2D matrix transformation (Brown-Conrady distortion model) fitting

Hello,

My question is how to fitting with a known model between one set of x and y and another set of x and y. The reason for this fitting is that I have a set of x and y data points (for example, 100 sets of x and y), and another set of corresponding xu and yu data points that the two sets of datapoints have the following relationship. How could I get the xc, yc, k1,k2...,p1,p2 parameters through fitting? The curve fitting app only fits x to y and x,y to z. The camera calibrator app needs an image as input to fit the distortion model. Both of them seem cannot be used for this type of fitting.

Best Regards

CZ

Answer 1

[Matt J]

You can use lsqcurvefit if you have the Optimization Toolbox.

[lizzy]

Hi Matt,

Thank you for your help! I searched lsqcurvefit. It seems a xy fit function in that y is a function of x. However, in my case, it is a 2D matrix projection fitting. Both x and y is a function of (x^2+y^2) ,x,y and parameters, like in the schematics below. The input is the blue grid of locations x and y, the output is the red grid of locations xu,yu. I wanted to fit the relationship between blue and red grid transformation based on a certain radial and tangential distortion relationship.

Best Regards

CZ

[Matt J]

It seems a xy fit function in that y is a function of x

Yes, but x and y can be of any dimension. It should apply to your problem.

[lizzy]

Thank you so much for the help! It worked wonderfully.