I am confused what is going on with the convolution at step 3?
motoole2
The first three steps here compute the components of our covariance matrix for all pixels in the image, as shown in this slide.
Step one involves computing our x- and y-gradients, through a convolution with two derivative filters. At a particular pixel $p$, we therefore get values $I_x(p)$ and $I_y(p)$.
Step two computes the element-wise product of these gradient values. At a particular pixel $p$, we now get $I_{x^2}(p) = I_x(p)^2$, $I_{y^2}(p) = I_y(p)^2$, $I_{xy}(p) = I_x(p)I_y(p)$.
Step three computes a weighted sum of these values within a given window. For example, suppose the kernel $G_{\sigma'}$ is a box filter, for simplicity. At pixel $p'$, we now get $$S_{x^2}(p') = \sum_{p\in P(p')} I_x(p)^2$$ $$S_{y^2}(p') = \sum_{p\in P(p')} I_y(p)^2$$ $$S_{xy}(p') = \sum_{p\in P(p')} I_x(p)I_y(p)$$
I am confused what is going on with the convolution at step 3?
The first three steps here compute the components of our covariance matrix for all pixels in the image, as shown in this slide.
Step one involves computing our x- and y-gradients, through a convolution with two derivative filters. At a particular pixel $p$, we therefore get values $I_x(p)$ and $I_y(p)$.
Step two computes the element-wise product of these gradient values. At a particular pixel $p$, we now get $I_{x^2}(p) = I_x(p)^2$, $I_{y^2}(p) = I_y(p)^2$, $I_{xy}(p) = I_x(p)I_y(p)$.
Step three computes a weighted sum of these values within a given window. For example, suppose the kernel $G_{\sigma'}$ is a box filter, for simplicity. At pixel $p'$, we now get $$S_{x^2}(p') = \sum_{p\in P(p')} I_x(p)^2$$ $$S_{y^2}(p') = \sum_{p\in P(p')} I_y(p)^2$$ $$S_{xy}(p') = \sum_{p\in P(p')} I_x(p)I_y(p)$$