digital image processing image enhancement part ii
TRANSCRIPT
Digital Image Processing
Image Enhancement
Part II
Intensity Histogram
Intensity Histogram
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0 1 2 3 4k 6 7 8 9 10 11 12 13 14 15
0 1 0 1 0 0 3 1 4 2 3 1 0 0 0 0
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H(k)
• Examplea 4x4, 4bits/pixel image
Intensity Histogram
From [Gonzalez & Woods]
Intensity Histogram
From [Gonzalez & Woods]
Fixed Intensity Transformations
Basic Transformations
From [Gonzalez & Woods]
rLs 1
)1log( rcs
crs
Negative:
Log:
Power-law:
1 cresInverse Log:
……
Negative Transformation
From [Gonzalez & Woods]
rLs 1
Log Transformation
From [Gonzalez & Woods]
)1log( rcs
Power-law (Gamma) Transformation
From [Gonzalez & Woods]
crs
Power-law (Gamma) Transformation
From [Gonzalez & Woods]
crs
Power-law (Gamma) Transformation
From [Gonzalez & Woods]
crs
mrif
mrifcs
0
Thresholding
From [Gonzalez & Woods]
m : threshold
Example: Fixed Intensity Transformation
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1)( rroundrTs
• A 4x4, 4bits/pixel image passes through
an intensity transformation
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1 round(0.0667) = 0;3 round(0.6) = 1;6 round(2.4) = 2;7 round(3.2667) = 3;8 round(4.2667) = 4;9 round(5.4) =5;10 round(6.6667) = 7;11 round(8.0667) = 8;
The resulting
image is:
Example: Histogram Change
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Contrast Stretch
General Idea: Make Best Use of the Dynamic Range
From [Gonzalez & Woods]
Contrast Stretch
minmax
min)12(rr
rrs B
1212
)12(12
12
0
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2
2112
1221
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BB
BB
B
rrr
rsr
r
s
rrrrr
rsrsr
rr
ss
rrrr
s
s
max2 rr
General form:
Special case Full-scale contrast stretch:
min1 rr
122 Bs
01 s
minmax
min)12(rr
rrrounds B
Typically used:
Example: Full-Scale Contrast Stretch4
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4min r
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• Full-scale contrast stretch of a 4x4, 4bits/pixel image
• Find 11max r 1512 B
)4(
7
15
411
415)12(
minmax
min rroundr
roundrr
rrrounds B
4 round(0) = 0;6 round(4.29) = 4;7 round(6.43) = 6;8 round(8.57) = 9;9 round(10.71) = 11;10 round(12.86) = 13;11 round(15) = 15;
The resulting
image is:
Example: Histogram Change
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Histogram Equalization
Histogram Equalization
From [Gonzalez & Woods]
Histogram Equalization
From [Gonzalez & Woods]
Example2
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2min r
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• A 4x4, 4bits/pixel image
• First try: full-scale contrast stretch
11max r
)2(
3
5
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215)12(
minmax
min rroundr
roundrr
rrrounds B
2 round(0) = 0;3 round(1.67) = 2;8 round(10.00) = 10;9 round(11.67) = 12;10 round(13.33) = 13;11 round(15) = 15;
The resulting
image is:
Example: Histogram Change
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big gap
full-scale contrast stretch
original
Cumulative Histogram
0 1 2 3 4k 6 7 8 9 10 11 12 13 14 15
0 0 2 4 0 0 0 0 3 3 2 2 0 0 0 0
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H(k)
0 0 2 6 6 6 6 6 9 12 14 16 16 16 16 16Q(k)
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H(k)
Q(k)
Intermediate Image
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0 1 2 3 4k 6 7 8 9 10 11 12 13 14 15
0 0 2 4 0 0 0 0 3 3 2 2 0 0 0 0
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H(k)
0 0 2 6 6 6 6 6 9 12 14 16 16 16 16 16Q(k)
intermediate image
original
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2min r
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16max r
)2(
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minmax
min rroundr
roundrr
rrrounds B
2 round(0) = 0;6 round(4.29) = 4;9 round(7.50) = 8;12 round(10.71) = 11;14 round(12.86) = 13;16 round(15) = 15;
final result:histogram equalized
image
Full-Scale Contrast Stretch of Intermediate Image
intermediate image
Histogram Comparison
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original direct full-scale contrast stretch
histogram-equalized
more equalize
d
Summary of the Histogram Equalization Algorithm
original image
histogram H(k)
cumulative histogram Q(k)
intermediate image
full-scale contrast stretch
histogram-equalized image