"Matt J" wrote in message <firstname.lastname@example.org>... > "Matt J" wrote in message <email@example.com>... > > > > > Now, i want to find all Ci of Rotation matrices Ri as well all elements of translation vectors Ti. What should i do to obtain local minimum value of this function ? > > =============== > > > > The problem has a closed form solution, so iterative minimization is unnecessary. Here is one implementation > > > > http://www.mathworks.com/matlabcentral/fileexchange/26186-absolute-orientation-horns-method > > I assume you don't really mean that you're applying a different rotation matrix Ri and translation vector Ti to each point. That wouldn't make sense. A translation is sufficient to make 2 points coincide and is given simply by Ti=Ui-Vi. Adding rotation component would just create infinite non-unique solutions.
Hi Matt J, For my case, each point has its own transformation described by a rotation matrix and a translation vector. Actually, my cost function have another term (third term) which constrains the movement of neighbor points to be smooth (equation of third term is complex, it is not easy for me to write with simple texts). I read a paper in finding minimum of this cost function. It mentioned that it applied Levenberg-Marquardt to obtain the minimum. Following this direction but i am now stuck in finding Jacobian for f(x), (where F(x) =f(x)'.f(x) ). I think you are an expert in math, i wish you can give me some suggestions. Thanks in advance, Toan