selected methods of texture analysis - urząd miasta...
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Selected methodsof texture analysis
[Brodatz 1966]
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There is no formal, mathematical definition of term “Texture”
Texture definition
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Texture definition
Texture – complex visual
patterns, composed of spatially
organized entities that have
characteristic brightness,
color, shape, size.
This local sub-patterns are
characterized by given
coarseness, fineness,
regularity, smoothness etc.
Texture is homogeneous for human visual system.
[Hajek et al. 2006]
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Texture properties• One of the first quantitative/physiological texture description: [Tamura et al. 1978]
• Definition of texture features that correspond to human visual perception:
coarseness, contrast, directionality, line-likeness, regularity, roughness
coarsecoarse finefine
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highhigh--contrastcontrast lowlow--contrastcontrast
directionaldirectional nonnon--directionaldirectional
Texture properties
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roughrough smoothsmooth
regularregular randomrandom
Texture properties
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MRF models artificial foam
brain(MRI)
bone(X-ray)
skin mast cells
derma andepidermis
toothenamel
plastic potato(MRI)
apple(MRI)
soft cheese(MRI)
Texture examples
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Texture analysis
Basic steps in quantitative texture analysis:
• Feature extraction
(computation of a vector of mathematical parameters which describe texture properties)
• Texture classification
(determination to which of predefined classes given texture belongs)
• Texture segmentation
(partition of image into disjoint regions containing homogenous textures)
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� statistical• image intensity domain• mathematical models• transform based
Texture feature extraction
� structural
� signal processing
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feature extraction in image intensity domain
• histogram
• co-occurrence matrix
2nd order histogram, [Haralick et al.1973]
• higher order statistics
[Kovalev and Petrou 1996]
• run-length matrix [Haralick 1979]
• gradient matrix
• …
0 50 100 150 200 250
0
200
400
600
800
Statistical approach
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mathematical model parameter estimation
• Markov random fields [Geman & Geman 1984]
• autoregressive model[Chelappa et al. 1985]
• fractals [Chen et al. 1990]
bone tissue GMRF modelmetatarsus GMRF model
tissue
sθ1
θ2 θ3 θ4
Statistical approach
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• Fourier transform
• Gabor filters [Dunn et al. 1994]
• Wavelet transform
[Choi & Baraniuk 2001]
50 100 150 200 250
50
100
150
200
250
10
20
30
40
50
60
inputimage transform output
image
Statistical approach
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• texel – a basic, repetitive texture element• placement rules
Structural approach
[Haralick 1979]
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Signal processing approach
linear filter
h
estimation of mean
and variance for ROI
∑
∑∑
=
= =
−−
= K
kk
K
k
K
jjk
V
KhF
1
2
1 1
2
11
)(
µµ
optimisation of h to increase F
[Randen & Husoy 1999]
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F=1056F=1056
feature
evaluation
Feature selection for classification
F=107F=107
f3f5
f2
fnf6
f4
f1
feature selection:Fisher, POE, MI
g2
g1
feature projection:LDA, PCA, NDA
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LDA
1-NN: 0/27
Texture classificationwrist bone X-ray images
healthy (1)osteopenia (2)
osteoporosis (3)
2nd order MRF
features
1-NN: 2/27
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Texture classification
NDA:
g1 g2 g3 …
f1 f2
statistical
features
trombitrombi (1)(1)
malignant (2)malignant (2)
benign (3)benign (3)
heart masses (USG)
class. errors:training: 10/108test: 5/55
test set
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• 16 textures from Brodatz album,
• each image was divided into 64 squares (64x64)
• 1024 samples of 16 texture classes altogether
Texture samples 64x6464x64
Texture classification
