My Math Forum  

Go Back   My Math Forum > College Math Forum > Linear Algebra

Linear Algebra Linear Algebra Math Forum

LinkBack Thread Tools Display Modes
August 1st, 2014, 01:38 AM   #1
Joined: Aug 2014
From: germany

Posts: 1
Thanks: 0

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!!
datameng is offline  
August 31st, 2014, 04:28 PM   #2
Senior Member
Joined: Aug 2008
From: Blacksburg VA USA

Posts: 346
Thanks: 6

Math Focus: primes of course
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 ...
billymac00 is offline  
September 3rd, 2014, 05:30 AM   #3
Senior Member
Joined: Apr 2014
From: Glasgow

Posts: 2,150
Thanks: 730

Math Focus: Physics, mathematical modelling, numerical and computational solutions
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.
Benit13 is offline  

  My Math Forum > College Math Forum > Linear Algebra

data, fitting, multidimensional, sets

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Two data sets fitting Simon39 Abstract Algebra 4 November 29th, 2013 09:41 PM
Interpolation of larga data sets godric Real Analysis 1 August 31st, 2012 05:53 AM
Combining 2 data sets Shakarii Advanced Statistics 1 August 10th, 2012 02:32 AM
Help on comparing differing sets of data carter22 Algebra 2 March 1st, 2010 05:49 PM
simple data fitting problem dimper129 Linear Algebra 0 October 7th, 2009 07:01 AM

Copyright © 2019 My Math Forum. All rights reserved.