1.cross-correlation
2.convolution
3.difference between cross-correlation and convolution
4.properties of these methods!
A mathematical representation for smoothing
F[3,3]
F[i,j]
In signal processing, cross-correlation is a measure of similarity of two waveforms as a function of a time-lag applied to one of them.
Also known as a sliding dot product or sliding inner-product
Cross-Correlation method
G[i,j] = kΣu=-k*kΣv=-k*h[u,v]F[i+u,j+v]
Box Filter
Gaussian Filter
size:21×21
Values: Gaussian or Normal distribution
σ1, 3, 6, 9
F[i,j], h[i,j], G[i,j]
G[i,j] = kΣu=-k*kΣv=-k*h[u,v]F[i-u,j-v]
Denoted by G = h * F
Flip filter in both dimensions
bottom to top
right to left
Then apply cross-correlation
Linear and shift invariants
behaves the same everywhere
the value of the output depends on the pattern in the image neighborhood, not the position of the neighborhood
identity: unit umpulse
E = […0,0,1,0,0…]
F * E = F
true of cross-correlation
Separable
if the filter is separable, convolve all rows, then convolve
0, 0, 0
0, 1, 0
0, 0, 0
x 2 =
1/9, 1/9, 1/9
1/9, 1/9, 1/9
1/9, 1/9, 1/9
