While watching through the computer vision lecture on interest point detection, computing $E(u,v)$ requires computing the quantity $$E(u,v) = \sum_{x,y}(I(x+u,y+v) - I(x,y))^2$$

In the lecture, $I(x+u,y+v)$ is approximated as $I(x+u,y+v) \approx I(x,y) + I_x(x+u - x) + I_y(y+v -y)$.

The 1st degree taylor polynomial approximation about point $(a,b)$ is given as $$f(x,y) = f(a,b) + f_x(a,b)f(x-a) + f_y(a,b)(y-b)$$

I do not see how to reconcile the equation given above with the $1$st degree taylor approximation about point $(a,b)$ ?

  • $\begingroup$ If the lecture you’re following has that equation, which makes no sense, I suggest you find a better lecture to follow. On the other hand, your Taylor expansion is wrong as well. $\endgroup$ – Cris Luengo Oct 10 '20 at 20:04

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