Thank you very much this is a really nice and clear answer !! Just to be sure I understand correctly, if we just consider one of the coordinate of a control point (for instance of a TPS), this point will modify the color map of the transformed image (ie locally change the appearance of the deformed image). The corresponding value in the 2*N grad_control matrix will basically correspond to (badly written as a finite difference):
sum( (sum (delta color map - current color map) / delta_step) * grad_transformed_image )
(should it be flatten instead of using the sum ?)
Thank you again
F