Levenberg-Marquardt-Algorithm

[Michael Liebschner]

Hallo everybody

I'am new in this system, but I even have a problem,
so here is my first message:


I am searching for a method to transform 3D-coordinates
and fit them on a known geometry from one system into another.

With the assumption that all measurement errors are independent and normally
distributed with constant standard deviation, I want to describe the
rotation (with euler angles) and translation in a 4x4-matrix.

| R t |
M = | |
| 0 1 |


| cosf*cosg -sinf*cosg sing
| |
|
R = | cosf*sing*sinh+sinf*cosh -sinf*sing*sinh+cosf*cosh
-cosg*sinh | |
|
| -cosf*sing*cosg+sinf*sinh sinf*sing*sinh+cosf*sinh
cosg*cosh |



For the approximation I want to take the Levenberg-Marquard-algorithm
in combinatoin with the least squares method, because this algorithmen works
normaly very good. But here I have some problems with it, because I have not
only a function but a 4x4-matrix with 6 unknowns
- 3 angles and 3 translations -

And there is my question, has anyone a solution for this problem???


Thank you for your time.



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| Michael Liebschner | Tel: +41 31 632 8679 |
| M.E.M. Inst. for Biomechanics | Fax: +41 31 381 0259 |
| University of Bern | Internet mike@mem.unibe.ch |
| Murtenstr. 35, P.O.Box 30 | |
| CH-3010 Bern, Switzerland | |
------------------------------------------------------------
------------------------------------------------------------
| Michael Liebschner | Tel: +41 31 632 8679 |
| M.E.M. Inst. for Biomechanics | Fax: +41 31 381 0259 |
| University of Bern | Internet mike@mem.unibe.ch |
| Murtenstr. 35, P.O.Box 30 | |
| CH-3010 Bern, Switzerland | |
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