I'm still a bit confused about the w(x,y) function. Why do we apply gaussian? On page 57, why is M defined as the covariance matrix without w(x,y)? Should sumation just be the sum of all covariance matrices in the small window? Thank you!
motoole2
Hi!
The window function $w(x,y)$ defines the window centered about two pixels. In this slides, the two windows are centered around $(u,v)$ and $(0,0)$. The error function computes the squared differences of the pixel values contained within these two windows. Now, the window function itself $w(x,y)$ determines (i) how large the windows are, and (ii) determines the weight of the elements within the window.
For example, we can define the window function $w(x,y)$ to be a box filter that simply sums up the squared differences of pixel values. Or, alternatively, we can use a Gaussian filter that provides a weighted sum of the squared differences.
With respect to slide 57, the $w(x,y)$ term goes away because this represents a box filter being used; the summation operator sums up derivatives over a small region, corresponding to the size of the box filter.
Hi?
I'm still a bit confused about the w(x,y) function. Why do we apply gaussian? On page 57, why is M defined as the covariance matrix without w(x,y)? Should sumation just be the sum of all covariance matrices in the small window? Thank you!
Hi!
The window function $w(x,y)$ defines the window centered about two pixels. In this slides, the two windows are centered around $(u,v)$ and $(0,0)$. The error function computes the squared differences of the pixel values contained within these two windows. Now, the window function itself $w(x,y)$ determines (i) how large the windows are, and (ii) determines the weight of the elements within the window.
For example, we can define the window function $w(x,y)$ to be a box filter that simply sums up the squared differences of pixel values. Or, alternatively, we can use a Gaussian filter that provides a weighted sum of the squared differences.
With respect to slide 57, the $w(x,y)$ term goes away because this represents a box filter being used; the summation operator sums up derivatives over a small region, corresponding to the size of the box filter.