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Transcript of Wavelet Transform in Image Regions &ODVVL¿FDWLRQdsp.vscht.cz/hostalke/upload/IMA08_poster.pdf[6]...
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Wavelet Transform in Image RegionsAles ázka, Eva Host’álková, and Andrea Gavlasová
Institute of C mi l T logy in PragueDept of Computing and Control Engineering
http://dsp.vscht.cz/
Processing Group
Digital Signal and Image
ICT PRAGUE
Texture segmentation and n form g t s ofe inter ry area of digital signal pr g wit
tions g e analysis of m r , biom , satellite, orr types of images. In s work, we ribe a pattern r
tion pr re g of image prepr , segmentationexploiting e water d transform, feature extr , andments n using ar l neural networks. Our aim is toem ze e possibilities of e wavelet transform in stagesof prepr g and features extr . T e proposed metare ver d for simulated images and subsequently applied to realbiom l images to t and y e d tissues.
Abstract
Pattern recognition procedure1. Image prepr
• Noise r n rete Wavelet Transform (DWT) [3,6]• Contrast ment
2. Segmentation: e transform, water d transform [4]3. Feature extr n [1,5]: DWT, rete Fourier Transf. (DFT)4. : ar l neural networks [2]
1. Introduction
Additional noise model of a noisy wavelet t observationw(k) = y(k)+ n(k)
re y(k) and n(k) rrespond to e noise free signal and iidGaussian noise, resp., for k= 0,1, . . . ,N 1. N is e no. s.
Wavelet shrinkage algorithm for image smoothing [3]1. MAD estimate of e standard deviation for iid Gaussian noise
ˆmad = median{|wj(0)|, |wj(1)|, . . . , |wj(Nj 1)|} / 0.6745 (1)
re wj(k) are wavelet s of all subbands of level jfor k = 0,1, . . . ,Nj 1
2. Universal r d for mposition level j(s)j = 2 ˆ 2mad log(Nj) (2)
3. Soft r g to obtain denoised ŷ j(k)
ŷ j(k) =sign{wj(k)} · (|wj(k) |
(s)j ) f or |wj(k) |>
(s)j
0 otherwise(3)
2. Noise Reduction
Fig. 1. Noise r n in biom l images by rinking wavelets from 2 mposition levels
(a) ORIGINAL (b) DENOISED (c) ABS. DIFFERENCE
2 4 6 8 10 12 14 16
x 104
0
1
2 WAVELET SHRINKAGE: SCALING AND WAVELET COEFFICIENTS OF 3 LEVELS
Fig. 2. Sm g biom l images by rinking wavelets of 3 levels using b splines bior l wavelets bior5.5
Image segmentation by the watershed method [4]1. Conversion a to bla k & e image by r2. e transform
• Assigns to pixel a value of e E n etween e pixel and its nearest nonzero
3. Water d transform• s ridge lines and separates e water d regions• Results in a matrix of labeled regions separated by e w
ter d pixels lines
3. Segmentation
T e n pr s requires a pattern matrix Pfeatures extr d from separate image segments.Methods used feature extraction [5]
• A n transformation of e boundary signal ofment d by e water d transform
Methods of features computation• DFT-based features
1. T e mean of e g2. T e mean abs. value of e detail s from level 1
• DWT-based features1. T e mean magnitude of e low fr y s from
e interval 0;Fs/ 8 , re Fs is e sampling fr2. T e mean magnitude of e fr y s from
e interval Fs/ 4;Fs/ 2• Combined features (best performing mbination of e above)
1. DFT based features 22. DWT based features 1
4. Feature Extraction
4060
80100160
180
200
0
0.2
0.4
(a) REGION CONTOUR
50 100 150 2000.1
0.2
0.3
0.4
(b) BOUNDARY SIGNAL
Index
0 100 200
2
4
6 (c) FOURIER TRANSFORM
Index
(d) REGIONS SETECTED FOR NN TRAINING
1
23
4
5
67
89
1011
12 1314
1516
Fig. 3. DFT based features extr n using e 1 dimensionalboundary of a d region (a, b, c) and e water d regions
