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RESEARCH Open Access

Segmentation of ultrasound images of thyroidnodule for assisting fine needle aspirationcytologyJie Zhao*, Wei Zheng, Li Zhang and Hua Tian

Abstract

The incidence of thyroid nodule is very high and generally increases with the age. Thyroid nodule may presage theemergence of thyroid cancer. Most thyroid nodules are asymptomatic which makes thyroid cancer different fromother cancers. The thyroid nodule can be completely cured if detected early. Therefore, it is necessary to correctlyclassify the thyroid nodule to be benign or malignant. Fine needle aspiration cytology is a recognized earlydiagnosis method of thyroid nodule. There are still some limitations in the fine needle aspiration cytology, such asthe difficulty in location and the insufficient cytology specimen. The accuracy of ultrasound diagnosis of thyroidnodule improves constantly, and it has become the first choice for auxiliary examination of thyroid nodular disease.If we could combine medical imaging technology and fine needle aspiration cytology, the diagnostic rate ofthyroid nodule would be improved significantly.The properties of ultrasound, such as echo, shadow, and reflection, will degrade the image quality, which makes itdifficult to recognize the edges for physicians. Image segmentation technique based on graph theory has becomea research hotspot at present. Normalized cut (Ncut) is a representative one, whose biggest advantage is not proneto small region segmentation but suitable for segmentation of feature parts of medical image. However, how tosolve the normalized cut has become a problem, which needs large memory capacity and heavy calculation ofweight matrix. It always generates over segmentation or less segmentation which leads to inaccurate in thesegmentation.The speckle noise produced in the formation process of B ultrasound image of thyroid tumor makes the quality ofthe image deteriorate. In the light of this characteristic, we combine the anisotropic diffusion model with thenormalized cut in this paper. After the enhancement of anisotropic diffusion model, it removes the noise in the Bultrasound image while preserves the important edges and local details. This reduces the amount of computationin constructing the weight matrix of the improved normalized cut and improves the accuracy of the finalsegmentation results. The feasibility of the method is proved by the experimental results.

Keywords: Thyroid, Ultrasound images, Image segmentation, Normalized cut, Anisotropic diffusion,Fine needle aspiration cytology

* Correspondence: Zhaojie_hbu@126.comCollege of Electronic and Information Engineering of Hebei University,Baoding 071002, China

© 2012 Zhao et al.; licensee BioMed Central. This is an Open Access article distributed under the terms of the CreativeCommons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, andreproduction in any medium, provided the original work is properly cited.

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IntroductionEpidemiological studies show that the incidence of thy-roid nodule is very high and increases with the age. Itmay presage the emergence of thyroid cancer [1]. Thy-roid carcinoma is different from other thyroid cancer. Itcan be completely cured if detected early. Therefore, it isvery necessary to correctly classify the thyroid nodule[2] to be benign or malignant. Fine needle aspirationcytology (FNAC) [3] is a recognized early diagnosticmethod of thyroid nodule with high success rate, but itstill has some limitations. Therefore, even if the patientswhose results is invisible through FNAC, they also can'tcompletely be ruled out the possibility of a tumor.Thyroid ultrasound technology [4] can ensure that you

get a lot of information about thyroid nodule before theoperation. Through the ultrasound images, we can locatethe position of the thyroid nodule, measure the size, anddecide whether an operation is needed or not. In ultra-sound images, in addition to the echo characteristics,nodules in degree, there are some other ultrasound charac-teristics which can also be acted as a judgment indicatorwhich shows possibility of nodular malignant, such as theshape and contour of nodules. The exact boundary detec-tion of ultrasound images [5] will provide accuracy positionfor pierce, but it exists a granular pattern which calledspots in the ultrasound images because of the impact ofimaging principle. In addition, the properties of echo,shadow, and reflection of ultrasonic will degrade theimage quality. This image quality degradation caused bythe nature of ultrasonic image makes it difficult torecognize its edges accurately even for an experiencedphysician. Especially it is very difficult to complete thenodules and tracheal of nodules positioning area of the re-gional segmentation.At present, the segmentation method which is widely

used in the clinical application of ultrasound imagingsystems is based on the threshold value method or thedoctor manual segmentation method. Although the im-plement method of threshold segmentation is conveni-ent and simple, inevitably, the speckle noise and texturein the ultrasound image make the method difficult toobtain satisfactory results [6]. In the above segmentationmethod, manual segmentation method is relatively easyto implement and the result is also easy to accept, butthe heavy workload and long time tend to make doctorsand patients difficult to accept. Using computer toimplement automatic, semi-automatic segmentationmethod is the ideal choice for ultrasound image seg-mentation in clinical application. As an importantbranch of image segmentation, the segmentation ofmedical ultrasound image almost covers all existing seg-mentation techniques. Aarnink et al. use the nonlinearLaplace filter to implement segmentation of prostateultrasound images automatically [7]. Fan et al. use the

