05 histogram processing DIP
description
Transcript of 05 histogram processing DIP
Histogram Processing : 1
HistogramsHistograms
Histogram
Discrete function h(rk) showing the number of occurrences nk for the kth gray level rk
Normalized Histogram
Gives estimate of probability of occurrence of gray level rk (probability distribution function)
( )k kh r n
1
0
( ) / , ( ) 1L
k k kp r n n p r
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Histograms: ExampleHistograms: Example
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Histogram EqualizationHistogram Equalization
High-contrast images are often desirable from a visual perspective
High-contrast images have histograms where the components cover a wide dynamic range
Distribution of pixels are close to a uniform distribution
Intuitively, low-contrast images can be enhanced by transforming its pixel distribution into a uniform distribution to achieve high contrast
Histogram Processing : 4
Histogram EqualizationHistogram Equalization
Let p(r) and p(s) denote the probability density functions of r and s
For s=T(r), p(s) can be expressed as,
Since we want to transform the input image such that the pixel distribution is uniform,
( ) ( )dr
p s p rds
( ) 1 , 0 1p s s
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Histogram EqualizationHistogram Equalization
What transformation will give you a uniform distribution for s?
Cumulative distribution function (CDF)
Why?
0( ) ( )
rs T r p w dw
0( )
( )
rd p w dwds
p rdr dr
1( ) ( ) 1
( )p s p r
p r
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Histogram EqualizationHistogram Equalization
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Histogram EqualizationHistogram Equalization
For discrete case,
1
0
( ) / , ( ) 1L
k k kk
p r n n p r
( ) ( )k
k k jj o
s T r p r
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Histogram Equalization: ExampleHistogram Equalization: Example
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Local Histogram EqualizationLocal Histogram Equalization
Global approach good for overall contrast enhancement
However, there may be cases where it is necessary to enhance details over small areas in image
Solution: perform histogram equalization over a small neighborhood
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Local Histogram Equalization:Local Histogram Equalization:ExampleExample
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Enhancement Using Arithmetic/Logic Enhancement Using Arithmetic/Logic OperationsOperations
Performed on a pixel-by-pixel basis between two or more images
( , ) ( , ) ( , )g x y f x y h x y
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Enhancement Using AND Operation: ExampleEnhancement Using AND Operation: Example
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Enhancement Using OR Operation: ExampleEnhancement Using OR Operation: Example
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Enhancement Using Subtraction Operation: Enhancement Using Subtraction Operation: ExampleExample
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Enhancement Using Subtraction Operation: Enhancement Using Subtraction Operation: ExampleExample
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Noise reduction by Image AveragingNoise reduction by Image Averaging