Spectral Feature Extraction - Cornell University

CEE 615: Digital Image Processing 5
W. Philpot, Cornell University
3. Algebraic Operations
Algebraic operations produce a single output image as a result of a pixel-by-pixel sum,
difference, product or quotient of two or more input images.
Note: input images must be accurately registered.
Concepts: 2-Dimensional histogram
Image addition - tends to extract information that is positively correlated from image to image.
Removes information that is uncorrelated from image to image. The output image gray value, k',
is given by:
k' = a 0 + a 1 k 1 + a 2 k 2 + . . . + a n k n
where:
k i = the gray value of a pixel in the i th image.
a i = weighting coefficient for the i th image with a i > 0
• Addition is often applied to data when the important information is correlated from band to
band.
• If the uncorrelated information is random noise, addition will tend to remove the random
noise.
• If the data are not noisy and image 1 and image 2 are different spectral bands, then:
uncorrelated data ==> "color" information
correlated data ==> intensity information.
Example 1: Removal of random noise:
If k 1 is the gray value of an image
contaminated with random noise, then we
might write:
k 1 = k 0 + n 1
signal+ noise
Note that k 0 > 0 ; n 0 may be positive or
negative. Similarly, for a second image of
the same scene:
k 2 = k 0 + n 2
Taking the average value of the two images gives:
Figure 1. Telescope photograph of a galaxy
1 1
k' = ( k + k ) = k + ( n + n )
1 2 0 1 2
2 2
Generalizing to the case when t images of the same scene are available:
1 1
k' = ( k + k + + k ) = k + ( n + n + + n )
1 2 n 0 1 2 t
2 t
Since n i may be positive or negative with a randomly varying magnitude,
1
noise = ( n + n + + n ) →0 as t →∞
1 2 t
t