| Least squares fit of a model to a skeleton consisting out of 3D points. [message #63934] |
Mon, 24 November 2008 05:33  |
Johan
Messages: 5
Registered: November 2008
|
Junior Member |
|
|
I have the following problem to solve and was wondering whether the
mpfit routines of Craig Markwardt will do the job?
Do have the following model:
Let g(X,Y,Z)=1 be a quadratic function in the coordinate system
(O,Z,Y,Z) defined by the long, horizontal and vertical axes
(ellipsoid). Write the equation of this quadratic function in matrix
notation as follows:
g(X,Y,Z) = [X, Y, Z]*[[A1,A4,A5],[A4,A2,A6],[A5,A6,A3]]*[[X],[Y],[Z]]
+ [X, Y, Z]*[[A7],[A8],[A9]]
Need to fit this model to a 3D skeleton of N points by using least
squares by calculating the coefficients Ai .
This is achieved by minimizing the total squared error between the
exact position of the points (Xi, Yi, Zi) on the quadratic surface and
their real position in the coordinate system (O, X, Y, Z). The
minimizing is performed from the derivative of the equation below with
respect to A1 ... A9:
J(A1 ... A9) = for i=0,N sigma(1 – (Xi, Yi, Zi))^2
This equation yields a linear system of nine equations in which the
values of coefficients A1 ... A9 are unknown.
Anyone that can help?
Johan Marais
|
|
|
|
comp.lang.idl-pvwave archive
Members
Search
Help
Login
Home
