local features and takagi-sugeno fuzzy logic based medical

RADIOENGINEERING, VOL. 22, NO. 4, DECEMBER 2013 1091

Local Features and Takagi-Sugeno Fuzzy Logic basedMedical Image Segmentation

Umer JAVED1, Muhammad Mohsin RIAZ2, Abdul GHAFOOR2, Tanveer Ahmed CHEEMA1

1School of Engineering and Applied Sciences, Isra University, Islamabad, Pakistan2College of Signals, National University of Sciences and Technology (NUST), Islamabad, Pakistan

[email protected], [email protected], [email protected], [email protected]

Abstract. This paper presents an improved region scalablefitting model that uses fuzzy weighted local features and ac-tive contour model for medical image segmentation. Localvariance is used with local entropy to extract the regionalinformation from the image which is then processed with theTakagi-Sugeno fuzzy system to compute weights. The use ofregional descriptors enables this model to segment the inho-mogeneous intensity images. The proposed objective func-tion is minimized by using level set function. Performanceevaluation of the proposed and existing model is achievedwith the help of a probability rand index, global consistencyerror, the number of iterations and computation time taken.Extensive experiments on a series of real X-ray and MRImedical images shows the proposed technique offers bettersegmentation accuracy in lesser number of iterations andcomputation time.

KeywordsImage segmentation, fuzzy logic, active contours.

1. IntroductionImage segmentation plays a vital role in several medi-

cal image analysis applications, including surgical planningand diagnosis. Numerous techniques have been introducedto achieve efficient and accurate medical image segmenta-tion [1], [2]. Active contours are being extensively used inimage segmentation. Earlier geometric active contours werebuilt on the level sets and curve evolution. The surface evo-lution problem is frequently solved by using level set method[3]-[5]. The initial contour is represented as a zero level setof a higher dimensional level set [3]-[5]. Evolution of thecontour is determined by solving the classic energy mini-mization problem. The basic principle is to evolve a curve,combined with constraints, to select a desired object. Ac-tive contours (for image segmentation) are categorized intoedge-based [6], [7] and region-based [3], [5], [8] methods.

The edge based model uses image gradients to con-struct an edge stoping function that guides the contour to-wards desired object’s boundary. Edge based methods are

generally sensitive to image noise and the weak objectboundaries [3], [9] and [10]. Such models may not workwell in MRI images because of weak boundaries (due to lowcontrast ratio between grey and white matter) [10]. The re-gion based models use region descriptors to guide contoursand do not use image gradients. Therefore these modelsare less sensitive to initial conditions, weak boundaries andnoise [10], [12].

Early region based models assume piecewise homoge-neous intensities [3]-[5]. Such models fail to guide con-tours in intensity inhomogeneous images such as MRI im-ages [12]. A classical active contour model, based on globalinformation of an image, provides good results for imageshaving smooth boundaries. It relies on piecewise homoge-nous intensities in regions [3]. However, its application to-wards MRI image segmentation is very limited because ofcomplicated procedures involved and heterogenous regions[9], [11]. Recently the Region Scalable Fitting (RSF) en-ergy model [9] (based on active contour and the variationallevel set) is used to address inhomogeneous intensities. ThisRSF model utilizes the intensity information of pixels lo-cated in the neighborhood defined by a scalable Gaussiankernel function. The model provides good result, however,it is prone to getting stuck in local minima [13] and is verysensitive to initialization of controlling parameters [11]. Heet al. [13], combined local entropy and RSF model to over-come the above mentioned limitation. However, local en-tropy highlights edge information in the image, whereas in-verse of local entropy can be used as region descriptor. Also,only local entropy is not a sufficient feature for obtainingaccurate and efficient segmentation results in region basedmethods.

A scheme based on image local features (entropy andvariance), in RSF model is proposed for medical image seg-mentation. Local variance is a region descriptor used fortexture analysis [14]. Takagi Sugeno (TS) fuzzy is used toassign higher weights to pixels having less local entropy andvariance, and vice versa. Qualitative and quantitative evalu-ations were carried out on medical image databases. The re-sults show that the proposed scheme gives the improvementof medical image segmentation results in terms of accuracyand efficiency.

1092 U. JAVED, M. M. RIAZ, A. GHAFOOR, T. A. CHEEMA, LOCAL FEATURES AND TAKAGI-SUGENO FUZZY LOGIC BASED . . .

(a) Original image (b) Local entropy image (c) Local variance image (d) Fuzzy combined image

Fig. 1. Different scenarios for evaluating features.

