Ultrasound Image Segmentation by Spectral Clustering Algorithm based on the Curvelet and

GLCM features

Ting Yun School of Computer Science, SouthEast University

School of Information Science,Nanjing Forestry University Nanjing China

njyunting@tom.com

Huazhong Shu School of Computer Science, SouthEast University

Nanjing China

Abstract—This paper address the issue of how to segmentation ultrasound image pathological region and propose a novel ultrasound image segmentation method by spectral clustering algorithm based on the curvelet and GLCM features. Firstly ultrasound image are subdivided into continuous small regions and each sub-region using curvelet transform and GLCM approach to get a series of feature vectors, including such as angle second-order moments,contrast,correlation, entropy, variance, mean,and the deficit moments etc; Secondly, a set of sampling pixels are selected to simplified data space and reduces the data dimension of spectral clustering algorithm.The small sample extraction method was designed to reduce the complexity of spectral clustering algorithm; Finally, priori classification of spectral clustering result as a guide, the remaining image data samples are classified using KNN method to complete the segmentation.Experimental results show that our method for pathological areas in the ultrasound image segmentation is highly accurate and effective. Keywords: Ultrasound image; image segmentation; curvelet transform; GLCM; spectral clustering;

I. INTRODUCTION Medical ultrasound images is an important type of

medical images and is widely used in medical diagnosis,Compared with other medical imaging methods, Ultrasound imaging has the advantages of non-traumatic to human body, real-time display, low cost, ease to use, as an ideal non-invasive method of diagnosis It has a brilliant and broad prospects of development.However, because of the principle of imaging factors lead to insufficient grayscale display range or unreasonable gray distribution, so the auxiliary diagnosis effect of the ultrasound images is constrained, especially in some local details,if the gray scale difference is not obvious, that will bring a lot of difficult to diagnosis. In order to improve ultrasound images quality and enhance the readability of ultrasound medical local details, make images suitable for human eyes observation or machine analysis, therefore in recent years automatic segmentation for pathological area of ultrasound images become the research focus.

Some scholars dealed with the ultrasound. image segmentation in the frequency domain, such as literature [1] used wavelet decomposition to achieve wavelet coefficients

then combined with neural network method to process segmentation problem. Sheng Y etc [2] constructed an accurate ultrasound image segmentation algorithm in the wavelet domain with the Chan-Vese model, Ali Kermani etc [3] combined the local histogram and wavelet transform to locate the position of breast lesions. J.Xie [4] proposed a new method which combined texture and shape as the prior information, then energy equation was constructed and texture of pathological area was classified by the shape parameter and Gabor filter coefficients.Other researchers processed ultrasound image in the time domain,Literature [5] proposed segmentation algorithm based on gray probability density function and fast matching ideas for vascular image, Literature [6] constructed an image segmentation method based on graph theory, which has the advantages of robust to noise, sensitive to the blurred edge, low residual error rate and fast calculation speed. After remove speckle noise, literature [7,8] adopted active contour model combining with prior information such as shape texture color to complete pathology region division.Christodou [9] used ten different texture feature include first-order statistics, gray level cooccurrencematrix, gray differential statistics, neighborhood gray difference matrix, statistical feature matrix, texture energy spectrum, characteristic of fractal dimension, power spectrum and shape parameters etc to extract carotid atherosclerotic plaques, then extracting separation results was got by the K-neighboring method.

In this paper, the curvelet transform and GLCM methods was used to obtain a series of feature vectors about each pixel, then these vectors were classified by spectral clustering methods to achieve the extraction of the pathological region from ultrasound images.

II. LTRASOUND IMAGE FEATURE EXTRACTION

A. GLCM GLCM(gray level cooccurrencematrix) is a method of

describe texture,it is widely used in various texture identification field. GLCM describe statistical properties about a pair of pixels in a certain direction keeping a certain distance away from each other. For example suppose an image

Foundationitem: The issue is subsidized by the National Key Basic Research Program Project 973 (2011CB707904),National Natural Science Foundation of China(30671639), Natural Science Foundation of Jiangsu Province (BK2009393), High academic qualifications fund of Nanjing Forestry University (163070052,163070036).