nonlinear wavelet threshold method to detect theboundary which is formed by lumen-intima - the innerwall and outer membrane of implantable ultrasoundimages. Yoshida et al. do a more in-depth study of medicalultrasound image segmentation which is based on the ac-tive contour models. Lee et al. take advantage of the dy-namic programming algorithm to segment differentmedical ultrasound image and have achieved good seg-mentation results [8]. Yan Jiayong et al. use Active ContourModel which is based on Gradient Vector Flow Law hasachieved a certain effect on soft tissue tumors segmenta-tion of ultrasound image. Cvancarova et al. put forwardSnake model of ultrasonic image segmentation methodbased on GVF algorithm [9]. According to characteristicsof ultrasound cardiac image with noise, fuzzy boundaries,uneven distribution of grayscale, Zhang Et al. propose po-larity filtering and edge sharpening, and then use CV Snakemodel to segment, extracted ventricular boundary finally.Yan Et al. use the average edge energy of zero level setcurves to control energy evolution speed and segmentationresults by studying Chan-Vese level set method. Liu Jinzhuet al. put forward ultrasound image classification methodof fatty liver which is based on threshold segmentation toanalysis of the characteristics of the lesions and non-lesiontissue in ultrasound images in detail. In the end, they pointout the main problem in the ultrasound image segmenta-tion.Yu Jiali et al. propose medical ultrasound image seg-mentation based on a random walk. Through solvingsparse, symmetric and positive definite equations of linearsystem to obtain the solution of the problem, and thenrealize the segmentation of medical ultrasound image.Since ultrasonic image exists serious artifact and noise,

at the same time the target has weak boundary orboundary breakpoints, which makes method based onboundary difficult to segment correctly. The segmenta-tion algorithm based on texture needs a predefinedimage mode, so the effect is not good in the ultrasonicimage segmentation, and often need to combine withother knowledge to improve the segmentation results.The method based on the model can effectively segmenttarget ,use the homogeneous area statistical informationto structure energy function, and search minimizationoptimal solution in the global range . But the image seg-mentation effect is not ideal for the target which is dis-orderly or uneven distribution of grayscale. Therefore,the present algorithm exists certain flaws in dealing withspeckle noise and weak boundary, and most of the algo-rithms need to manually draw the outline of the initialcontour which is close to the real boundary of the target,so it is difficult to get wide application in clinical.According to the above problems which exist in theultrasonic image segmentation in this paper and com-bined with the characteristics that the thyroid ultrasonicimage is seriously polluted by the speckle noise and

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images is usually fuzzy, we propose an improved imagesegmentation algorithm based on normalized cut is,combining homomorphism filtering, the anisotropic dif-fusion model, fractional differential into normalized cut.The speckle noise is removed, important edge details arepreserved, and the amount of computation of weightmatrix is reduced. And the algorithm is compared withsome traditional segmentation method including edgedetecting, threshold segmentation, region splitting andmerging and some modern segmentation method in-cluding watershed segmentation, active contour model,and graph segmentation method [10]. Simulation experi-ment show that only the improved segmentation methodbased on normalized cut can segment the importantparts, such as tumor, thyroid, and windpipe and so on.The segmented parts is the important reference valuefor the doctors to diagnose thyroid tumor in clinical.The remainder of this paper is organized as follows. In

Section 2, we analyze the characteristics of thyroid nod-ule ultrasound image .The traditional method for seg-mentation of thyroid ultrasound image is introduced inSection 3. Ultrasound image segmentation based onNcut is introduced in Section 4. The proposed methodand the implementation and results are given in Section5.This paper is summarized in Section 6.

Characteristics analysis of thyroid nodule ultrasound imageThe following group of thyroid ultrasound images shownin Figure 1 is provided by Affiliated Hospital of HebeiUniversity.

Figure 1 The original ultrasound image of thyroid of one patient.

