enhancing obstetric and gynecology ultrasound images by adaptation of the speckle reducing...

Enhancing obstetric and gynecology ultrasoundimages by adaptation of the speckle reducinganisotropic diffusion filter

Cristian Munteanu a,*, Francisco Cabrera Morales b,Javier Gonzalez Fernandez c, Agostinho Rosa a, Luıs Gomez Deniz c

a Instituto de Sistemas e Robotica, Instituto Superior Tecnico, Lisboa, PortugalbHospital Universitario Materno Infantil, Las Palmas de Gran Canaria, SpaincCentro de Tecnologıa Medica, Universidad de Las Palmas de Gran Canaria, Las Palmas, Spain

Received 6 June 2007; received in revised form 23 March 2008; accepted 1 April 2008

Artificial Intelligence in Medicine (2008) 43, 223—242

http://www.intl.elsevierhealth.com/journals/aiim

KEYWORDSUltrasound speckle;Anisotropic diffusion;Interactive geneticalgorithm

Summary

Objective: So far there is no ideal speckle reduction filtering technique that iscapable of enhancing and reducing the level of noise in medical ultrasound (US)images, while efficiently responding to medical experts’ validation criteria whichquite often include a subjective component. This paper presents an interactive toolcalled evolutionary speckle reducing anisotropic diffusion filter (EVOSRAD) thatperforms adaptive speckle filtering on ultrasound B-mode still images. The medicalexpert runs the algorithm interactively, having a permanent control over the output,and guiding the filtering process towards obtaining enhanced images that agree to his/her subjective quality criteria.Methods and material: We employ an interactive evolutionary algorithm (IGA) toadapt on-line the parameters of a speckle reducing anisotropic diffusion (SRAD) filter.For a given input US image, the algorithm evolves the parameters of the SRAD filteraccording to subjective criteria of the medical expert who runs the interactivealgorithm. The method and its validation are applied to a test bed comprising bothreal and simulated obstetrics and gynecology (OB/GYN) ultrasound images.Results: The potential of the method is analyzed in comparison to other specklereduction filters: the original SRAD filter, the anisotropic diffusion, offset and medianfilters. Results obtained show the good potential of the method on several classes ofOB/GYN ultrasound images, as well as on a synthetic image simulating a real fetal USimage. Quality criteria for the evaluation and validation of the method includesubjective scoring given by the medical expert who runs the interactive method,as well as objective global and local quality criteria.

* Corresponding author at: Universidad Tecnica de Lisboa, Instituto de Sistemas e Robotica, Instituto Superior Tecnico, Av. Rovisco Pais,1-Torre Norte 6.21, 1049-001 Lisboa, Portugal. Tel.: +351 21 841 8277; fax: +351 21 841 8291.

E-mail address: [email protected] (C. Munteanu).

0933-3657/$ — see front matter # 2008 Elsevier B.V. All rights reserved.doi:10.1016/j.artmed.2008.04.001

mailto:[email protected]

http://dx.doi.org/10.1016/j.artmed.2008.04.001

224 C. Munteanu et al.

1. Introduction

Ultrasound (US) B-mode images are corrupted by aform of locally correlated multiplicative noisecalled speckle [1]. Small objects in the scene cap-tured by the US equipment can be easily confoundedwith speckle in the final US image, even by trainedexperts. Even though in the early days of medicalultrasound imaging it was thought that speckle mayconvey useful information regarding insonified tis-sue, later it was found that speckle is purely anartifact of the imaging system [1]. Thus, in medicalultrasound imaging, speckle should be filtered outwithout affecting important features in the image.Two main denoising techniques are currentlyapplied [2]: (a) compounding which combinesimages of the same region to form a singlespeckle-reduced image [1,2]; (b) filtering appliedto the B-mode images. Examples of filters used inthe literature are the adaptive filters including theFrost, Lee and Kuan filters [3], homomorphic [4],order statistics [5], anisotropic diffusion [2,6] andwavelet filters [3,7]. There is no general agreementon what should be the preferred filter for specklereduction in US medical images. Moreover, differentexperts might have distinct opinions on the qualityof the filtering results according to experience,particular clinical needs, and subjective opinions.For example, in a recent study [3] the authors per-form an extensive experimental comparisonbetween various filters used for despeckling ultra-sound images of the carotid artery, and prove thatwhen evaluated by human experts more elaboratealgorithms such as anisotropic diffusion, or waveletfiltering receive low scores, while simple filters suchas local statistics or median filtering are to bepreferred. Other recent studies such as [2] arguethat adaptive anisotropic diffusion filtering as wellas a nonlinear gaussian filtering performs quite wellboth on real ultrasound images and on syntheticimages. The combination of both spatial compound-ing/averaging and nonlinear gaussian filteringscored best in the respective study (see Ref. [2]).In Ref. [8] the authors propose a nonlinear variant ofanisotropic diffusion and demonstrate its usefulness

for real-time ultrasound B-mode image filtering.However, most despeckling methods may confoundspeckle granules with fine anatomical detail, andtherefore filter it out. This occurs even with moreadvanced anisotropic diffusion techniques which arefully automatic (i.e. fixed parameters and fixednumber of diffusion steps). In what follows wepropose an adaptive and interactive method thatallows the medical users gaining more control overthe filtering technique. The medical expert inter-actively and iteratively guides the method towardsobtaining filtered images that respond to particularclinical requirements. An interactive evolutionaryalgorithm (IGA) performs optimization over thecoefficients’ space of a SRAD filter used for denoising[9]. The optimization criterion is a subjective scoregiven by the user expert who evaluates the qualityof a despeckled version of the original input image.The method evolves the coefficients of the SRADfilter (SRAD filter realizations) such as to select,randomly combine and modify filter realizationsthat scored well in the early stages of the algorithm.

2. Speckle reducing anisotropicdiffusion (SRAD) filter

The SRAD filter has been proposed in Ref. [9], and wewill briefly describe the filter in what follows. SRADis based on the Lee filter designed by taking intoaccount the linear speckle noise model and theminimum mean square error design approach. Thefiltered image is Is ¼ Is þ ksðIs � IsÞ with Is the aver-age of pixels intensities within the filter window hsand ks the adaptive filter coefficient defined as: ks ¼1� C2

u=C2s with: C

2u;C

2s two coefficients depending on

the local statistics of the US image. Casting the Leefilter (that proved efficient for ultrasound speckleremoval [9]) into a partial differential equation(PDE) framework, the authors in Ref. [9] proposean anisotropic diffusion version of the Lee filter. Tobe more precise the method is not anisotropic butrather inhomogeneous, nonlinear and isotropic how-ever for short we prefer the term ‘‘anisotropicdiffusion’’ the same adopted in the seminal work

Conclusions: The method presented allows the medical expert to design its ownfilters according to the degree of medical expertise as well as to particular and oftensubjective assessment criteria. A filter is designed for a given class of ultrasoundimages and for a givenmedical expert whowill later use the respective filter in clinicalpractice. The process of designing a filter is simple and employs an interactivevisualization and scoring stage that does not require image processing knowledge.Results show that filters tailored using the presented method achieve better qualityscores than other more generic speckle filtering techniques.# 2008 Elsevier B.V. All rights reserved.