Author:Y.Ting (born 1980.10), postdoctor,lecturer, main research include Medical Image Processing and Machine Vision; S.huazhong, professor, doctoral supervisor, main research include Medical Image Processing and Pattern Recognition;Shen Lirong,doctor,lecturer, main research include Medical Image Processing;W.yixiong, lecturer, main research include Data Mining and Pattern Classification.

920978-1-4244-8165-1/11/$26.00 ©2011 IEEE

pixel ( ),x y ,its gray-scale is i , we calculate the frequency

( ), , ,p i j d θ of the pixel ( ),x dx y dy+ + which gray-scale is j

and with interval d from point ( ),x y . Its mathematical

expression:

( ) ( ) ( ) ( ) ( ){ }, , , , , , , , ,p i j d x y x dx y dy I x y r I x dx y dy jθ = + + = + + = (1)

where θ is the generation direction of GLCM, its values usually is 0 ,45 ,90 ,135° ° ° ° . I is the image domain.

We continuously divide image (512 512)I ∗ into multiple blocks of size (16 16)∗ ,total get (497 497)∗ blocks after decomposition. for each block GLCM method is used to extract seven parameters, they are angular second moment 1w , contrast 2w , correlation 3w , entropy 4w , variance 5w ,mean 6w , deficit moment 7w ,then these parameters

{ }1 2 3 4 5 6 7, , , , , ,blockGlcp w w w w w w w= are prepared for

characteristics class.

B. Curvelet transform Curvelet transform provide a new multi-scale target

representation method of image , its frame elements include scale and position, and still have direction description that wavelet do not provide, so it has great potential in segmentation and classification of texture.In this article we use multiresolution and multi-direction fine characteristics about curvelet transform to extracted ultrasound image features. In frequency domain curvelet transform definition is:

( )( )

( ) ( )

( )( ) ( ) ( )

, ,2

,2

1 ˆ ˆ, ,2

1 ˆ exp ,2 i

j l k

j lj k

c i l k I d

I U R i x dθ ω

ω ϕ ω ωπ

ω ω ωπ

= =

< >(2)

Where ( ), ,j l kϕ ω is mother curvelet,its scale is 2 j− and

direction angle is [ ]22 2 jl lθ π −= × × , k is displacement,

iRθ ω is fourier frequency window. This paper then adopte unequally spaced fast fourier transform(USFFT) alogrithm, It is a fast discrete Curvelet transform method [10,11], Implementation of this method is as follow:

1) For a given two-dimensional function [ ]1 2,I t t

1 20 ,t t ω≤ ≤ in cartesian coordinates, we used two-dimensional fast Fourier transform (2DFFT), and get two dimensional frequency domain representation:

[ ]1 2 1 2ˆ , , 2 , 2I n n n n n n− ≤ ≤

2) In the frequency domain, for each pair of scale j and angle l , resampling [ ]1 2

ˆ ,I n n will get

[ ] ( )1 2 1 1 1 2ˆ , tan , jI n n n n n Pθ− ∈ ,where

( ){ }1 2 1,0 1 1,0 1, 2,0 2 2,0 2,, : ,j j jP n n n n n L n n n L= ≤ < + ≤ < +

1, jL is parameter about 2 j2, jL is parameter about 22 j ,

They respectively represent the length and width about support interval of window function [ ]1 2,jU n n

3) Multiply the interpolated I with window function jU ,then will get jlI :

[ ] [ ] [ ]1 2 1 2 1 1 1 2ˆ, , tan ,jl jI n n I n n n U n nθ= − ;

4) jlI do inverse 2DIFFT transformation,so get discrete

curvelet coefficient set ( ), ,DC j l k We continuously divide image (512 512)I ∗ into multiple

sub-blocks of size (16 16)∗ ,total get (497 497)∗ sub-blocks after decomposition.Then for each sub-block take three layer USFFT transform, according to the direction angle we decompose each sub-block into{ }1,16,1 directions, then from

these directions we proportionally chose { }1, 4,1 directions, for every direction we take curvelet inverse transformation to get characteristic block ( )ˆ 16*16p , finally using the following formula to calculate characteristic values.

