MATLAB: Efficient way to apply fsolve to large 2D array element

fsolvemultiple variablesnonlinear

Hello
I have 2 nonlinear equations. I figure out that it can be solved by fsolve. The outputs of the 2 nonlinear equations are the [x,y] position of a point. The inputs of the system are initial estimate of the point [x0,y0] and some constants. I first tried to solve the nonlinear equations for one point, with the following code:
options = optimoptions('fsolve', 'Display', 'off');
x0 = [ud(1,1);vd(1,1)]; % Initial guess of undistorted point [x,y]
[x, fval] = fsolve(@myfunction,x0,options, kc, x0);
function F = myfunction(x, kc, x0)
r = sqrt(x(1)^2 + x(2)^2);
F = [ -x0(1) + (1 + kc(1)* r.^2 + kc(2)* r.^4 + kc(5)* r.^6 ).*x(1) + 2*kc(3).*x(1).*x(2) + kc(4)*(r.^2+2*x(1).^2), ...
      -x0(2) + (1 + kc(1)* r.^2 + kc(2)* r.^4 + kc(5)* r.^6 ).*x(2) + kc(3)*(r.^2 + 2*x(2).^2) + 2*kc(4) .*x(1) .*x(2)];
end
The above code runs perfectly fine with one point [x,y]. However, I would like to apply it to large set of points. The set of points are stored in two m x n arrays, ud and vd, where [ ud(row,col), vd(row,col) ] forms the initial estimiate [x0,y0] for each array element. I tried to use nested for loop to run the above fsolve code for each array element. While it works, it takes decades to complete because m and n are large (>1500×1500). Is there any efficient way to apply the above code to each array element? Or is there any other way to do the same thing? Thanks!

Best Answer

It looks like you solve for pixel position of some distorded images, and you has a model for a distorsion.
If you approximate the inverse of the model, either symbolically or approximate by some sort of truncated taylor expansion of the inverse, might be you don't need to use FSOLVE at all.
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