d for e neural network training (d)
Classi cation using self-organizing neural networks [2]• n of Q segments
using R features organized inpattern matrix PR,Q
• T e no. S equalsno. output layer elements
P21
P11
Class C
Class B
Class A
W, b
• T e learning pr– T e w s matrix WS,R is r rsively r d to m
mize e s between input v r and e rresponding w s of e winning neuron (wit
t to e rrent pattern)– S l n e network w s belonging to separate
output elements represent l s individualsThe Cluster Segmentation Criterion (CSC)
• Proposed for results evaluation
• E i= 1,2, · · · ,S mprising Ni segments n be rrized by e mean E n Dist of e mn
feature v rs p jk of s segments jk for k= 1,2, · · · ,Ni frome s r in i t row of matrix WS,R = [w1,w2, · · · ,wS]
by relationClassDist(i) =
1Ni
Ni
k= 1Dist(p jk,wi) (4)
• T e mean value of average s s related to e meanvalue of s rs
CSC = mean(ClassDist)/ mean(Dist(W,W )) (5)• Gives low values for m t and well separated rs and
values for e rs wit extensive dispersion
0 0.1 0.2 0.3 0.4 0.50
0.5
1
1.5
2
2.5
3
1
2 3
4
5
67
8
9
10111213141516A
B
C
W(:,2), P(2,:)
W(:,
1), P
(1,:)
0.005 0.01 0.015 0.02 0.025 0.03
0.2
0.3
0.4
0.5
0.6
0.7
1
23
45
6 78
9
101112
13
141516
A
B
C
W(:,2), P(2,:)
W(:,
1), P
(1,:)
0.2 0.3 0.4 0.5 0.6 0.70
0.1
0.2
0.3
0.4
0.5
1
23
4
5
67
8
9
101112 1314
1516
A
B
C
W(:,2), P(2,:)
W(:,
1), P
(1,:)
Fig. 4. Comparison of e n results after sm g fore DFT, DWT, and mbined features (from left to r ) extr
from e regions d in Fig.3d and used for training of tneural network. r s boundaries are d by e wematrixWS,R for R= 2 evaluated by a l algor m divides
e plane into S= 3 s s.
Table 1. COMPARISON OF FEATURES COMPUTATION METHODSACCORDING TO THE CSC CRITERION V E
Smoothing DFTFeaturesDWT
FeaturesCombinedFeatures
es 0.12 0.10 0.18No 0.14 0.11 0.14
Results
(a) WATERSHED TRANSFORM (b) DFT+DWT SEGMENTATION
(c) DFT SEGMENTATION (d) DWT SEGMENTATION
Fig. 5. n of e MR image into 3 s and e baground (bla k) without smoothing
(a) DENOISED IMAGE (b) DFT+DWT SEGMENTATION
(c) DFT SEGMENTATION (d) DWT SEGMENTATION
Fig. 6. n of e MR image into 3 s and e baground (bla k) after smoothing
• We demonstrated e n of e above m s to realbiom l magneti r e data
• T e water d transform d most of image regions, owever, revealed oversegmentation
• We d 3 pairs of s for features mputationfrom regions boundaries and provided e mparison of e
s using e CSC riterion• Amongst e 3 feature extr n s, e DWT based
m d performed best bot wit and t image smas a prepr g step
• T e DWT transform was also implemented in e smpr s d a positive im t on e water d segmtation results
Conclusions
[1] S. Ariv n and . Ganesan. Texture n UsingWavelet Transform. Pattern Recogn. Lett., 24(9 10):1513–1521,2003.
[2] C. M. B p. Neural Networks for Pattern Recognition. OxfordUniversity Press, 1995.
[3] D. B. Per val and A. T. Walden. Wavelet Methods for Time Se-ries Analysis. Cambridge Series in S l and PrM m s. Cambridge University Press, New ork, U.S.A.,2006.
[4] R. C. Gonzales, R. E. Woods, and S. . Eddins. Digital ImageProcessing Using MATLAB. Pr e Hall, 2004.
[5] M. Nixon and A. Aguado. Feature Extraction & Image Process-ing. NewNes Elsevier, 2004.
[6] Saeed V. V Advanced Digital Signal Processing andNoise Reduction. Wiley & Teubner, West Sussex, U.K.,edition, 2000.
References
8t International Confon s in Signal
IMARoyal Agr ral College & IET,
16 – 18 r 2008
Work was supported by resea grant MSM6046137306.
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