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August 1st, 2014, 01:38 AM   #1
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Multidimensional fitting of two sets of data

My problem is the following:

A lasers gives out a bunch of data points which are reflected off a metal surface and recorded by a camera attached to the side of the laser. The image the camera receives is however distorted.

In order to calibrate the camera I need to find a function of two variables (f(x,y)) which transforms the distortet(wrong) data points back into their originals so that the camera image can be used for accurate analysis.

I know the location (x and y values) of the original image and their corresponding camera positions (x' and y').

How can I use these to find a transfer function between the two data sets?
I have already used SVD and a 6th order polynom merit function for multidimensional fits I found in "Numerical Recipes", and although I get resonable results, they are not accurate enough.

Any help is greatly appreciated!!
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August 31st, 2014, 04:28 PM   #2
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transformed coordinates

I am not an optics expert but a 6th degree polynomial seems way overkill. I know an ARMA can be applied to time-based data. I imagine there's a parallel for such transformed coordinate data. I will try to research a bit ...
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September 3rd, 2014, 05:30 AM   #3
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Are you sure it's the method that is responsible for your loss of accuracy? It's difficult to say what you can do without seeing the output. I would check the experimental setup for possible sources of systematic errors and check the formats for your numbers and the operations between them to ensure that you can minimize things like truncation error. Using 8-byte floating point numbers and improving the computational algorithms might solve your problem without needing an alternative method.
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