at

Se

c

dtdf

afibnspEU

aSitfifttblupmSuutt

Ultrasound images by adaptation of SRAD filter 225

[10] for a nonlinear diffusion technique which is notactually anisotropic. SRAD filter better preservesand enhances edges in the ultrasound image whileefficiently removing speckle in homogeneousregions. Given an intensity (input) image havingfinite power and no zero values over the imagesupport denoted as V the output or image under-goes a process of iterative change of pixels valuesaccording to the filter’s PDE which is

@Iðu; v; tÞ@t

¼ div½cðqÞrIðu; v; tÞ�

Iðu; v; 0Þ ¼ I0ðu; vÞ;@Iðu; v; tÞ

@~h

� ��@V

¼ 0

8>><>>:

(1)

with Iðu; v; tÞ the intensity image evaluated at posi-tions u, v, at time t (the initial image at t = 0 beingthe input image I0ðu; vÞ); @V denotes the border ofthe image support V, while~h is the outer normal to@V; div[�] is the divergence operator while r is thegradient operator; c(q) in Eq. (1) represents thediffusion coefficient defined as [9]:

cðqÞ ¼ 1

1þ ð½q2ðu; v; tÞ � q20ðtÞ�=½q2

0ðtÞð1þ q20ðtÞÞ�Þ

(2)

In Eq. (2) qðu; v; tÞ is a function of the image normal-ized gradient magnitude 5Ij/I and the normalizedLaplacian 52Ij/I defined in relation with the adap-tive coefficient of the Lee filter (see Ref. [9]). Theauthors in Ref. [9] call qðu; v; tÞ the instantaneouscoefficient of variation and define it as:

qðu; v; tÞ ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið1=2ÞðjrIj=I2Þ � ð1=42Þðjr2Ij=IÞ2

½1þ ð1=4Þðr2I=IÞ�2

vuut (3)

In Eq. (2) q0(t) represents the speckle scale func-tion computed in a homogeneous area inside theimage:

q0ðtÞ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffivar½zðtÞ�

pzðtÞ

(4)

where var[z(t)] and zðtÞ are the intensity varianceandmean over a homogeneous area inside the imageat time t, respectively. Because computation ofq0(t) using Eq. (4) is difficult due to the automaticselection of a homogeneous area in the image, theauthors in Ref. [9] derive an approximation of thespeckle scale function as

q0ðtÞ � q0 exp½�rt� (5)

with q0 and r two positive parameters less than orequal to 1. In order to be solved numerically, thecontinuous differential equation in (1) defining SRADhas to be put in discrete form and this is done in Ref.[9] by using an iterative Jacobi method.

The discrete version of the diffusion Eq. (1) ispplied iteratively for a fixed number of iterations

max, which is a parameter of SRAD.So far we have described the original definition of

RAD [9]. Moreover, we can put Eq. (2) in thequivalent form

ðqÞ ¼ q20ðtÞð1þ q2

0ðtÞÞq2ðu; v; tÞ þ q4

0ðtÞ(6)

From Eqs. (6) and (1) instability appears when theenominator of (6) approaches 0 much faster thanhe numerator. This will be taken into account wheneveloping the adaptive version of SRAD in theollowing.Because SRAD has been designed taking into

ccount the speckle statistics (through the Leelter on which is based) it is expected to performetter than a generic anisotropic diffusion tech-ique on US images. Recent studies such as [11]how that when comparing to advanced anisotro-ic filters such as variants of the Coherencenhancing Diffusion, performs better on clinicalS images.To improve contrast in the filtered image we

dded a final processing step: after performingRAD on the input image the output despeckledmage undergoes a linear contrast stretch [12] suchhat the output image pixel intensities occupy theull dynamic range: 0—255. A tol fraction of themage pixels are saturated (saturation of equalractions at low and high pixel values), whereol is a parameter to be adapted by IGA. That is,he image histogram is taken and the top as well asottom tol% pixels corresponding to the upper andower tail, respectively, are identified. Next, thepper threshold is the minimum of the upper tol%ixel intensities, while the lower threshold is theaximum of the lower tol% pixel intensities.aturation means that all pixel values above thepper threshold are given the intensity of thepper threshold, while pixels below the lowerhreshold are given the intensity of the lowerhreshold.

3. Interactive genetic algorithm (IGA)

3.1. Genetic algorithms

Genetic algorithms (GAs) are population-based, sto-chastic search and optimization methods inspired bythe natural evolution process [13]. A GA employs apopulation (or set) P of individuals xi (‘‘chromo-somes’’) and evolves this population through theapplication of stochastic variation and selectionoperators. A population P with its corresponding


chromosomes xi (viewed as potential solutions tothe optimization problem) is defined as

P ¼ fxiji ¼ 1; 2; . . . ;Ng and

xi ¼ ðxi1; . . . ; xilÞ; xi j 2 ½vlb j; vub j� �R;

8 i2f1; . . . ;Ng; 8 j2f1; . . . ; lg(7)

where xi is a vector of l genes xij; vlbj and vubjrepresent the lower and upper bound, respectively,of the genes’ values. Each chromosome xi bears anutility score F(xi) called ‘‘fitness’’ in direct relation-ship with the optimization criterion. It is expectedthat by repeated application of stochastic operatorsthat are selection of the best chromosomes andvariation operators called crossover and mutationto the whole population, the algorithm evolves suchas the average fitness of the chromosomes increases(if the problem is one of maximization). The finalpopulations contain the optimal or near optimalsolutions. Fig. 1 depicts the pseudocode of theGA. In the first generation (t = 0) each xij is initi-alized as a sample from a uniform distributionbetween imposed fixed lower and upper boundsU([vlbj, vubj]). The termination criterion of thealgorithm (Line 4 in Fig. 1) is the expiration ofthe maximum number of generations the GA is letto run (Tmax). The evaluation stage on Line 3 and 4.3in Fig. 1 consists of the calculation of F(xi) for alli 2 {1, . . ., N} and all t 2 {1, . . ., Tmax}. The fitnessevaluation will be described in greater detail inSection 3.3.

3.2. Chromosome coding

Each chromosome xi is a vector of 4 genes (i.e. l = 4in Eq. (7)) in a one-to-one correspondence to the 4parameters that are to be adapted: q0, r (seeEq. (5)), tmax (i.e. the maximum number of itera-tions of the anisotropic diffusion, see Section 2),and tol (see Section 2). Tmax should take onlyinteger values, therefore when evaluating thechromosome we perform a round off of the respec-tive gene. Thus, one chromosome xi represents afilter realization.

Figure 1 Pseudocode of the GA.