a) angular second moment: ( )1 1

28

0 0

ˆ ,bs bs

i jw p i j

− −

= =

=

b) contrast: ( )1 1

29

0 0

ˆ , ,bs bs

i jw n p i j i j n

− −

= =

= − =

c) correlation: ( ) ( )1 1

2 210 1 2 1 2

0 0

ˆ ,bs bs

i jw ij p i j μ μ σ σ

− −

= =

= −

where ( )1 1

10 0

ˆ ,bs bs

i ji p i jμ

− −

= =

= ( )1 1

20 0

ˆ ,bs bs

j ij p i jμ

− −

= =

=

( ) ( )1 1

221 1

0 0

ˆ ,bs bs

i ji p i jσ μ

− −

= =

= − ( ) ( )1 1

222 2

0 0

ˆ ,bs bs

j ij p i jσ μ

− −

= =

= −

d) entropy: ( ) ( )1 1

110 0

ˆ ˆ, log ,bs bs

i jw p i j p i j

− −

= =

= − ,where the

block p represent the result of a certain direction subband converted by curvelet inverse transformation. 16bs = is block size.

Then feature vector { }8 9 10 11, , ,blockCurvelet w w w w= was obtained. eigen vectors

{ },block block blockEigenvectors Glcp Curvelet= are composed by each block’s relevant GLCM and curvelet coefficients, and later they are served as classifying instances of spectral clustering algorithm.

III. TRASOUND IMAGE SEGMENTATION WITH SAMPLING SPECTRAL CLUSTERING METHOD

Spectrum graph theory is a kind of image segmentation theory. It use matrices and linear algebra theory to research adjacency matrix of graph. According to the matrix spectrum

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to determine the some properties of graph. Spectrum graph theoretical analysis is based on Laplacian matrix of graph,suppose an nondirectional weighted graph ,G V E= its representation is a symmetric matrix:

ij n nW w

×= where ijw is the weight connecting vertices i

with j .The graph Laplacian matrix Lp is expressed as:

Lp D W= − ,where D is diagonal matrix,1

n

ii ijj

D w=

= Lp is

symmetric positive semidefinite matrices, so its eigenvalues are all real non-negative, that 2 1 0nλ λ λ≥ ≥ ≥ = If nondirectional weighted graph G with c number connected components, Lp has c number feature vector with value 0. If G is connected graph, 2 0λ ≠ 2λ is fiedler value of G , Corresponding vector is fiedler vector. When k-way division is considered,recursive binary algorithm is not stable enough,N-cut objective function based on k-way division is used, the function is:

( ) ( ) ( )

1

1 11 2

, ,, ,

k

c ck k

Ncut kij ij

i A j i A j

cut A A cut A AJ A A A

W W∈ ∈

= + + (3)

Minimize the objective function (3) is equivalent to solve the function(4) to seek number k smalle eigenvalue:

( )

1 12 2Z D D W D x xλ

− −= − =

(4)

that N-cut objective function optimal solution based on k-way division is in subspaces which composed by eigenvectors corresponding to number k smallest eigenvalue of eq (4).

We defines ijw expression is :

( ) ( ) ( ) ( )

( ) ( )2222

2

0

ll

I i I jE i E j

ije if I i I j rw e

otherwise

σσ

− −− −

− <= ∗

(5)

Where ( )I i represent the position of current block

(16*16 size) center ( ),i ix y in the image domain, and ( )E i represents the corresponding feature vector of the block.

( ) { },i i iblock block blockE i Eigenvectors Glcp Curvelet= = according

to the principle of spectrum clustering method, one dimensional characteristic vector sec smallE corresponding to the second small eigenvalue of matrix Z in equation (4) is calculated, then the appropriate threshold is selected in equation (6) for classification:

( )( )

sec

sec

1 1,

1 1,small

small

if E i thresholdgategory

if E i threshold

≥=

− < (6)

Due to enormous calculation of W matrix, so we randomly sample 1000 pixels to construct similar matrix W , subsequently curvelet transform and GLCM methods is used to get two class features, then spectral clustering has been used to identify two clusters. Next KNN method is adopted and the remaining points are assigned to the respective cluster depending on the principles of the nearest distence.

