what is texture? strictly random texturejmca/02501/lectures/02501_texture.pdf · what is texture?...
TRANSCRIPT
What is texture?
Texture is a region that can – in some sense – be perceived as being spatially homogeneous.
Strictly random texture
Strictly deterministic textures Real-world textures
Semi-stochastic Semi-deterministic
More textures Texture perception
Texture analysis
• Extraction of textural features for regression or classification
• Texture segmentation• Texture modelling• Texture synthesis
Food industry
• Meat • Cheese• ...
Medical applications
Normal mouse liver cell
Cancer mouse liver cell
Source: Norwegian Radium Hospital, Oslo
Materials
Basic properties
• Translation invariance• Rotation invariance• Scale invariance• Warp invariance• Discrete/continuous• Relabelling/grayscale invariance• Shading invariance
Preprocessing orWhat do we want to characterize?
• Masking• Graylevel transformations• Texture equalization• Scale space representation
Masking Graylevel transformations
• Linear• Non-linear• Histogram matching
– Histogram equalization– Gaussian histogram match– Beta histogram match
Texture equalization Scale space representation
First-order statistics• Mean
•Variance
•Coefficient of variation
•Skewness
•Kurtosis
∑−
=
=1
0
1 N
iix
Nµ
( )21
0
2
11 ∑
−
=
−−
=N
iix
Nµσ
µσ
=cv
( ) ( )31
031 1
1 ∑−
=
−−
=N
iix
Nµ
σγ
( ) ( ) 31
131
042 −−
−= ∑
−
=
N
iix
Nµ
σγ
First-order statistics• Mean
•Variance
•Coefficient of variation
•Skewness
•Kurtosis
∑−
=
⋅=1
0
G
iiHiµ
( ) i
G
i
Hi ⋅−= ∑−
=
1
0
22 µσ
µσ
=cv
( ) i
G
i
Hi ⋅−= ∑−
=
31
031
1µ
σγ
( ) 31
31
042 −⋅−= ∑
−
=i
N
i
Hi µσ
γ
HistogramsExample: first-order statistics
Mean 167.9
Variance 669.0
CV 0.15
Skewness -0.82
Curtosis 0.01
Mean 105.1
Variance 720
CV 0.26
Skewness 1.15
Curtosis 0.30
Uniformity measures
• Energy (non-uniformity)
•Entropy (uniformity)
Given a discrete distribution with probabilities { }ip
∑=i
ipe 2
ii
i pps log∑−=
EntropyEnergy
0.81 (1)
0.69 (2)
0.08
0.00
0.60 (2)
0.50 (1)
0.080.080.76
0.000.500.501p 2p 3p 4p
0.86 (1)0.02 0.46 (1)0.020.480.48
Uniformity measures
Bias ?
First-order statistics in scale-space Second-order statistics
• Cooccurrence matrices (GLCM)• Fourier power spectrum features• Auto-correlation• Laws’ filters• Eigen-filters
Cooccurrence matrices (GLCM)
4320210004234444320120012
10200
3
2001421003001120002103130
4210GLCM
20=hN
)1,0(=h { }1,..,0,| −∈ Gjicij
Cooccurrence matrices (GLCM)
( ) ( ) hhchC N/=Normalized GLCM
Symmetric GLCM
( ) ( ) ( )( ) ( ) ( )( )hChChChChC Ts +=−+=
21
21
Isotropic GLCM
( ) ( ) ( ) ( ) ( )( )1,11,10,11,041
1 −+++= ssssi CCCCC
GLCM GLCM after Gaussian match
GLCM after histogram equalization GLCM features
∑∑−
=
−
=
1
0
1
0
2G
i
G
jijC• Energy
• Entropy
• Maximum probability
• Correlation
ij
G
i
G
jij CC log
1
0
1
0∑∑
−
=
−
=
−
∑∑−
=
−
=
−−1
0
1
0
))((G
i
G
j yx
ijyx Cji
σσ
µµ
ijCmax
Correlation
50 100 150 2 0 0 250
5 0
1 0 0
1 5 0
2 0 0
2 5 0
∑∑−
=
−
=
−−=
1
0
1
0
))((G
i
G
j yx
ijyx Cji
σσ
µµρ
Diagonal correlation
50 100 150 200 250
5 0
1 0 0
1 5 0
2 0 0
2 5 0
∑∑−
=
−
= ++−+
−−++−−=
1
0
1
02222 22
)(||G
i
G
j yxyxyxyx
ijyxyxdiag
Cjiji
σρσσσσρσσσ
µµµµρ
Diagonal correlation
17.0−=diagρ 25.0=diagρAfter Gaussian histogram match
Brodatz D69 Brodatz D91
Sum correlation
50 100 150 200 250
50
100
150
200
250
∑∑−
=
−
= ++
−−+−−=
1
0
1
022
2
2
))()((G
i
G
j yxyxyx
ijyxyxs
Cjiji
σρσσσσσ
µµµµρ
Sum correlation
18.0−=sρ
After Gaussian histogram match
Brodatz D106
Difference correlation
50 100 150 200 250
5 0
1 0 0
1 5 0
2 0 0
2 5 0
∑∑−
=
−
= −+
+−−−−=
1
0
1
022
2
2
))()((G
i
G
j yxyxyx
ijyxyxd
Cjiji
σρσσσσσ
µµµµρ
Difference correlation
78.0−=dρAfter Gaussian histogram match
Brodatz D77
13.0=dρ
Graylevel difference histogram (GLDH)
102003
20014210030011200021031304210GLCM
42
14
03
10510GLDH
20=hN
20=hN
GLDH features
∑−
=
1
0
2G
kkD• Difference energy
• Difference entropy
• Inertia or variogram
• Inverse difference moment
∑−
=
−1
0
logG
kkk DD
∑−
= +
1
021
G
k
k
kD
( )ρσ −=∑−
=
12 21
0
2k
G
k
Dk
Graylevel sum histogram (GLSH)
102003
20014210030011200021031304210GLCM
14
35
06
37
42
28
13
3310GLSH
20=hN
20=hN
Exercise
112212011010210GLCM
Consider the cooccurrence matrix
What is the difference energy?
Solution
3/92/94/9210GLDH
In the normalized GLCM we have to divide by 9. Then we can compute the graylevel difference histogram.
The difference energy, DE, can then be found as
358.08129
93
92
94 222
==
+
+
=DE
Higher-order statistics
• Graylevel run-length matrices (GLRLM)• Neighboring graylevel dependence matrices
(NGLDM)
GLRLM
4320210004234444320120012
01034000330006200031011204321GLRLM
20=rNHorizontal direction
NGLDM
4320221004232444320120012
00000001040020000003000020000200010000010000021000876543210NGLDM
2
1
=
=
d
a9=dN