We show a group of three-dimensional ultrasoundimages of the SPECT images in Figure 1. The width of theimage is 640 pixels, height 480 pixels, with 150 DPI reso-lutions both in horizon and vertical, and a depth of 24 bits.Such groups of image must be preprocessed before imagesegmentation, which requires us to transform SPECTimage into independent images before processing.The size of the cut image is 128 by 128, 150 DPI. The

histogram is an important statistical characteristic of theimage. It represents the statistical relationship betweenthe probability of each gray level and the gray-scale, pro-vides the whole distribution of the grey value. The histo-gram of original thyroid ultrasound image of Figure 2has shown in Figure 3.As we can see from the grey distribution of Figure 3,

the grey composition of the image is mainly concen-trated in dark side, basically in the gray level of 180 orso, and do not cover the gray level to get all the range,so the dynamic range is very small.

The traditional method for segmentation of thyroidultrasound imageThe method of edge detectionEdge detection is the most basic image segmentationmethod. In generally, between the different regionsappears necessarily in different gray mutations namelyedge. We can detect the first derivative maximum orsecond order derivative zero to test the edge. In general,different edge detection operator [11] templates weredesigned and used to complete the image convolution.

Figure 2 The single layer of thyroid ultrasound image aftercutting.

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Commonly, the first derivative operators include gradi-ent operator, Prewitt operator, and Sobel operator. Thesecond order derivative operators, such as Laplace oper-ator, are particularly sensitive to edge information andnoise, so the unnecessary noise should be removed be-fore the edge detection.In order to reduce the influence of noise to the image,

we usually conduct image filtering before the derivation.Commonly we use Canny operator or LOG operator.LOG operator is developed on the basis of the Laplace op-erator. It firstly uses a Gaussian function to smooth theimage, and then use the Laplace operator to detect theedge of the smoothed image. Similarly, Canny operatorfirst uses Gaussian filter to smooth the image, and thenadopts the maximum inhibition and double threshold to

Figure 3 The histogram of thyroid ultrasound image.

detect the edge of the gradient image, which can lead togood detection results and high precision.From the results of traditional edge detection we can

see that the edge is discontinuous, and a lot of falseedges were detected.

The method of threshold valueUsing the difference of gray image level between the tar-get object and the background area, we divide grayimage into target area and background area, then useone or several threshold value of gray image to dividegray image into several parts. This method is calledimage threshold segmentation, which is widely used inimage segmentation. That is to say, the threshold seg-mentation method is based on the assumption thatsimilar pixels have similar gray values, not similar pixelshave great differences between gray value, which isreflected on the histogram that the different classescorrespond to different peaks. We always select the valleybetween the two peaks as the segmentation threshold dur-ing the image segmentation, which will separate eachpeak, and then complete the image segmentation. It isthus clear that the key to threshold segmentation is to findthe optimal threshold so that we can separate two types oftarget. However, not all images have the obvious bimodalor multi-peak in histogram, so the choice of thresholds isbecoming more and more difficult. In this case, manyother improved methods to determine the threshold [12]have been put forward, such as the approach based ontransition zone, the changed threshold method of pixelspatial location information, the threshold method com-bined with the connectivity information and so on.The threshold segmentation is simple for the different

types of objects that have big difference on gray value orother characteristic values, which would be very effectivein image segmentation.From the results, we can see that the histogram of ori-

ginal thyroid ultrasound image is not bimodal image, sothe result is wrong. In conclusion, threshold segmenta-tion method can not be adopted in this situation.

Region splitting and merging methodRegion growing method mainly considers the relation-ship between the pixels and it’s spatially neighborhoodpixels. It is a way of extracting connected region in aimage according to predefined standard. Specific ap-proach is as follows: first, identify one or more seedpoints as the starting point(s) of growth, and then mergethe pixels which have the same or similar characteristicswith the seed pixels in the neighborhood into the area ofthe seed pixels. Regard these new pixels as new seed pix-els to continue the process above until there is no pixelswhich suffice the conditions. The core of the region

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growing method is the selection of seed point and themeasure of regional similarity [13].Region growing method has the advantage of simple

calculation, and it also considers the pixel similarity andspatial neighborhood, thus it can effectively eliminateisolated noise points, and it is especially suitable for thesegmentation of small structures, such as tumor and scardetection and segmentation. The disadvantage is that wehave to manually implant a seed point to every area weneed to extract, and it is particularly sensitive to the selec-tion of seed points, for different seed points may get verydifferent segmentation results. Meanwhile, this method isparticularly sensitive to noise and it is easy to cause inanityin the area. Regional split and merge method is developedon the basis of region growth method, it does not need toartificially determine the seed point and has overcome thedefects that the region growing method needs to manuallyselect the seed points. It splits and merges the whole imageat the same time according to some consistency criterion,not liking the region growing method to start from a singlepixel; splitting and merging focus on the design of the splitand merge guidelines. The split and merge algorithm is ef-fective in segmentation of complex scene images, but thereare also shortcomings. It generally cannot reach pixel-levelsegmentation accuracy, because the pixel-level split andmerge would increase the algorithm's time complexity, andalso easily form the meaningless area.From the split and merge results of the ultrasound

images, we can see that it splits neither the nodules northe trachea, so the result has no practical significance.

