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I'm trying to solve a computer vision problem whereby I wish to use Levenberg-marquardt non-linear optimization to solve the following equation:

enter image description here

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.

enter image description here

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