digital image processing week iii
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Digital Image Processing Week III
Thurdsak LEAUHATONG
• Problem of Histogram Equalization•Histogram Matching
• Histogram equalization may not always produce desirable results, particularly if the given histogram is very narrow.• It can produce false edges and regions.• It can also increase image “graininess” and “patchiness.”
•Histogram MatchingTransfer to a pre-specified histogram
• In this case, transformation that yields an output image with a pre-specified histogram may produce the preferable result.
• This technique is called histogram matching.
•Histogram MatchingAlgorithm
• Let be the pre-specified PDF of the output image.
tp t
r T( ) s G-1( ) t
0
255r
rs T r p r dr • Perform the histogram equalization of the input image.
• Compute the CDF of . tp t 0
255t
tG t p t dt • HM is the inverse of G(s).
T
G
r
s T r
1G s
• Example•Histogram Matching
Intensity( s )
# pixels
0 20
1 5
2 25
3 10
4 15
5 5
6 10
7 10
Total 100
Intensity ( t )
# pixels
0 5
1 10
2 15
3 20
4 20
5 15
6 10
7 5
Total 100
Pre-specifiedHistogram
Histogram ofInput Image
• Example (cont.)•Histogram Matching
r (nj) SPr s
0 20 0.2 1
1 5 0.25 2
2 25 0.5 3
3 10 0.6 4
4 15 0.75 5
5 5 0.8 6
6 10 0.9 6
7 10 1.0 7
1. Histogram Equalization of both
t (nj) SPt v
0 5 0.05 0
1 10 0.15 1
2 15 0.3 2
3 20 0.5 4
4 20 0.7 5
5 15 0.85 6
6 10 0.95 7
7 5 1.0 7
s T r v G t
• Example (cont.)•Histogram Matching
r s
0 1
1 2
2 3
3 4
4 5
5 6
6 6
7 7
v t
0 0
1 1
2 2
4 3
5 4
6 5
7 6
7 7
r t
0 1
1 2
2 2
3 3
4 4
5 5
6 5
7 6
t # Pixels
0 0
1 20
2 30
3 10
4 15
5 15
6 10
7 0
Actual Output Histogram
s T r 1t G v
r s
s v
v t
• Example (cont.)•Histogram Matching
Desired histogram
Transfer function
Actual histogram
• Example (cont.)•Histogram Matching
Originalimage
After histogram matching
After histogram equalization
• Global Histogram Processing
• The intensity of a pixel depends on the PDF of intensities of an entire image.
• Global vs Local Histogram Processing•Local Histogram Processing
• Local Histogram Processing• The intensity at a position
(x,y) depends on the PDF of intensities in a small window whose center locates at (x,y).
GLOBAL MEAN AND NTH MOMENT• Global Mean
LOCAL MEAN AND NTH MOMENT
•Local Histogram ProcessingGlobal and Local Statistics
1 1
0 0
1 ,M N
Gx y
m r x yMN
1 1
,0 0
1 ,M N n
n G Gx y
r x y mMN
1 1
20 0
1 ,2 1
M N w w
xyx y i w j w
m r x i y iw
1 1
, 20 0
1 ,2 1 1
M N w w n
n xy xyx y i w j w
r x i y i mw
• Global nth Moment
• Local Mean
• Local nth Moment
•Local Histogram ProcessingGlobal and Local StatisticsGLOBAL MEAN AND NTH
MOMENT• Global Mean• measures the intensity’s
average of the entire image.
• Global 2nd Moment or called Variance
• measures how the intensity of the entire spread about the mean.
• It is useful to measure the global contrast of the image.
• Local Mean• measures the average of the local
intensity.
• Local 2nd Moment or called Variance
• measures how the local intensity spread about the local mean.
• It is useful to measure the local contrast, edge, and texture of the image.
LOCAL MEAN AND NTH MOMENT
1 1 22
0 0
1 ,M N
G Gx y
r x y mMN
1 1 22
20 0
1 ,2 1 1
M N w w
xy xyx y i w j w
r x i y i mw
•Local Histogram ProcessingLocal Statistics Examples
ORIGINAL IMAGE MEAN 3X3 MEAN 5X5
•Local Histogram ProcessingLocal Statistics Examples
STANDARD DEVIATION 3X3
STANDARD DEVIATION 5X5
2xy xySD
• For example• Want to enhance the dark
objects.
• How to separate the dark objects from the dark background.
•Local Statistics ProcessingVision Feature• Vision feature• a piece of information which is relevant for solving the
computational task related to a certain application.
• Intensity : Simple vision feature
Dark Objects
Dark Background
• Assumption:• The dark objects are the
areas whose intensity is
• .
• Result:• Cannot separate the dark
objects from the dark area.
• Intensity is not a good feature to detect the dark objects.
•Local Statistics ProcessingUsing intensity to detect the dark objects
0.4 Gr m
• Assumption:• The dark objects are the
areas whose local mean is
• .
• Result:• Cannot separate the dark
objects from the dark area.
• Local mean is not a good feature to detect the dark objects.
•Local Statistics ProcessingUsing local mean to detect the dark objects
0.4xy Gm m
• Assumption:• The dark objects are the
areas whose local variance is• .
• Result:• The local variance does not
detect the dark backgrounds, but detects both of the bright and dark objects.
• Local variance is not a good feature to separate the bright objects from the dark objects.
•Local Statistics ProcessingUsing local variance to detect the dark objects
2 2 20.02 0.4G xy G
• Assumption:• The dark objects are the
areas whose local mean and local variance are
• .
• Result:• Can well detect the dark
objects.
•Local Statistics ProcessingUsing the combination of the local mean and local variance.
2 2 20.4 and 0.02 0.4xy G G xy Gm m window size 3x3window size 5x5
window size 7x7
•Local Statistics ProcessingUsing the local statistics to enhance the dark objects.
2 2 24 , if 0.4 and 0.02 0.4,
, otherwisexy G G xy Gr x y m m
s x yr x y
window size 3x3Original Image
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