IV. EXPERIMENTAL RESULTS After the text edit has The experiment of three ultrasound images is shown in Fig 1

a b c

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a b c

a b c

Fig. 1 Segmentation of ultrasound images, First columns: the original ultrasound images;Second columns: three snapshot for our segmentation results; Third columns: Segmentation of our algorithm, using 1000 sampling pixels.

In the experiment, the appropriate parameters are selected and compare with manual segmentation results, the conclusion as follows:

Table 1. Experimental results and selected coefficients

The distance d of GLCM

sampling pixels count

Windows size threshold

similarity with the manual

segmentation ultrasound

image1 d=2 1000 16*16 -0.036 98% ultrasound

image2 d=2 1000 16*16 0.0 95% ultrasound

image3 d=2 1000 16*16 0.070 96%

V. CONCLUSION AND FUTURE WORK We have proposed a novel ultrasound image

segmentation method. Our main contributions are:1) curvelet transform and GLCM is adopted to get ultrasound image features for better estimating pathological region and background area. 2) a set of sampling pixels are selected to simplified data space and reduces the data dimension of spectral clustering algorithm. 3) KNN method is used to the remaining pixels,a term of spatial constraints is added to realize the ultrasound image segmentation. Experiments demonstrate the efficacy of our approach. Future work includes extending the variational image features for automatic label pathological region.

REFERENCES [1] Zafer can, Mehmet Nadir Kurnaz.Ultrasound Image Segmentation by

Using Wavelet Transform and SelfOrganizing Neural Network. Neural Information Processing-Letters and Reviews.Vol. 10(8),pp.183–190,2006.

[2] Sheng Yan, Jianping Yuan, Chaohuan Hou. Segmentation of Medical Ultrasound Images Based on Level Set Method with Edge Representing Mask. 2010 3rd International Conference on Advanced Computer Theory and Engineering(ICACTE),Chengdu.

[3] Ali Kermani, Ahmad Ayatollahi.Medical ultrasound image segmentation by modified local histogram range image method. Biomedical Science and Engineering, 2010,3, pp.1078-1084

[4] J.Xie Y.Jiang and H.T.Tsui.Segmentation of kidney from ultrasound images based on texture and shape priors.IEEE Transaction on Medical Imaging, 24(1), pp 539-51,2005.

[5] Marie-Hélène Roy Cardinal, Jean Meunier, Gilles Soulez, Roch L. Maurice, Éric Therasse, and Guy Cloutier. Intravascular Ultrasound Image Segmentation: A Three-Dimensional Fast-Marching Method Based on Gray Level Distributions.IEEE Trans On Medical Imaging ,25(5),2006

[6] Grady L Funka Lea G.Multi-label image segmentation for medical applications based on graph-theoretic electrical potentials[C]. Proceedings of Conference on Computer Vision and Mathematical Methods in Medical and Biomedical Image Analysis ECCV20042004 3117 230-245.

[7] Cremers, D., Rousson, M., and Deriche, R. A review of statistical approaches to level set segmentation:integrating color, texture, motion and shape. Int. J.Comput Vision, 2007,72(2),195-215.

[8] Dydenko, I., Jamal, F., Bernard, O., D Hooge, J.,Magnin, I. E., and Friboulet, D. A level set framework with a shape and motion prior for segmentation and region tracking in echocardiography. Medical Image Analysis,2005,10(2),162-177.

[9] C.I.Christodoulou,C.S.Pattichis.Texturebased classification of atherosclerotic carotid plaques.IEEE Transacion on Medical Imaging.22(7),pp 902-12,2003.

[10] CAND ES E J, DEMANET L. Curvelets and fast wave equation solvers[D].California, CA:California Institute of Technology,2005.

[11] CANDES E J, DONOHO D L. New tight frames of curvelets and optimal rep resentations of objectswith C2 singularities[J]. Communications on Pure and Applied Mathematics, 2004, 57(2):219-266.

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