) ) . For this definition to be meaningful, you would have to ensure that you have a uniformly spaced grid over the region of interest.

There may be other definitions, depending on your application. For instance, if you are trying to find the height at a center of a room, with points sampled along the walls and interior, then replacing mean with median might be more appropriate.