filtering, Fourier, smoothing, and noise thi d i
Nuno Vasconcelos ECE Department, UCSD p , (with thanks to David Forsyth)
Images
the incident light is collected by an image sensor
E
that transforms it into a 2D signal
Po V Pi
2
2
2D-DSP
in summary:
image is a N x M array of pixels each pixel contains three colors overall, the image is a 2D discrete-space signal g each entry is a 3D vector
x [ n 1 , n 2 ] = ( r , g , b ), n 1 { 0 ,..., N } n 2 { 0 ,..., M }
for simplicity, we consider only single channel images g
x [ n 1 , n 2 ], n 1 { 0 ,..., N } n 2 { 0 ,..., M }
but everything extends to color in a straightforward manner
3
2D convolution
the operation
y [n 1 , n 2 ] =
k x [k k
1 = - 2
= -
1
, k 2 ] h [n 1 - k 1 , n 2 - k 2 ]
is the 2D convolution of x and h
we will denote it by
y [n 1 , n 2 ] = x [n 1 , n 2 ] h [n 1 , n 2 ]
this is of great practical importance:
for an LSI system the res...
Filtering