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1-NN classification results for
different feature selection methods
14714559798160
LDAraw LDAraw LDAraw raw
POEFisherMIoptimalsubset*
Number of misclassiedfied samples (total no. of samples: 1024)
Texture classification
* Optimal subset with 4 features: (Sigma, MinNorm, GrMean, S(0,2)Correlat) found based on exhaustive search
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- splitting of the image into disjoint, homogeneous regions
IMAGE ACQUISITION,
PREPROCESSINGSEGMENTATION
QAUNTITATIVE IMAGE
ANALYSIS
TEXTURE FEATURE ESTIMATION
f11=(f1, f2, … ,fn)
f21=(f1, f2, … ,fn)
f31=(f1, f2, … ,fn)
f12=(f1, f2, … ,fn)
f22=(f1, f2, … ,fn)
f32=(f1, f2, … ,fn)
Texture segmentation
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dermal-epidermisjunction
epidermis
skin mast cells
derma
Texture segmentation
Example of biomedical image analysis:
• detect skin mast cells
• calculate their parameters(eg. area, distance from D-E junction
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• “classical” approaches (region- and gradient based
methods) [Reed et al. 1990, Yhann & Young 1995]
• Bayes estimation (MRF models) [Cohen i Cooper 1987]
• artificial neural networks (Hopfield,
multilayer perceptrons, network of synchronized oscillators)[Raghu & Yegnanarayana 1998, Augusteijn 1995, Hu & Hwang 2002,
Wang 1995, Strzelecki et al. 2006]
• unsupervised segmentation (k-means, Kohonen, AHC) [Yin & Allinson 1994, Klepaczko 2006]
Texture segmentation
Image texture segmentation techniques:
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Texture segmentation
statistical
features
Brodatz texture mosaic
feature maps
DiffEntropyContrast
SumOfSqrk-meanssegmentation results
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Texture segmentationMR image of foot cross-section
multilayer perceptron (MLP)segmentation results
statistical
features
GMRF model
parameters
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Texture segmentationHeart mass echocardiogram (benign tumor)
MLP oscillator network
NDA feature mapstatistical
features, NDA
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Texture segmentationDetection of texture edges
oscillator network
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Brodatz P., “Textures - A Photographic Album for Artists and Designers”, Dover, 1966.
Hajek M., Dezertova M., Materka A., Lerski R. (Ed.), “Texture analysis for Magnetic Resonance Imaging “, Med4 publishing, 2006
Tamura H., Mori S., Yamawaki T., “Textural Features Corresponding to Visual Perception, IEEE Trans”. on Systems, Man, and
Cybernetics, SMC-8, pp. 460-473, 1978
Haralick R., “Statistical and Structural Approaches to Texture”, Proc. IEEE, 67, 5, 1979, 786-804.
Haralick R., Shanmugan K., Dinstain I. , “Textural Features for Image Classification”, IEEE Transactions on Systems, Man and
Cybernetics, 3, 6, 1973, 610-622.
Kovalev V., Petrou M., “Multidimensional Co-Occurrence Matrices for Object Recognition and Matching”, GMIP, 58, 3, 1996,
187-197.
Geman S., Geman D., “Stochastic Relaxation, Gibbs Distribution and the Bayesian Restoration of Images”, IEEE Trans. Pattern
Analysis and Machine Intelligence, 6, 11, 1984, 721-741.
Chellappa R., Chatterjee S., Bagdazian R., “Texture Synthesis and Compression Using Gaussian-Markov Random Field Models,
IEEE Trans. on Systems, Man, and Cyber., 15, 2, 1985, 298-303.
Dunn D., Higgins W. E., Wakeley J., Texture Segmentation Using 2-D Gabor Elementary Functions, IEEE Trans. on Pattern
Analysis and Machine Intelligence, 16, 1994, pp. 130-149.
Chen C-C., Daponte J., Fox M., “Fractal Feature Analysis and Classification in Medical Imaging”, IEEE Trans. Medical Imaging, 8,
2, 1990, 133-142.
Choi H., Baraniuk R., “Multiscale Image Segmentation Using Wavelet-Domain Hidden Markov Models”, IEEE Trans. on Image
Processing, 10, 9, 2001, 1309-1321.
Randen T., Husoy J., “Filtering for Texture Classification: A Comparative Study”, IEEE on Pattern Analysis and Machine
Intelligence, 21, 4, 1999, 291-310.
Yhann S., Young T., “Boundary Localisation in Texture Segmentation”, IEEE Trans. Image Processing, 4, 6, 1995, 849-856.
Augusteijn M., “Texture Segmentation and Classification Using Neural Network Technology”, Applied Mathematics and Computer
Science, 4, 1995, 353-370
References
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References