3.3. Fitness evaluation

Each chromosome xi in the population should bear afitness value indicating how well the filter employ-ing the respective set of parameters (xi) manages toremove speckle and meets the clinical requirementsof the human interpreter who makes the visualassessment of the filtered image. Accordingly, fit-ness evaluation consists mainly in subjective eva-luations of despeckled variants of the input image(Line 3 and 4.3 in Fig. 1). A human interpreterevaluates visually the quality of the input imagethat has been filtered using xi and gives a score:xi! F(xi) 2 [0,10]. The IGA works like a parameteradaptation algorithm producing and evolving var-ious filter realizations according to a subjectivequality criterion (see Fig. 3). The main problemwith IGAs is that human—machine interaction mightbecome tedious (e.g. the user undergoes lengthysessions for evaluating all the filtered variants of theinput image during the GA run) [14]. We focus onreducing the number of images the user has toevaluate subjectively without affecting the usercontrol on the process of image evaluation. Eachchromosome xk to be evaluated is placed in a sepa-rate table or ‘‘history of evaluations’’ P, with a zerofitness initially: F(xk) = 0. The entries inP are tuples{xi, F(xi)}. All members of P undergo a clusteringprocedure. Clustering applies to the first elementsin the tuples (xi). Suppose that xk falls within somecluster Q. F(xk) is calculated as the average fitnessof chromosomes in Q excluding xk itself:

FðxkÞ ¼ ½1=ðjQj � 1Þ�XQj

j¼1; j 6¼ k

Fðx jÞ (8)

If Q is a one element cluster then the evaluationof xk is deferred to the human evaluator. In the firstgeneration (t = 0) all chromosomes in the populationare evaluated subjectively. In subsequent genera-tions chromosomes are evaluated subjectively withsome periodicity z (a parameter of the algorithm).The rest of the chromosomes are evaluated usingthe clustering strategy previously described. Theclustering method adopted was agglomerative hier-archical tree clustering and a consistency level j

was used to form the individual clusters from thedendrogram [15]. The parameter t works as a cutofffor the dendrogram the method employs. Cuttingthe dendrogram at a smaller cutoff level usuallyproducesmany clusters with smaller values of incon-sistency [16], where inconsistency is defined overthe computed linkage of the tree. Due to its com-putational simplicity single linkage was used [15].Good fitness estimates in Eq. (8) suggests focusingnot on the number of clusters produced but on their


consistency. Smaller values for t are to be adoptedas this leads to clusters which are consistent (e.g.contain similar individuals).

Next we must not allow for the user to evaluateimages with ‘‘spurious’’ pixels due to instability ofthe diffusion process, as discussed in Eq. (6). Suchimages are visually unacceptable (see Fig. 2)because they present a ‘‘salt & pepper’’-like addi-tional noise. We decide that instability occurs bycounting for how many pixels ðu; vÞ (percentage u ofthe total number of pixels in I) we may consider thatEq. (6) presents singularities, that is: jq2ðu; v; tÞ þq40ðtÞj< e � jq2

0ðtÞð1þ q20ðtÞÞj in (6) with e a given

threshold (parameter of the method). If instabilitywas detected for a given filter realization (i.e. agiven xk) then automatically F(xk) is set to zerowithout showing the result of the filtering on thescreen.

3.4. Selection, crossover and mutation

Selection (Line 4.4 in Fig. 1) is a probabilisticmechanism which chooses the best filter realiza-tions with some probability (Ps–—intrinsic to theselection method adopted) from the current gen-eration and passes them to the next generation. Weemploy a tournament selection scheme [13] due toits constant selection pressure over time (roughlyspeaking, this means that the expected stochasticbehavior of selection remains constant in time) [17].Two individuals are picked up at random from thepopulation with replacement. The individual withthe biggest fitness gets selected, which means thatit is placed into the next generation’s population(i.e. P(t + 1) in Fig. 1). The process is repeated Ntimes to form the entire population P(t + 1). Anelitist replacement of the worst individual in eachgeneration with the previous best individual pre-

Figure 2 Example of a filter realization xk which brings on in(the output is a visual unacceptable image having an additio

vents losing the best individual from the population[18].

The first variation operator (Line 4.1 in Fig. 1) isthe Arithmetic Crossover (AX) defined in Ref. [19]and applied with some probability Pc to pairs of filterrealizations in P. Any pair of chromosomes in P has aprobability Pc (a parameter of the GA) to undergocrossover which randomly combines the chromo-somes (denoted as ‘‘parents’’) using linear combi-nation to yield a new pair of individuals (denoted as‘‘offspring’’). AX proceeds as follows: randomly pairall the population of N real-coded chromosomes;next, for each pair of parents: x p1 ; x p2 withp1; p2 2f1 . . .Ng, choose a sample r1 of a randomlydistributed variable r1 � R1([0,1]) (R1 uniform dis-tribution on [0,1]). Test if r1 < Pc. If negative go tothe next pair and repeat the procedure. If affirma-tive do the following: pick a second sample a of arandomly uniform distributed variable a � A([0,1]),and perform the following linear combination ofparents (seen as real element vectors), to obtainthe offspring:

xo1; j ¼ ax p1; j þ ð1� aÞx p2; j

xo2; j ¼ ax p2; j þ ð1� aÞx p1; j8 j ¼ 1 . . . l (9)

where the offspring are indexed {o1, o2} while theparents are indexed {p1, p2}.

The second variation operator (Line 4.2 in Fig. 1)is the gaussian mutation (GM) [13]. This operatorapplies to all individuals in P with some probabilityPm (a parameter of the GA). Each gene xkj in P has aprobability Pm to be mutated that is to change itsvalue according to a normal distribution centered onxkj. We propose a variation from the standard defi-nition of GM, as follows: for each gene in thepopulation xik (at the genes’ level, the populationmay be seen as a gene pool) a sample u is pickedfrom a uniform distribution: u � U([0,1]). If u � Pm

stability in the diffusion equations defining the SRAD filternal salt & pepper noise).


mutate respective gene. Otherwise, go to next genein the gene pool. The actual mutation is performedas follows: a parental gene pxkj is substituted by anoffspring gene oxkj:oxk j ¼ pxk j

þminð½ pxk j � vlb j�; ½vub j � pxk j�Þ3

& (10)

with � N(0,1) a sample from a normal distribution(mean:m = 0, standard deviation s = 1). Themuta-tion in Eq. (10) requires that offspring genes becontained in the interval [vlbj, vubj], where as before(see Eq. (7)), vlbj and vubj stand for the lower andupper bounds of the xkj genes’ values, respectively.We first assume that values 3 skj (3 standard devia-tions) away from the mean are not frequent for agaussian distribution with a skj standard deviation[20]. The random variable oxkj =

pxkj + (Dkj/3) ,Dkj 0 is distributed according to a gaussian distri-bution centred on the mean pxkj and having a stan-dard deviation of (Dkj/3)s = (Dkj/3). Taking intoaccount the previous assumption the lowest andhighest values the random variable oxkj can takeare ox

ð�Þk j ¼ pxk j � 3ðDk j=3Þ 1 ¼ pxk j �Dk j and

oxðþÞk j ¼ pxk j þ 3ðDk j=3Þ 1 ¼ pxk j þDk j, respec-

tively. Thus, we should have that½oxð�Þk j ;

oxðþÞk j � � ½vlbk j; vubk j� which implies that Dkj

be taken as: Dk j ¼ minð½ pxk j � vlbj�; ½vub j � pxk j�Þ.This concludes the explanation on the rationalebehind the mutation mechanism in Eq. (10).

