Nonlinear optimization problem in Matlab

Hi all, i want to find the maximum likelyhood of this problem but i really don't know how to do it. The problem also said that "the optimization can be initialized with R = I3(identity) and d = 0".

Answer 1

[Alan Weiss]

Are you really allowed to take any d you want? If so, why not just take any R in SO(3), maybe the identity, and take d to be the value of the resulting matrix multiplication?

If, instead, you have a fixed d, then you need to characterize the R in SO(3) by a set of variables, and minimize the expression over those variables. You can try using fminsearch, though you may have to start it from a variety of initial points to get a global minimum.

Alan Weiss

MATLAB mathematical toolbox documentation

[Torsten]

Are you really allowed to take any d you want? If so, why not just take any R in SO(3), maybe the identity, and take d to be the value of the resulting matrix multiplication?

I think you missed the summation over k.

Best wishes

Torsten.

[Alan Weiss]

Indeed I did, thanks! I should spend more time looking when the problem seems nonsensical.

The suggestion stands, though: parametrize SO(3) matrices, and have at it with a minimizer.

Alan Weiss

MATLAB mathematical toolbox documentation

[Flore Flore]

Thank you for reply. The problem also said that "the optimization can be initialized with R = I3 and d = 0".

Answer 2

[Flore Flore]

i all,

please nobody has an idea?

even a helpful suggestion please

[Torsten]

Do you know how an element of SO(3) is sensefully parametrized ?

I don't.

Best wishes

Torsten.

[Flore Flore]

Can we parametrize it like this? and consider the two parameters d and phi instead of R?

Best wishes

Flore

[Torsten]

Why only rotations in the xy-plane ? The representation you choose for R in the objective function must include all possible cases, e.g. a composition of a rotation in the xy-plane with a rotation in the xz-plane.

Best wishes

Torsten.

[Flore Flore]

Thank you for your reply.

If we consider that this R is a scalar. Please i want to know how to build the function with the summation over k in Matlab.

Best wishes

Flore

[Torsten]

The objective function should somehow look like

summe=objfunc(x,y_zk,y_mk,invD0,o)
d=x(1:end-1);
r=x(end);
summe=0.0;
for k=1:K
  summe = summe + norm(d-y_zk(k,:)*r*invD0*(y_mk(k,:)-o)');
end

Best wishes

Torsten.