Hello,
What are the differences between the SVDbased and the Levenberg Marquardtbased estimations of a rigid transform? I wikipedia'd both, and they seem to be two different numerical methods of solving equations. I'm guessing that both have similar precision, but is one more stable than the other (converges faster?) What are the advantages of each? Are there any other differences? Thanks! Dave 
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Hi Dave,
I assume you are referring to the absolute orientation problem, i.e. the problem of determining the rigid transform between two sets of points with known correspondences. This problem could be solved in an iterative manner by the standard LevenbergMarquardt leastsquares algorithm, however as you mentioned, a closedform solution based on the singular value decomposition of a covariance matrix of the data exists. Unlike the iterative approach, it provides the best possible solution in a single step and does not require initial guess. So normally you would just use the SVD method. It is available in PCL (pcl::registration::TransformationEstimationSVD). P.S. The reason why LM transformation estimation as also implemented in PCL is because it is needed in the ICP algorithm, where a control over the optimization function is required. (This is just my guess though.) Regards, Sergey 
Hi Dave,
as already stated by Sergey, SVD gives a closedform solution, while LM is an iterative method, like GaussNewton. Another big difference is that the SVD technique makes more assumption on the problem, eg, your points must belong to only two different sets (ie only two camera poses) and the only variable you can have in your problem is the unknown relative transformation between those two sets. Instead, LM not only can handle more general nonlinear least squares problems, but it can also be used when the cost function changes at each iteration, as in Generalized ICP. Hope this helps! :) cheers Nicola On Sat, Jul 14, 2012 at 1:24 AM, taketwo <[hidden email]> wrote: Hi Dave, _______________________________________________ [hidden email] / http://pointclouds.org http://pointclouds.org/mailman/listinfo/pclusers 
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