3.5. Summary of evolutionary specklereducing anisotropic diffusion filter(EVOSRAD)

The algorithm we propose in this paper is calledEVOSRAD and it consists mainly of a SRAD filtercoupled with a simple contrast enhancement

Figure 3 Summary of t

mechanism (Fig. 3), the parameters of the filteringstrategy being optimized according to the subjec-tive criterion of the physician through a parameteradaptation algorithm. The latter is implementedwith an IGA which combines (through crossover)and modifies (through crossover and mutation) filterrealizations, while pruning these filter realizationswith a selection process. By running EVOSRAD on agiven input US image, themedical expert after a fewiterations is able to produce a filtered image (andthe corresponding filter realization) which suits his/her particular needs in clinical analysis. After run-ning EVOSRAD the medical expert will use therespective fine-tuned filter on other US images,pertaining to the same class of images as the imageon which the filter was built. Thus, the physicianmay create his/her own filters for different classesof US images, and later employ them in clinicalpractice.

4. Results

4.1. Experimental setup

The experimental setup comprises three sections.The first section investigates the results obtainedwith EVOSRAD in comparison to other filteringstrategies, on several OB/GYN ultrasound images.The second section examines the capability ofEVOSRAD to ‘‘generalize’’, that is how does a filterbuilt (or trained) on a particular input image per-form on a different image (test image) from thesame class as the training image. The third partcomputes the true quality measures employedbefore, from a more sound perspective, that iscomparing the filtered image with the ‘‘ideal’’one, which in practice is unknown, by using a

he EVOSRAD strategy.


Table 1 EVOSRAD parameters

Parameters Value Genes’ bounds Value

N 10 vlb(q0) 0Tmax 5 vub(q0) 1Pc 0.8 vlb(r) 0Pm 0.05 vub(r) 1z 6 vlb(tmax) 1j 0.75 vub(tmax) 5u [%] 0.01 vlb(tol) 0e 0.001 vub(tol) 0.15

1 The term ‘‘SRAD filter realization’’ actually refers to the filterrealization comprising SRAD + the contrast enhancement step asdescribed in Sections 2 and 3.5.

synthetic US image generated from a phantomimage of a foetus.

Table 1 summarizes all parameter’s values of thefiltering method. The parameters values related toGA have been selected after extensive experimen-tation: the smallest value of the population sizethat still assures a good exploration of the searchspace was found to be N = 10, 5 generations(Tmax = 5) were found to be sufficient to reach agood solution, a higher mutation rate (Pm) wasused in order to combat loss of diversity in smallpopulations, while good mixing of genetic materialwas assured by a crossover rate (Pc) close to 1. Asmall inconsistency value j was used as explainedin Section 3.3. For the SRAD filter we took amaximum number of 5 diffusion steps (tmax = 5)with a sufficiently small time step size ofDt = 0.08, as we noticed that letting the diffusionprocess evolve for more steps produced a negativefiltering-out of important small details in theimages. The OB/GYN images were acquired usinga General ElectricTM Voluson Pro 730 ultrasoundequipment. The probes used were RAB 4—8L(4—8 MHz Convex, Realtime 4D transducer), andRIC 5—9H (5—9 MHz Intracavity, Realtime 4Dtransducer).

Images filtered with EVOSRAD are compared toimages produced by the offset filter [21], anisotro-pic diffusion (ANDIFF) with 3 different numbers ofdiffusion steps (tmax) [3], the original SRAD filter [9]with ‘‘standard’’ fixed-parameters: q0 = 0.2 andr = 1 [9] and with 3 different numbers of diffusionsteps (tmax), and themedian filter with a 3 3 pixelswindow [12].

Typically running EVOSRAD consisted in visualisa-tion of around 25—30 filtered versions of the inputimage (outputs of SRAD filter realizations) per giveninput image, thus human—computer interactionmay be considered reasonably small.

The quality of the despeckled images wasassessed using several criteria grouped primarilyin objective quality indicators and in subjectivescores given by the human expert. The objectivequality indicators may be further divided into global

and local quality indicators. The global quality indi-cators are:

� T
he peak signal to noise ratio (PSNR) employed forultrasound images in Ref. [3]. A higher PSNRindicates a higher quality filtered image.
� T
he structural similarity index (SSIN) defined inRef. [22] and employed for ultrasound images inRef. [3]. SSIN 2 (�1, 1), with SSIN!�1 indicat-ing a bad similarity between the original and thedespeckled image, while SSIN! +1 indicating agood similarity.
For mathematical definitions of the previousquality indicators one may check Ref. [3].

Next we have the local quality indicators com-puted in a region of interest (ROI) defined by theexpert as an overlay rectangular area over thewhole image. Examples of such ROIs are given inFig. 4. The local quality indicators are:

� T
he Michelson contrast measure CM [23]. � T he Beghdadi-Le Negrate contrast measure CBN
defined as a measure of visibility of contours [23].

Definitions of both contrast measures may bechecked in Ref. [23].

After visually inspecting the results of applyingEVOSRAD to the input images a subjective score wasrecorded by the expert who has produced therespective SRAD filter realization1. The expertassessed the visual quality of the despeckled imagein comparison to other filtering methods and pro-duced a score for each despeckled image. Thescoring was done on a one-to-five scale (1-low qual-ity, 5-high quality). To avoid adaptation 1 week timelapse has been used between running the EVOSRADalgorithm and the evaluation sessions. When visua-lizing the results, images produced by all filteringmethods were first randomly shuffled and next pre-sented to the human evaluator (e.g. blind evalua-tion).
A) P reliminary experiments on EVOSRAD capability
to remove speckle and enhance OB/GYN USimages. In what follows we present a series ofimages on which EVOSRAD was evaluated incomparison to other despeckling filters. InFig. 4 the input images for the filtering methodsare: image (a) represents the vertebral columnof a foetus. The physician focuses on visualizingthe vertebrae and on correctly assessing varioustypes of malformations such as for example the


Figure 4 Input images: (a) fetal vertebral column–—534 364 pixels, 8 bits/channel, 15.4 cm/29 Hz, RAB 4—8L probe;(b) fetal nuchal fold–—520 407 pixels, 8 bits/channel, 11.8 cm/23 Hz, RAB 4—8L probe; (c) sagittal fetal view–—483 393 pixels, 8 bits/channel, 15.4 cm/29 Hz, RAB 4—8L probe; (d) fetal head–—526 375 pixels, 8 bits/channel,17.2 cm/20 Hz, RAB 4—8L probe; ROI is depicted superimposed over each image.

spina bifida [24,25]. In image (b) the expert isinterested in enhancing the nuchal fold which isan important indicator of Down syndrome infoetuses (nuchal translucency test) [26] image(c) is a sagittal view of the foetus where thephysician’s interest may be placed on severalanatomic indicators such as the head bones(the shape of the nasal bone being also an indi-cator of the Down syndrome [26]), the shape ofthe column, the limbs, etc. image (d) is a fetalhead where the physician is interested in thefetal brain anatomy and the anatomy of thecranium.

