How is the Harris Corner detector derived from a Taylor Expansion?

Question

It looks more like an assumption about local linearity of the function when the shifts u and v are small. This description of the Harris corner detector (used in computer vision) is as thorough as the original paper, and yet I don't see how it relates to the Taylor Series expansion. Could someone connect the two? In the image below, $I_x$ refers to the derivative of I wrt x.

enter image description here

score 1 · Answer 1 · answered May 10 '14 at 08:27

1

Taylor in a mild form is invoked when $f(a+h)-f(a)$ is approximated as $hf'(a)+O(h^2)$, that is we use only the first term of the Taylor expansion and the estimate for the error term from Taylor's theorem; here in the form $I(x+u,v+u)-I(x,y)=uI_x(x,y)+vI_y(x,y)+O(u^2,v^2)$

answered May 10 '14 at 08:27

Hagen von Eitzen

382,479

Thanks! Could you relate what $O(u^2, v^2)$ means in terms of the image I added to the bottom of my question? – Rose Perrone May 10 '14 at 09:09
@RosePerrone In case you were still wondering after 9 years or if anyone runs into this. $O(u^2, v^2)$ is an upper bound. See this question. – Alex Feb 07 '23 at 16:04

How is the Harris Corner detector derived from a Taylor Expansion?

1 Answers1