MATLAB: Least squares solution of a point cloud to a surface

fittingpoint cloudprocrustessurface

Hi, I have a point cloud in the form of 3 vectors (x,y,z), that have come from a 3D imaging technique. These represent a surface, plus noise and some bigger deviations (wrinkles).

To understand the extent of these wrinkles I want a least squares solution of the perpendicular distance of these points to the ideal surface (lets say a hemisphere).

procrustes is no good… I can't create a point cloud of the same number of points as my data. Even if I could the grouping of points on my data due to parts of the image would skew the results when compared to randomly distributed points…

Any ideas? Thanks in advance

Best Answer

The perpendicular distance to the sphere surface would be easiest. Describe your hemisphere as in the Wikipedia article on Sphere, then do a nonlinear least squares fit to it with nlinfit, lsqcurvefit, fminsearch, or the Curve Fitting Toolbox functions.

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MATLAB: Weighted least square fit

Yes. There is LSCOV.

MATLAB: How to find the normal to a hemisphere surface

Think about what the normal vector means. It points straight out from the hemisphere. What other known point is on the same line? (Hint: What do you know about the center of the sphere? What property does it have?)

That means, from ANY point on the surface of the hemisphere, call it [x,y,z], the normal vector is as simple as:

C = [2 1 3];
normalvec = [x y z] - C;

This vector is normal to the surface, and points outwards. Just negate the vector if you want it to be inward pointing.

Best Answer

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MATLAB: Weighted least square fit

MATLAB: How to find the normal to a hemisphere surface

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