B) E
VOSRAD on different classes of OB/GYN images.At this stage we check the results obtained whenthe SRAD filter realization designed with EVOS-RAD for a given input ‘‘training’’ image is appliedto a different ‘‘test’’ image pertaining to thesame class as the ‘‘training’’ image. Both trainingand test images are compared to images pro-duced by the other despeckling filters asdescribed at the beginning of the present sec-tion. Moreover, the quality assessment is doneusing the same objective and subjective qualityindicators as in the previous subsection, with anadditional remark: the human evaluator whoruns EVOSRAD and scores the output image(e.g. the filtered training image) will be theone who later evaluates the filtered test image,
as well. Two classes of OB/GYN US images will beemployed: class (a) represents the axial view of afoetus head, while class (b) is the cervix utericlass of images. Fig. 5 depicts the images usedfor training and testing.

C) E
VOSRAD on a synthetic image of a foetus. Theobjective quality indicators PSNR and SSIN com-pute some kind of difference between twoimages [3] one should be the noise-less ‘‘ideal’’ultrasound image the other should be the filteredversion of the real image (the ideal image cor-rupted by noise). However, in practice we do notknow the ‘‘ideal’’ image, as we only posses thereal noise-corrupted version of the image. Someauthors (see for example [3]) approximate thedifference by taking it between the input image(real ultrasound image, noise-corrupted) and thefiltered image. This computation can only give anindication that the filtering method does notchange much the structure of the input image.This approach is however incorrect as for exam-ple an input—output system which does notactually perform any filtering (e.g. leaves theinput image unchanged) will receive the highestvalue for the objective quality measures. In Ref.[27] the authors try to estimate the ‘‘ideal’’image from the US real image by performing alearning vector quantization (LVQ) segmentationof the real image. However, this approach is


Figure 5 Input images for two classes: (e) fetal head for training EVOSRAD–—382 324 pixels, 8 bits/channel, 15.4 cm/21 Hz, CrossXBeam spatial compounding, RAB 4—8L probe; (f) fetal head for testing EVOSRAD–—405 312 pixels, 8 bits/channel, 15.4 cm/21 Hz, CrossXBeam spatial compounding, RAB 4—8L probe; (g) cervix uteri for training EVOSRAD–—470 364 pixels, 8 bits/channel, 6.5 cm/24 Hz, RIC 5—9H probe; (d) cervix uteri for testing EVOSRAD–—398 389 pixels,8 bits/channel, 6.5 cm/24 Hz, RIC 5—9H probe; ROI is depicted superimposed over each image.

unpractical due to the fact that it yields poorestimates of the ideal image for more complexUS images. One sounder solution is to first simu-late an ultrasound image from an ideal andknown phantom image, next filter the simulatedimage and compute the objective quality mea-sures over the ideal image and the filtered ver-sion of the simulated image [9]. We take thesame approach here, by simulating a foetus USimage. The program used to simulate the B-modeUS image is Field II (see details regarding theprogram in Ref. [28]), and the phantom image isthat of an approximately 12—14 weeks foetus(see Fig. 6). Field II is capable of simulatingultrasound imaging using linear acoustics andsummed spatial impulse responses. Field II pro-poses a point scatterer approach for simulation.It approximates the medium as filled with ele-mentary objects distributed randomly fromwhich ultrasound deflects and disperses, i.e.‘‘scatters’’. The contributions of the spatialimpulse responses at each scatterer are thussummed to form the simulated image. TheseUS reflective points emulate the real tissue scat-ters in the body insonified by the US transducer. A

convex probe similar to the real abdominal con-vex probe used to capture most of the real USimages in this study (i.e. RAB 4—8L) has beensimulated. The probe has a central frequency of5 MHz, 128 physical elements and captures a45.478 image sector from the phantom imagebuilt with 200,000 scatterers distributed accord-ing to a gaussian distribution. The initial imagethe simulator generates is depicted in Fig. 6 (thesecond image on the first row). To produce arealistic US image as generated by a convexprobe a further geometric correction step wasrequired followed by a linear interpolation to fillthe gaps which appear after geometric correc-tion. The corrected image is depicted in Fig. 6(third image on the second row). Next, we cropthe phantom image (‘‘ideal’’ image) and thesynthetic US image around a ROI. For a betteralignment between these two images we per-form an affine registration [29] to the US image.Thus we obtain an improved spatial correspon-dence between the synthetic image and thephantom image. The final images employed forthe calculation of the PSNR and the SSIN are theideal image labelled as (a) in Fig. 6 and the


Figure 6 From left to right, top to bottom: initial phantom image (‘‘ideal’’); point scatterers in the synthetic phantom;simulated US image; simulated US image + geometric correction; phantom image cropped around a ROI; simulated USimage + geometric correction and affine registration; corrected US image cropped around the same ROI as the phantomimage; QI1 and QI2 computed on images marked as: (a) the ideal image and (b) the synthetic ultrasound image.

filtered ultrasound image, where the filter isapplied to the US image labelled as (b) in Fig. 6.

4.2. Main experimental results

4.2.1. Case AFor the input images in Fig. 4 results are given inFig. 7(a) and (b) and in Table 2. Three experts leadedby the first co-author where involved both in runningEVOSRAD on the input images as well as in validatingthe respective results and in evaluating the finaloutput images obtained with EVOSRAD and all otherdespeckling methods. We clarify the procedure ofrunning EVOSRAD and performing the final subjec-tive evaluation of the methods with an exampletaken from Table 2 and Fig. 7. For image (a) inFig. 4 the first expert E1 runs the interactive EVOS-

RAD method and produces an output image (alongwith the associated filter realization) which is thesecond image on the first row in Fig. 7(a). Next,after a time lapse discussed in Subsection 4.1 (A) thesame expert E1 evaluates the output image andgives it a subjective score (i.e. 4 in Table 2). More-over, he gives a subjective score to the output of thefiltering methods involved in comparison. For exam-ple, the offset filter yields an image that is scored 1by the expert E1. The second and third expert (E2,E3) do the same with image (a) in Fig. 4 producingwith EVOSRAD different output images according totheir particular analysis criteria. One may note fromTable 2 that as we employ 3 experts to run EVOSRADon each given input image, there will be a triplet ofoutput filtered images (one corresponding to eachexpert), and thus we will have 3 values foreach quality indicators (both objective as well as


subjective indicators). It is apparent that eachexpert produces a different image each with adistinct quality indicator value. From Table 2 thebest values of the quality indicators are registeredmore often for the case of A1 (EVOSRAD outputimage), with several exceptions: in the case ofimage (a) the highest QI1 is for the output imageof A6–—SRAD (tmax = 3), while EVOSRAD obtains goodvalues of the PSNR in two cases (output images in thecase of experts E1 and E2). QI4 is highest in the case

