Least squares solution of a point cloud to a surface

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

Answer 1

[Star Strider]

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.

[Samuel Arnold]

I over simplified it with the example of a hemisphere, but I think fminsearch is the way to go. It's part of hemisphere with a tangential cone extending from it. I guess I'll need to split the data points at the intersection point and have two separate fminsearch function for the sections? Just a case of geometry Thanks

[Star Strider]

My pleasure!