Watershed segmentation methodMorphological watershed algorithm is an algorithmwhich is based on region segmentation. The basic idea isto simulate the process that water flow submerges land-form, to split the different areas through forming thedams between different regions. Watershed transformregards gray scale image as a geomorphic surface, andassumes to make a hole in the surface of each minimumarea, water will slowly immerse in the surface from theseholes, and starting from the minimum of lowest point,water will gradually submerge the catchment basin of theimage. In addition, at a certain point, when the water fromtwo different minimums increasingly rises to come to-gether, it will build a dam at this point, at the end of thesoaking process; each region minimum is surrounded bythe dam of corresponding catchment basin, all the damcollection constitutes the watershed, which divide theimage we input into different regions.The whole watershed process can be described by

mathematics:Let M1,M2,,,,,MR represent a minimal area of the image

f(x,y),C(Mi) represents the catchment basin related to theminimal area Mi, min and max represent Gray-scale

maximum and minimum of the image f(x,y) respectively.Suppose that T[n] represents a set in which all points (s,t)suffice g(s,t)<n, that is to say: T[n] = {(s, t)|g(s, t) < n}. Froma geometric perspective, T[n] is the set of points locatedbelow plane g(s,t)=n in image f(x,y) , that is to say, nrepre-sents the immersion depth of step n. For a given catch-ment basin, in the step n, it will appear a certain degree ofimmersion (may not appear). Suppose that in step n , theminimal area Miis immersed, let Cn(Mi) represent a partof the catchment related to minimal area Mi, which is thehorizontal surface area formed in the catchment basin Cn(Mi), when the immersion depth is n. In order to facilitatethe discussion, we may regard Cn(Mi) as a two valueimage, which can be represented by the following equa-tion: Cn(Mi) =C(Mi)\ T[n]. In other words, if it is at theposition (x,y), suffice (x, y) ∈C(Mi) and (x, y) ∈T[n], thanCn(Mi) = 1, otherwise Cn(Mi) = 0. If the Gray value of theminimal area Mi is n, than in the step n+1, the immersedpart of the catchment and the minimal area are exactlythe same, that is Cn + 1(Mi) =Mi. Suppose that C[n] repre-sents the union of the immersed part of all the catchment

basin, that is C n½ � ¼ [Ri¼1

Cn Mið Þ , than C[max + 1] is the

union of all the catchment, that is to say: C maxþ 1½ � ¼

[Ri¼1

Cn Mið Þ.From the final results of the watershed segmentation, we

can see that the phenomenon of over-segmentation is quiteserious. It does not accurately segment nodules or trachea.

Active contour model methodCurve evolution model segmentation method unifies theimage, the initial contour, the target contour and theconstraint condition and sets the initial curves andcurved surface in image space and defines the internalenergy related to curve or curved surface shape and theexternal energy related to the image. The internal energycontrols the smooth and continuity of curve or curvedsurface, and the external energy relates to edge charac-teristics. In the interaction of internal energy and exter-nal energy, the contour deforms, so we can get thecontinuous edge images finally. This model, when seg-menting an image, makes full use of the prior knowledgeabout the position, size, and shape of the interested re-gion and the inherent information of medical image toreflect this prior knowledge in the energy functionalform. It links with image data in a dynamic way, the en-ergy function acts as a measure about coincidence de-gree between priori model and image data, minimizationof energy function makes the final result of the curveevolution that contour curve approaches target contour.In addition, active contour model provides an interactiveoperating mechanism, which brings the professional