Figure 7 (a) Results for images (a)—(b) in Subsection 4.1 (AEVOSRAD by E1, EVOSRAD by E2, EVOSRAD by E3, offset filterSRAD (tmax = 3), SRAD (tmax = 5), SRAD (tmax = 10), median filteleft to right, top to bottom: original/input image, EVOSRAD b(tmax = 3), ANDIFF (tmax = 5), ANDIFF (tmax = 10), SRAD (tmax =

of A2 followed closely by A1 (EVOSRAD). In this caseQI4 does not correlate well with the subjectiveassessment of the quality as it might be seen fromTable 2 and Fig. 7(a) all experts agree that A2 doesnot yield acceptable results. In the case of image (b)the best QI1 and QI2 values are obtained by A6 whileA1 produces acceptable values. In the case of image(c) the best QI1 and QI4 values are obtained by the A9

filter, but again this does not correlate with thepoor visual (subjective) assessment scoring for the

): from left to right, top to bottom: original/input image,, ANDIFF (tmax = 3), ANDIFF (tmax = 5), ANDIFF (tmax = 10),r. (b) Results for images (c)—(d) in Subsection 4.1 (A): fromy E1, EVOSRAD by E2, EVOSRAD by E3, offset filter, ANDIFF3), SRAD (tmax = 5), SRAD (tmax = 10), median filter.


Figure 7. (Continued ).

median filter. The objective quality indicators showa general good behaviour of EVOSRAD when com-pared to the other filtering methods, while thesubjective quality indicators clearly indicate thatEVOSRAD is the best filtering method adapted to theparticular analysis criteria, expertise, and subjec-tivity of the each human evaluator.

4.2.2. Case BFor the images in Fig. 5 the first co-author ran theEVOSRAD method and did the subjective scoring onthe result image. Moreover, he did a subjectivescoring of the result images when applying the filter

realizations discovered through EVOSRAD on the‘‘training’’ images (images on first column inFig. 5) to the ‘‘test’’ images (images on secondcolumn in Fig. 5). For example, the medical experttakes the filter (obtained after running EVOSRAD)which produced the second image on the first row inFig. 8(a) and applies it to the first image on thefourth row in Fig. 8(a), the result being the secondimage on the fourth row in Fig. 8(a). Table 3 givesthe quality assessment of both the filtered trainingimages as well as the filtered test images.

From Table 3 the best values of the quality indi-cators are registered more often for the case of A1


Table 2 Quality assessment for images (a)—(d); objective assessment indicators and subjective assessment by 3independent experts E1—3; algorithms employed: A1: EVOSRAD, A2: offset, A3: ANDIFF (tmax = 3), A4: ANDIFF(tmax = 5), A5: ANDIFF (tmax = 10), A6: SRAD (tmax = 3), A7: SRAD (tmax = 5), A8: SRAD (tmax = 10), A9: median; objectiveglobal quality indicators: QI1: PSNR [dB], QI2: SSIN; objective local quality indicators QI3: CM 100, QI4: CBN 100;subjective quality indicator QI5: Score (best values in boldface)

A1 A2 A3 A4 A5 A6 A7 A8 A9

(a) E1/E2/E3QI1 21.76/17.75/21.540 19.10 24.01 22.50 20.63 26.17 22.22 18.29 25.58QI2 0.846/0.841/0.944 0.476 0.763 0.672 0.544 0.825 0.664 0.422 0.836QI3 99.218/99.218/99.218 99.215 99.218 99.218 99.209 99.218 99.205 99.218 99.218QI4 5.981/6.134/6.861 7.145 4.484 4.070 3.025 5.346 4.025 3.221 6.285QI5 4/2/3 1/1/1 2/1/2 2/2/2 1/1/1 2/2/1 2/1/1 1/1/1 1/2/2

(b) E1/E2/E3QI1 25.81/27.64/29.39 25.36 30.53 29.30 27.54 36.87 30.31 24.99 30.48QI2 0.739/0.754/0.849 0.754 0.964 0.940 0.881 0.979 0.927 0.764 0.975QI3 99.218/99.218/99.218 99.209 99.218 99.215 99.206 99.215 99.218 99.218 99.218QI4 9.490/10.323/9.692 10.317 9.095 6.799 4.678 9.867 9.293 9.095 9.967QI5 3/3/2 1/1/1 2/2/1 1/2/1 1/1/1 1/2/2 1/2/1 1/1/1 1/1/2

(c) E1/E2/E3QI1 23.20/24.34/22.63 19.53 26.6 24.64 22.17 28.29 24.01 19.30 29.30QI2 0.928/0.935/0.926 0.545 0.851 0.780 0.668 0.923 0.801 0.603 0.904QI3 99.218/99.218/99.218 98.419 98.443 98.437 98.406 98.437 99.196 99.218 98.44QI4 11.499/11.586/11.509 12.319 8.655 7.279 5.537 10.076 8.483 10.924 13.68QI5 5/4/4 1/1/1 3/2/3 2/2/2 1/2/1 4/3/4 3/2/3 1/2/1 1/2/3

(d) E1/E2/E3QI1 23.92/27.56/20.22 17.971 20.86 20.23 19.22 22.88 21.17 17.991 22.168QI2 0.955/0.878/0.916 0.553 0.892 0.841 0.752 0.944 0.845 0.617 0.920QI3 99.218/99.218/99.218 64.575 67.765 66.300 64.444 90.243 87.351 99.218 71.71QI4 5.131/4.403/4.961 5.117 3.080 2.545 1.887 3.729 2.868 2.237 4.228QI5 4/4/3 1/1/1 3/3/3 2/2/1 1/2/1 3/3/3 2/1/2 1/1/1 2/1/2

(EVOSRAD output image) with several exceptionswhere A6 comes first in terms of the QI1, QI2 andQI3 values for several input images, as well as for theA9 which yields the best QI1 value followed closelyby A6 and A1. The point here is that both on thetraining images and more importantly on the testimages EVOSRAD outperforms in most cases theother filters, and this is supported by both objectiveand subjective quality metrics.

