Customising the lsqcurvefit function for an user defined error metric??

I am currently trying to use a Levenberg-Marquardt solver with the lsqcurvefit function for the registration(Minimization stage) of 2 point clouds.

I am able to modify the objective function of the lsqcurvefit, and obtain a good fit.

But for my application, I would like the change the error metric on which the solver works on. If I my understanding is right, the solver works on minimizing the squared deviations between the 2 data sets. I would like to add another term into the error, and let the solver minimize the new error metric. Does the lsqcurvefit allow such modifications?

Thank you in advance!

[Torsten]

Which kind of error modification do you want to introduce ?

Best wishes

Torsten.

[Guruprasad]

Thank you Torsten for your reply.

I have a set of points which are a part of my actual data set(known already). I would like to introduce more weights on the deviations on these points, when compared to the other points.

So, if I could include, a term which could increase the error more for deviations on these points, I believe these points would be considered as priority.

I am also open to other suggestions for implementation.

Thank you,

Guru.

Answer 1

[Torsten]

Use "lsqnonlin" instead of "lsqcurvefit" and define the f_i as

f_i = sqrt(w_i)*(y_i-ydata_i)

where w_i is the weight for the deviation of the ith data point.

Best wishes

Torsten.

[Torsten]

And here is a suggestion if you want to stick to "lsqcurvefit":

https://de.mathworks.com/matlabcentral/newsreader/view_thread/42584

Best wishes

Torsten.

[Guruprasad]

Thank you very much Torsten!

The "weights" solution works perfectly. The only problem is that I have close to 25000 points :D

Weighing the errors for every iteration of my registration loop makes it computationally expensive. Is there a way to make this faster?

[Torsten]

But multiplying the residual vector by the weights is just

res=res.*sqrtw

where "sqrtw" can be set before the call to "lsqnonlin" and passed to the residual function as an argument. This should not take that much time.

Best wishes

Torsten.