# Taylor series approximation in Harris corner detection

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 $$(a,b)$$ ?

• 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. Oct 10 '20 at 20:04