4.2.3. Case CFor the synthetic image the first co-author per-formed the visual assessment (subjective scores)and ran EVOSRAD. From Table 4 and Fig. 9 the bestsubjective score was attained by A1 (EVOSRAD)while the same method obtains good objectivequality values. It is important to notice that thedifferences between methods are rather small andthe fact that EVOSRAD outperforms the fixed para-meters (non-adaptive) versions of SRAD in terms ofQI1. Moreover, taking into account the same indi-cator QI1 it seems that basic anisotropic diffusionvariants outperform the more advanced SRAD stra-tegies. A possible explanation comes from the fact

that QI1 (PSNR) is a global indicator that does notcapture information regarding edge-preservation inthe output image (e.g. edges being fundamentalinformation in medical images). From Fig. 9 thebasic anisotropic diffusion clearly blurs more theedges as compared to the SRAD variants, but thisdrawback is not captured in the final global PSNRvalue which weights more the capacity of the ani-sotropic diffusion to blur the inter-edge tissue indetriment of edge-preservation. The point here isthat the percent difference between the PSNRvalues on EVOSRAD output images and other des-peckle filter outputs diminishes when taking thePSNR between the ideal image and the filter image,as compared to the approximate case when onecomputes the PSNR between the filtered and theunfiltered image. Here, percent differencebetween two positive quantities x1 and x2 is definedas: %Diff = (jx1 � x2j)/(0.5 (x1 + x2)) 100. Fromthe results presented before, themaximumpercentdifference of the PSNR is obtained between theoutput of EVOSRAD on image ( f) from class (a)(PSNR = 22.51 dB) and the output of SRAD (tmax = 3)on the same input image with a PSNR = 34.37 dB


Figure8 (a) Results for class (a) and images (e)—(f) in Subsection 4.1 (B) from left to right, top to bottom: first three rows:original/input EVOSRAD training image (e), EVOSRAD output, offset filter, ANDIFF (tmax = 3), ANDIFF (tmax = 5), ANDIFF(tmax = 10), SRAD (tmax = 3), SRAD (tmax = 5), SRAD (tmax = 10), median filter; remaining three rows: original/input EVOSRADtest image (f), output when filtering image (f) with the SRADfilter realization obtained from training EVOSRAD on image (e),offsetfilter,ANDIFF(tmax = 3),ANDIFF(tmax = 5),ANDIFF(tmax = 10),SRAD(tmax = 3),SRAD(tmax = 5),SRAD(tmax = 10),medianfilter.Filterrealization:(q0,r,tmax,tol) = (0.82,0.49,2,0.03).(b)Resultsforclass(b)andimages(g)—(h) inSubsection4.1(B)from left to right, top to bottom: first three rows: original/input EVOSRAD training image (g), EVOSRAD output, offset filter,ANDIFF (tmax = 3), ANDIFF (tmax = 5), ANDIFF (tmax = 10), SRAD (tmax = 3), SRAD (tmax = 5), SRAD (tmax = 10), median filter;remaining three rows: original/inputEVOSRADtest image (h), outputwhenfiltering image (h)with theSRADfilter realizationobtained from training EVOSRAD on image (g), offset filter, ANDIFF (tmax = 3), ANDIFF (tmax = 5), ANDIFF (tmax = 10), SRAD(tmax = 3), SRAD (tmax = 5), SRAD (tmax = 10), median filter. Filter realization: (q0, r, tmax, tol) = (0.87, 0.12, 2, 0.03).


Figure 8. (Continued ).

(see Table 3). This difference is thereforeDiff = 41.70%.

From Table 4, the percent difference betweenthe PSNR computed on the EVOSRAD output(PSNR = 8.880 dB) and the best PSNR value for thefiltered output of the simulated US image

(PSNR = 9.094 in the case of ANDIFF (tmax = 10))gives a difference of 2.38%, more than one orderof magnitude lower than the same difference whenthe PSNR is computed between the filtered and theunfiltered image. For the SSIN the maximum percentdifference is registered for the case of EVOSRAD


Table 3 Quality assessment for images (e), (f), pertaining to class (a), and for images (g), (h), pertaining to class (b);algorithms employed: A1: EVOSRAD, A2: offset, A3: ANDIFF (tmax = 3), A4: ANDIFF (tmax = 5), A5: ANDIFF (tmax = 10), A6:SRAD (tmax = 3), A7: SRAD (tmax = 5), A8: SRAD (tmax = 10), A9: median; objective global quality indicators: QI1: PSNR[dB], QI2: SSIN; objective local quality indicators QI3: CM 100, QI4: CBN 100; subjective quality indicator QI5: Score(best values in boldface)

A1 A2 A3 A4 A5 A6 A7 A8 A9

(e) Train class (a)QI1 25.36 18.91 24.91 23.45 21.91 30.94 26.68 22.06 25.56QI2 0.929 0.572 0.874 0.815 0.724 0.920 0.839 0.666 0.925QI3 99.218 82.481 85.401 84 82.417 96.124 94.531 99.218 86.813QI4 8.882 6.925 4.553 3.787 2.815 5.402 4.296 3.603 6.352QI5 4 1 3 2 2 3 3 2 2

(f) Test class (a)QI1 22.51 20.90 24.62 23.34 21.91 34.37 28.89 25.07 26.17QI2 0.921 0.675 0.9193 0.870 0.780 0.968 0.918 0.826 0.947QI3 99.218 96.412 97.391 97.368 96.380 98.425 99.187 99.218 98.443QI4 18.115 14.938 11.09 9.431 7.087 12.669 11.293 10.292 14.336QI5 3 1 2 2 1 2 2 1 2

(g) Train class (b)QI1 24.98 19.93 23.50 22.12 20.76 25.24 21.65 18.56 25.45QI2 0.933 0.450 0.740 0.630 0.477 0.839 0.572 0.289 0.830QI3 90.298 86.029 88.191 86.766 85.239 99.218 99.218 99.218 98.44QI4 3.709 3.930 2.681 2.170 1.548 2.999 1.999 1.309 3.748QI5 3 1 2 3 2 3 2 1 2

(h) Test class (b)QI1 16.70 18.95 21.57 20.50 19.408 24.17 20.73 18.18 22.50QI2 0.881 0.357 0.615 0.497 0.358 0.793 0.490 0.226 0.715QI3 99.218 73.333 75.969 74.319 72.549 99.177 99.218 99.218 82.795QI4 5.998 3.656 2.727 2.114 1.418 3.407 2.110 1.755 4.088QI5 3 1 2 1 1 2 1 1 1

(SSIN = 0.739) against SRAD (tmax = 3) —SSIN = 0.979, see Table 2, and amounts to 27.93%while in the case of the synthetic image the max-imum percent difference registered between theoutput of EVOSRAD (SSIN = 0.146) and the output ofSRAD (tmax = 10) — SSIN = 0.163, see Table 4,amounts to 11.00%, again lower than the similarpercent difference computed when SSIN is takenbetween the filtered and unfiltered image. Eventhough the PSNR and SSIN may still be consideredas lacking sheer accuracy for ranking the filters’results, when computing the indicators betweenthe ideal image and the filtered image, the differ-ences in values obtained for methods which producevisually acceptable results are not as pronounced as

Table 4 Quality assessment for the synthetic US image of a fANDIFF (tmax = 3), A4: ANDIFF (tmax = 5), A5: ANDIFF (tmax =(tmax = 10), A9: median; objective global quality indicators: QQI5: Score (best values in boldface)

Synthetic A1 A2 A3 A4

QI1 8.880 8.809 8.918 9.007QI2 0.146 0.154 0.131 0.145QI5 4 1 2 2

in the case of computing the respective indicatorsbetween the filtered and the unfiltered images.Moreover, such values of the PSNR and SSIN correlatebetter with the subjective assessments (scores) ofthe human evaluators.

