What does p represent here? I recall that we take image gradients in regions not pixelwise right? Does the p represent the center of these regions?
motoole2
Large $P$ represents the set of pixels within a window centered about the pixel of interest. Small $p$ represents the individual pixel coordinates contained within that window. So perhaps more accurately, one should rewrite the sum as $\sum_{p\in P} I_x(p)I_y(p)$.
As for the image gradients, we have a gradient value at every pixel in the image.
Roger
just to make sure, so this is $\sum_{p\in P} I_x(p)I_y(p)$, not $\sum_{p\in P} (I_x * I_y)(p)$?
motoole2
Correct---it's the former. (The asterisk in the slide refers to an element-wise product between two windows.)
What does p represent here? I recall that we take image gradients in regions not pixelwise right? Does the p represent the center of these regions?
Large $P$ represents the set of pixels within a window centered about the pixel of interest. Small $p$ represents the individual pixel coordinates contained within that window. So perhaps more accurately, one should rewrite the sum as $\sum_{p\in P} I_x(p)I_y(p)$.
As for the image gradients, we have a gradient value at every pixel in the image.
just to make sure, so this is $\sum_{p\in P} I_x(p)I_y(p)$, not $\sum_{p\in P} (I_x * I_y)(p)$?
Correct---it's the former. (The asterisk in the slide refers to an element-wise product between two windows.)