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knowledge into image analysis to significantly improvethe robustness of the algorithm. Active contour modelhas now been widely used in object recognition, com-puter vision and other fields.At present, according to the basic expression method of

the curve, active contour model is divided into parameter-based active contour line model and geometry-based ac-tive contour line mode. Parameter active contour linemodel is also known as the Snake model. The basic ideaof the Snakes model for image segmentation is to gain theedge of the image through deforming the initial curve.The basic process is firstly to delineate the detected targetblock in the image plane, then evolve and deform theclosed curve, so that it can automatic stop when it arrivesat the target boundary. The deformation process isobtained through minimizing an energy function. It ismainly composed of two parts, one part controls thesmoothness of curve, another part forces curves to tend tothe edge of the image. But the model has three disadvan-tages: first, it is sensitive to the initial curve location; sec-ond, curve in the course of evolution easily falls into localminimum point because of the non-convexity of the en-ergy functional, making the segmentation failure; third,the topology of curves does not change in the course ofevolution. Therefore, in the original model, we must pre-define an initial curve which surrounds it for each targetobject in the image, so that we can get the correct seg-mentation results. But this is a cumbersome and time-consuming work.Based on the above problems, people present the geo-

metric active contour line model to overcome the short-comings of the parameter active contour line model.Geometric active contour line model concept was firstproposed by Caselles in 1993. It is better to overcomethe defects that the parametric model cannot handletopological changes. The biggest difference with theparametric active contour model is that it introduceslevel set method. Its initial contour moves toward thetarget edge under the impetus of contour curve geomet-ric characteristics, and it has nothing to do with theparameters characteristic of the contour. It avoids thedeficiency that parametric active contour model mustrepeat parametric curve and can automatically handlethe question about curve topology changes.From the segmentation results of the geometric con-

tour model method, we can see that even after 500 itera-tions, it does not get a meaningful segmentation areadue to the low contrast of the ultrasound image.

A segmentation method based on graph theoryAmong many image segmentation algorithms, theGraph-based segmentation method shows a powerfuladvantage, which can effectively combine the image graylevel, texture, color and other information of the image

to achieve a satisfactory segmentation results. Inaddition, many mature and perfect classical algorithmsof Graph-based segmentation methods provide a power-ful computational tool. So the algorithms attract widelyattentions in recent years.The algorithm based on the cut value of image [14] is

one of the most important kinds of the Graph-basedsegmentation method. The theory of this methodregards the image as an undirected weights graph , thevertex of the image corresponds to the pixels or regionsof the image, the weights of edge reflects the similaritybetween two pixels or regions. We solve the extremevalue of the objective function which is defined to use acertain cut value to achieve segmentation. There are sev-eral classic algorithms based on the cut value of image.The Min Cut is presented earlier as a optimization cri-terion, it can obtain better segmentation result forsome images. However, it will segment isolated pointsor small regions. Because the base value Cut(A, A )will increase along with the increase of the edgenumbers between A and A. Then many optimizationcriterions are proposed to solve this disadvantage.They average the cut value from different angles, in-cluding averaging the volume of A ( isoperimetricsegmentation, normalized cut value ) and the poten-tial of A (average the cut value ). Ncut is a kind ofthem, its biggest advantage is not prone to small re-gion segmentation, and it suits to segment the of fea-ture parts of medical image.

Ultrasound image segmentation based on NcutIn graph theory, a image is a method to describe the rela-tionship between things. Image represents for G = (V, E,W),Vis the set of all the nodes in the graph, E is the set ofthe edge with connecting the two nodes, W is composedby the matrix Wij, Wij represents similarity between thetwo nodes. Assume that divided graph G into two disjointsubsets A and B, then A[ B =V, A\ B =∅ , so the dis-similarity between two subsets can be expressed as the cutvalue (1):

Cut A;Bð Þ ¼X

i∈A; j∈Bi; jð Þ∈E

wij ð1Þ

The best effect of image segmentation is to make thecut value minimum. Ncut [15] uses the normalized cutvalue as criterion:

Ncut A;Bð Þ ¼ Cut A;Bð Þ 1Vol Að Þ þ

1Vol Bð Þ

� �ð2Þ

Figure 4 The segmentation results of normalized cut.

Figure 5 Ultrasound image processed by the homomorphismfilter.

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Vol Að Þ ¼ assoc A;Vð Þ ¼X

u∈A;v∈V

w u; vð Þ ð3Þ

Vol Bð Þ ¼ assoc B;Vð Þ ¼X

u∈B;v∈V

w u; vð Þ ð4Þ

The ultrasound images segmented by the normalizedcut criterion are shown in Figure 4.From the results, we can see that the normalized cut

produces less segmentation phenomenon, the dividedareas have no practical significance, nodules and trachealhave not been segmented.

