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## Ellipsoid Fitting

version 1.0 (1.17 KB) by

Two matlab files to demonstrate how to fit an ellipsoid directly to a set of 3D points.

Updated

The code implemented a special case of the ellipsoid fitting technique proposed in the paper Least Squares Ellipsoid Specific Fitting, corresponding to case k= 4. Just put the two files in the same directory and run "testFit4". You can change the noise level to observe the fitting accuracy and efficiency of the algorithm. It works well when the underlying shape characterized by the data points is quite spherical. However, if this is not the case, some modification is required. For the technical detail of the fitting method, please refer to the above mentioned paper, which can be found from the following webpage:
http://www2.computer.org/portal/web/csdl/doi?doc=abs/proceedings/gmp/2004/2078/00/20780335abs.htm

### Comments and Ratings (4)

Jean-Yves Tinevez

### Jean-Yves Tinevez (view profile)

The code cannot be used in a general manner.

Toni

### Toni (view profile)

Why is the size of the points in the testfit (11,6)?

Should it not be 11,3 for xyz?

what is the meaning here?

chuk Zhu

### chuk Zhu (view profile)

where I check your test, I find the values of the major, medium and short radius from the equation u^3 - I*u^2 + J * u - K = 0 have some problems...

Here I = a + b + c
J = ab+bc+ac-f^2 - g^2 - h^2
K = |a h g; h b f; g f c|;

from "least squares ellipsoid specific fitting" GMP-04

MATLAB 6.5 (R13)