I'm trying to solve a computer vision problem whereby I wish to use Levenberg-marquardt non-linear optimization to solve the following equation:
Whereby xi is the x,y coordinates in the image, I function is the grayscale value of the x,y coordinate in the image, and H is the homography function.
Because gradient related optimization requires the calculation of the Jacobian, can someone tell me how do I formulate the partial deriviatives of the Image function I? I understand that the size of the Jacobian of n * 2n, where n is the number of points to be used in the optimization.
The author of the paper did stated the following, but I did not quite get it.