The ultrasonic image segmentation based on improvednormalized cutThe algorithmic principleCompare Figure 2 with Figure 3, the numbers of blackpixels are large in grayscale distribution of the originalimage. To obtain an image which can segment andrecognize the following image better, the dynamic rangeof the image must be compressed meanwhile the con-trast of the image must be improved. Homomorphismfilter is a method that the brightness range of image iscompressed and the contrast of image is improved sim-ultaneously in the frequency domain. The thyroid ultra-sound images are processed by homomorphism filtershowing as Figure 5.The general image denoising is isotropic diffusion

which removes noise while makes the boundary fuzzysimultaneously. The biggest characteristic of the aniso-tropic diffusion is that it is a selective smooth processwhich is not restricted in uniform regions but is limitedin crossing boundary part. So noise and some irrelevantdetails are smoothly away, which can effectively achievethe smooth image edge. Gradient calculation based on thefractional differential can nonlinearity keep the low fre-quency components of signal and nonlinearity strengthensits high frequency texture detailed information [16]. So,

this paper brings anisotropic diffusion filter model andfractional differential in normalized cut for processingimage segmentation, as its pre-treatment, it obtains the ac-curate segmentation results of thyroid ultrasound images.

Image enhancement based on anisotropic diffusion modelAnisotropic diffusion model is structured by utilizingtransformation of local coordinates, first second order de-rivative method of edge local details and hyperbolic tan-gent function combining anisotropic diffusion equations.Anisotropic diffusion model derives from thermo diffu-

sion equation (7), thermo diffusion equation is followingas (6):

→q ¼ �→D:∇u ð6Þ

The symbol →q means heat flux fields, the symbol ∇umeans gradient field of temperature, and the symbol D

Table 1 Fractional differential operatorv2�v2 0 v2�v

2 0 v2�v2

0 − v − v − v 0v2�v2 0 8 0 v2�v

2

0 − v − v − v 0v2�v2 0 v2�v

2 0 v2�v2

Figure 6 The image after the anisotropic diffusion.

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means heat conductivity. From conservation of energyprinciple, thermal energy differential form is follow-ing as (7):

∂u∂t

¼ div→D:∇u� �

ð7Þ

In image processing, the every bit value u oftemperature field in planar region is regarded as greyvalue of this point of image, thermal diffusion processchanges into the denoising processing of image. But thediffusion behavior of controlling every image bit shouldbe done in local coordinate system, utilizing the coord-inate transformation transform X-Y to local coordinateM-N.Conversion expressing is following as (8),

mn

� �¼ 1

∇uj jux uy�uy ux

� �xy

� �ð8Þ

The image u gradient in local coordinate system is[Um,Un], along M,N direction, the diffusion coefficientsare f1(x, y, t), f2(x, y, t)

q ¼ � f1 00 f2

� �: um

un

� �ð9Þ

The diffusion equation:

∂u∂t

¼ �div qð Þ ¼ ∂ f1:umð Þ∂m

þ ∂ f2:unð Þ∂n

ð10Þ

In any pixel of image, the diffusion coefficients are thevariables of time. Diffusion equation is rewritten to:

∂u∂t

¼ div D:∇uð Þ ¼ f1 x; y; tð Þumm þ f2 x; y; tð Þunn ð11Þ

Function (11) is the denoising anisotropic diffusionmodel, f1(x, y, t), f2(x, y, t) are smooth coefficients. Inorder to achieve the edge smooth, it must add edge en-hancement in this model.Because hyperbolic tangent function can gently control

increasing and decreasing of the grey level of image edgeon both sides of the center, reducing the edge width tostrengthen edge. Therefore, the anisotropic diffusionmodel of finishing denoising and edge enhancementis (12),

∂u∂t

¼ α x; y; tð Þdiv D:∇uð Þ� β x; y; tð Þf3 x; y; tð Þth lvmmð Þ umj j

ð12Þ

v =Gt∗ u; th lvmmð Þ ¼ elvmm � e�lvmm=elvmm þ e�lvmm�

,th(lvmm) are hyperbolic tangent function. The symbolsα(x, y, t), β(x, y, t) mean anisotropic diffusion and edgeenhancement respectively. The symbol f3(x, y, t) meansedge enhance coefficient. The symbol l means controlcurve slope. The symbol Gt means Gaussian smoothfunction.In view of above factors and human visual cover effect,

the diffusion coefficient is:

f1 x; y; tð Þ ¼ 1= 1þ a vmj j2 þ b vmmj j2� ð13Þ

f2 x; y; tð Þ ¼ 1=ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ a vmj j2 þ b vmmj j2

qð14Þ

f3 ¼ 1� 1= 1þ c vmj j2� ð15Þ

Coefficient a controls the anisotropic diffusion forkeeping edge and the local details, coefficient b controlsthe anisotropic diffusion for keeping the article light, co-efficient c controls selectively the area of edge enhance-ment. The image enhanced by anisotropic diffusion is asFigure 6:

Figure 7 Fractional gradient image.