4.3. SRAD parameter sensitivity analysisand genetic algorithm convergenceanalysis

We perform a brief experimental analysis regardingthe influence of EVOSRAD parameters on the finalappearance of the filtered image. The influence ofthe tol parameter (see Section 2) on the contrast ofthe image is clear and will not be discussed here (see

oetus; algorithms employed: A1: EVOSRAD, A2: offset, A3:10), A6: SRAD (tmax = 3), A7: SRAD (tmax = 5), A8: SRADI1: PSNR [dB] and QI2: SSIN; subjective quality indicator

A5 A6 A7 A8 A9

9.094 8.617 8.700 8.684 8.9070.142 0.147 0.155 0.163 0.1331 3 2 1 2


Figure 9 Results for the synthetic image; from left to right, top to bottom: foetus phantom (‘‘ideal’’ image); correctedand registered synthetic US image; US simulated image filtered with: EVOSRAD; offset, ANDIFF (tmax = 3), ANDIFF(tmax = 5), ANDIFF (tmax = 10), SRAD (tmax = 3), SRAD (tmax = 5), SRAD (tmax = 10), and median filter.

Figure 10 Sensitivity analysis for the SRAD parameters on the synthetic foetus image.


Figure 11 Typical GA run on image (e) for 5 + 1 (initial population) generations.

for example [12,30] on methods of contrastenhancement based on thresholding). We consideronly the parameters in SRAD that we take as ‘‘free’’variables that is: q0, r, and, tmax. According to [9]and to experiments presented in this paper theseparameters may take the standard values: (q0, r,tmax) = (1, 0.2, 5). In the sensitivity analysis we letone parameter to vary within ranges indicated inFig. 10 the rest being set to their standard values.We plot the PSNR and the SSIN for the EVOSRADfiltered version of the input image which is thesynthetic image in Figs. 6 and 9.

We obtain the plots (a)—(c) in Fig. 10. Next, we dothe same but letting two parameters vary and weobtain the plots (d)—(f) in Fig. 10. It is apparent bothform 1D and 2D plots in Fig. 10 that each parameterwhen varied contributes to a variation of the globalquality indicators (PSNR and SSIN) that is nonlinear,and quite irregular. This means that it makes senseto include all three parameters of SRAD as freevariables of an optimization problem which appearsto be a multimodal and complex optimization pro-blem suitable to be tackled with a GA.

Next, we present the evolution of the fitnessstatistics over time. We take image (e) to analysehow the population fitness changes in time, howeversimilar conclusions may be derived from any imageused in this study. In Fig. 11 we present the evolutionof the best, worst and average fitness in the upperplot and of the standard deviation of the fitness inthe lower plot, statistics being performed over thepopulation in each generation of the GA. It is clearthat the overall trend is the increase of the popula-

tion fitness in time (upper plot) and a diminishing ofthe fitness standard deviation in time (e.g. thepopulation becomes more homogeneous), whichare signs of convergence of the GA towards goodsolutions, as we deal with maximization (see Ref.[13] for conditions on convergence).

5. Conclusions

This paper introduces an adaptive medical USimage filtering system that ‘‘includes in the loop’’the human expert which is the final beneficiary ofthe despeckled images and of the respective filter.Thus one achieves two kinds of adaptations (e.g.filter tuning): one with respect to the particularanalysis criteria, expertise and subjectivity of thehuman expert and another with respect to parti-cular categories of ultrasound images. Resultspoint out that our proposed-method is robust inthe sense that we obtain good results, comparableand in many cases better than the results obtainedwith diffusion techniques with the best choice ofthe parameters. Nonetheless, such objective qual-ity criteria are quite generic, as they may beapplied to a whole range of different imagingmodalities and image classes without modifica-tions. The price to pay for the generality of theseobjective criteria is the lack of correlations withparticularities of medical ultrasound images, orwith the quality assessment criteria of the medicalexperts, the degree of medical expertise, and theultimate subjectivity present in the clinical


assessment. In addition to these drawbacks whichare true for all objective indicators, the globalindicators such as PSNR and SSIN compute differ-ences between the despeckled image and theinput image. As discussed in Subsection 4.1 (C)this represents only a crude approximation of theactual difference to be taken into accountbetween the reference noise-free image(unknown) and the filtered image. We made useof these indicators here for completeness reasonsas they have been previously employed in otherrecent studies on medical ultrasound images [3].However, we have also included an experimentwhere these computations were carried outbetween an ‘‘ideal’’ and known image and thecorresponding filtered ultrasound image. The realUS image had to be simulated from the idealimage. Subjectively, from Tables 2—4 the pro-posed method always scores best (some ties withother methods occur). There is no perfect filter forall images and clinical criteria and results supportthis assertion as adapted SRAD filter realizationsare different for different images and experts.The method is meant to produce filters that areadapted to each user. As from the preliminaryanalysis in Subsections 4.1 (B) and 4.2 it followsthat a user who produced a filter on a ‘‘training’’image will employ it directly with good results inclinical practice to other images of the same kind.There is no need of re-running EVOSRAD on thenew images. In this preliminary study inter-expertevaluation has been avoided because the methodwas introduced as an adaptive strategy on a per-user basis (that is, a user runs the algorithm, findsthe filter that suits him/her best and next evalu-ates and applies it on images of the same class).For future work we propose studying the tradeoffbetween the adaptability on a per-user basis andobtaining more general filters capable of yieldinggood results on a given class of images with theagreement of various medical experts. This futurestudy may include a machine learning approach inwhich a learning strategy will be first trained usingthe EVOSRAD method on several classes of imagesusing several medical experts. A set of filters willbe generated in this phase, with the respectiveparameters learned taking into account bothintra- and inter-observer variability. Next, in thetest phase new images will be presented themethod being expected to generalize from thetraining phase to yield the best filter parametersfor these test images.

The adaptability of the method to particularclinical criteria, the control the physician has overthe filter obtained through a simple visual evalua-tion interactive process, makes the proposed

method a robust adaptive despeckling tool able todesign filters tailored for particular clinical needs,under direct medical supervision.

Acknowledgments

The authors wish to thank the medical experts withthe High Risk Pregnancy Unit at the ‘‘Hospital Uni-versitario Materno Infantil’’ from Las Palmas de GranCanaria, Spain. This work was supported in part bythe Portuguese Ministry of Science & Technology —‘‘Fundacao para a Ciencia e a Tecnologia’’ throughGrant POCTI — SFRH/BPD/30347/2006, the EU pro-ject FP6-507609 and the Spanish Ministry of Educa-tion under Grant TEC2004-06647-C03-02.

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enhancing obstetric and gynecology ultrasound images by adaptation of the speckle reducing...

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