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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