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The gradient image of ultrasound images based onFractional DifferentialIf the duration of one source f(t) is t∈[a,t], then parting

the duration to equal part as unit interval h=1 so n ¼t�ah

� �h¼1 ¼ t � a½ � , then derived difference expression ofone source f(t) fractional derivatives (16),

dvf tð Þdtv

≈f tð Þ þ �vð Þf t � 1ð Þ þ �vð Þ �vþ 1ð Þ2

f t � 2ð Þ

þ �vð Þ �vþ 1ð Þ6

f t � 2ð Þ

þ �vð Þ �vþ 1ð Þ �vþ 2ð Þ6

f t � 3ð Þ

þ . . .þ Γ �vþ 1ð Þn!Γ �vþ nþ 1ð Þ f t � nð Þ ð16Þ

Figure 8 Segmentation results of improved normalized cut.

Generally speaking, in the image f of M×N,, we use thefilter masking of m×n linear filtering according to (17):

g x; yð Þ ¼Xas¼�a

Xbt¼�b

w s; tð Þf xþ s; yþ tð Þ ð17Þ

a = (m − 1)/2, b = (n − 1)/2, x = 0, 1, 2, . . .,M − 1, y = 0,1, 2, . . ., N − 1. In allusion to the characteristics of thyroidcancer in the ultrasound images, The Mask operator offractional differential is shown in Table 1.In order to extract detail information of image texture,

the sum of coefficient in the fractional differential maskis not zero. In order to make the image fractional differ-ential process has a better rotation invariant, we selectfour kinds of fractional differential mask operator at thesame time which is in the x, y, right diagonal, left diag-onal direction, we calculate the image pixels and neigh-borhood pixels, and then compare the four operationresults, we make the maximum as pixel fractional differ-ential gray value, finally we point-to-point stack theoriginal image and its fractional differential diagram cor-responding pixel grayscale value, at last, we obtained thegradient image of the fractional differential process asshown in Figure 7.

Improved normalized cut of ultrasound imagesegmentationThe normalized cut adopts a cut value of the image toexpress the objective function, through solving extremeof the objective function to realize segmentation. Thefeatures are as follows: 1) It maps the problem of imagesegmentation to the problem of graph partitioning. 2) Itpresents new segmentation criteria of overall situation,extract the overall effect of the images. 3) Effectivelymeasure the dissimilarity between different groups andthe overall similarity between the same groups. 4) Itmakes the problem simplify by changing the probleminto solving extensive characteristic value problem. The

Figure 9 The edge detection of thyroid ultrasound image.

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specific detailed introduction of the normalized cut algo-rithm is as follows.If the weight-function is:

wij ¼ e

F ið Þ�F jð Þk k2

2σ21 � e

F ið Þ � F jð Þ 2

2

σ2Xif F ið Þ � F jð Þ 2 < r

0 else

8><>:

ð18ÞF(i) is the gray value of pixels; X(i) is the spatial coor-

dinates of pixels; σ I2 is the standard deviation of gray-scale Gaussian function; σX

2 is the standard deviation ofspatial distance Gaussian function; r is the effective dis-tance between two pixels, that we consider the similaritybetween two pixels as zero if the distance exceed. So thecloser the gray values between the two pixels, the greatersimilarity between the two pixels and the closer the dis-tance between the two pixels, the greater similarity is.The normalized cut criterion not only measures the

overall similarity between the different groups, but alsomeasures the overall similarity within each group. As the

Figure 10 Threshold segmentation of thyroid ultrasonic images.

principle of Ostu threshold segmentation method, thebest image segmentation threshold value is the greyvalue which is minimum variance in the class and thebiggest variance between the classes, Ncut criterion cal-culates the similarity between the classes, the smallersimilarity between the class and the bigger similarity inthe class illustrates the better segmentation results.According to the literature and considered the form ofReyleigh quotient, the rules of Ncut is transformed intosolving generalized characteristic values:

D�Wð Þy ¼ λDy ð19Þ

Working out Fiedler value and Fiedler vector, we finishthe segmentation combined the characteristic vector ofthe smallest several figures. We conducted the nor-malized cut segmentation process after homomorphicfiltering contrast enhancement, anisotropic diffusionedge-preserving smoothing and fractional differentialgradient processing, the results is shown in Figure 8.

Figure 11 The split and merge result of thyroid ultrasoundimages.

Zhao et al. Health Information Science and Systems 2012, 1:5 Page 11 of 12http://www.hissjournal.com/content/1/1/5

Comparing the simulation result based on improved nor-malized cut with the six kinds of segmentation method inthe previous mentioned,it is easy to find only the algorithmcan produce correct segmental result on thyroid ultra-sound image. Edge detecting method is not able to obtaincontinuous, practical value boundary (showed in Figure 9).It is very difficult to find an appropriate threshold inthreshold segmentation method as a result of small gray

Figure 12 Watershed segmentation of thyroid ultrasound images.

difference between object and background (showed inFigure 10). Region splitting and merging method producesan insignificant segmental region (showed in Figure 11).Severe over-segmentation phenomenon arises in Water-shed segmentation (showed in Figure 12). Practical seg-mental region is not able to be obtained in active contourmodel owing to low gray contrast (showed in Figure 13).Normalized cut based graph theory produces under-segmentation; the segmental result cannot be used for clin-ical diagnosis as before (showed in Figure 4). From the seg-mentation results (showed in Figure 8) of improvednormalized cut we can see that the position of the tracheaand nodule have been divided out, which provides accuratepierce position for fine needle aspiration cytology (FNAC).

ConclusionThe biggest advantage of normalized cut is that it doesnot prone to small region segmentation, and it is suit-able for segmentation of medical image feature. How-ever, there is a problem to solve the normalized cut. Thehigh memory is needed and the weight matrix calcula-tion is large. It is easy to generate the over segmentationor less segmentation, which leads to inaccuracy in thesegmentation. This paper presents an improved methodof the normalized cut, introducing homomorphic filter-ing, anisotropic diffusion and fractional differential intothe normalization process. The experimental resultsshow that this method can extract nodules and tracheaof the thyroid ultrasound images. The edge of this seg-mentation for fine needle aspiration cytology provides

Figure 13 The geometric active contour model segmentationof thyroid ultrasound image.

Zhao et al. Health Information Science and Systems 2012, 1:5 Page 12 of 12http://www.hissjournal.com/content/1/1/5

the position of piercing, assisting fine needle aspirationcytology to complete the discrimination that whetherthe thyroid nodule is benign or malignant.In the procedure of using the algorithm, establishment

of parameters of anisotropic diffusion model and similar-ity definition is the crucial to the fianl results. The para-meters of anisotropic diffusion model including Δt, n, a,b, c, l are selected in according to simulation experimentresults. Range of iteration step Δt is 0.06 ∼ 0.3. If the stepis configured smaller than 0.06, an ideal processing resultcannot be obtained. If the step is configured greater than0.3, a result image is not be true to the original. Iterationfrequency n is configured as 50, and (a, b, c, l) = (0.15, 1.4,0.015, 0.015). Weight matrix is used to define similarity def-inition and parameters of the weight matrix show para-meters of similarity. Simulation experiment shows thebelow configuration, Ncut = 0.065, σX = 0.1, σI = 0.3, r = 20.However there still exists the problem of the algorithm'sversatility and universality in the using of the algorithm, es-pecially the problem of the setting and optimization of mul-tiple initial parameters is also needed to deeply study.

Competing interestsThe authors including support units declare that they have no competinginterests. The authors include Jie Zhao, Wei Zheng, Li Zhang, and Hua Tian.Support units include the Science Research Program of the EducationDepartment of Hebei Province, the Open Foundation of BiomedicalMultidisciplinary Research Center of Hebei University, and Main Item ofMedical Science Research Plans of the Health Department of Hebei Province.

Authors’ contributionsJZ carried out the image segmentation algorithm studies, participated in thealgorithm design and software programming and debugging, and draftedthe manuscript. WZ carried out the image studies, participated in theexperimental comparison work, and further improved the manuscript. LZ

carried out the collection of early data. HT collated and studied the literature.All authors read and approved the final manuscript.

AcknowledgementsThe work is supported by Science Research Program of the EducationDepartment of Hebei Province (2010218), Open Foundation of BiomedicalMultidisciplinary Research Center of Hebei University(BM201103)and MainItem of Medical Science Research Plans of the Health Department of HebeiProvince [Project No. 20120395].

Received: 21 July 2012 Accepted: 26 September 2012Published: 10 January 2013

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doi:10.1186/2047-2501-1-5Cite this article as: Zhao et al.: Segmentation of ultrasound images ofthyroid nodule for assisting fine needle aspiration cytology. HealthInformation Science and Systems 2012 1:5.

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