2. PreliminariesHere a brief overview of the existing RSF model [9] is

presented. Let C be a closed contour for the gray scale im-age I in domain Ω (divided into regions Ω1 = inside(C) andΩ2 = outside(C), λ1 and λ2 are positive constants [9], [13].The Gaussian kernel function K(u′,v′) (used to control thesize of a local region), weighted average values f1(u,v) andf2(u,v) (used for an approximation of local image intensitiesin Ω1 and Ω2) are given as [9],

K(u′,v′) =

(1

2πρ2

)exp(−||u′− v′||2

2ρ2

),

f1(u,v) =K(u,v)∗ [Hφ(u,v)I(u,v)]

K(u,v)∗Hφ(u,v),

f2(u,v) =K(u,v)∗ [(1−Hφ(u,v))I(u,v)]

K(u,v)∗ (1−Hφ(u,v))(1)

where m,n,u,v ∈ Ω, u′ = m− u,v′ = n− v, ρ is the stan-dard deviation, Hφ(u,v) is the Heaviside function (used to de-termine the integrals inside and outside regions of contour)and ∗ denotes convolution operator. The smooth approxima-tion of Hφ(u,v) and its derivative δφ(u,v) are

Hφ(u,v) =12

[1+

2π

tan−1(

φ(u,v)ε

)],

δφ(u,v) = H ′φ(u,v) =

ε

π(ε2 +φ2(u,v))(2)

where ε indicates a constant value and φ is the level set func-tion. The local entropy LE(u,v) is

LE(u,v) =−1

u1× v1∑is

p(is) log2 p(is) (3)

where is ∈ [0,1] are intensities in u1× v1 block of an imagecentered at (u,v) pixel and p(is) represents the intensity his-togram.

3. Proposed Fuzzy Active ContourThe weighted RSF model [13] assigns weight in pro-

portion to the local entropy of each pixel. The use of local

entropy as a regional descriptor is not sufficient. A noisy im-age is shown in Fig. 1(a), results after applying local entropyare given in Fig. 1(b). It can be seen that local entropy over-looks the rectangular shaped region in the presence of noise.Results after applying local variance [14], [15] on the noisyimage can be seen in Fig. 1(c). The image shows differentvalues for local entropy and local variance due to presenceof noise. This regional descriptor couldn’t identify the trian-gular region. TS fuzzy logic is used to address this problemby combining the attributes of different features (i.e. localentropy and variance). Fig. 1(d) shows the effect of combin-ing the attributes of local features by using TS fuzzy logic.The local variance LV (u,v) is defined as

LV (u,v)=1

(2u1+1)(2v1+1)

k=u+u1

∑k=u−u1

l=v+v1

∑l=v−v1

(I(k, l)−I(u,v))2

(4)

where I(u,v) is the mean value of u1× v1 window centeredat (u,v) pixel. The modified gradient flow of the proposedscheme is

∂φ(m,n)∂t

= δφ(m,n)

[ηdiv

(∇φ(m,n)|∇φ(m,n)|

)−λ1

∫Ω

K(u′,v′)WEV (u,v)|I(m,n)− f1(u,v)|2dudv

+λ2

∫Ω

K(u′,v′)WEV (u,v)|I(m,n)− f2(u,v)|2dudv]

+µ(

∇φ(m,n)−div(

∇φ(m,n)|∇φ(m,n)|

))(5)

where WEV are the weights calculated by TS fuzzy logic.Note that, for WEV (u,v) = 1 and WEV (u,v) = LE(u,v) thegradient flow in (5) reduces to the gradient flow given in [9]and [13], respectively.

In contrast to the Mamdani inference engine (where theoutput MFs are either linear or constant) [18], TS inferenceprovides the flexibility to adjust output MFs using adaptiveor optimization methods [19].

Let A1, A2 and A3 (represent “High”, “Medium” and“Low” respectively) be defined for LE . The Gaussian MFsare

µA1(x1)=exp

(−(x1− x(1)1

σ(1)1

)2),


(a) 15 Iterations (b) 30 Iterations (c) 60 Iterations (d) 130 Iterations (e) 220 Iterations

(f) 15 Iterations (g) 30 Iterations (h) 60 Iterations (i) 130 Iterations

Fig. 2. Convergence analysis of algorithms (a)-(e) RSF model [9], (f)-(i) Proposed model.

µA2(x1)=exp

(−(x1− x(2)1

σ(2)1

)2)

and

µA3(x1)=exp

(−(x1− x(3)1

σ(3)1

)2).

Similarly, let B1, B2 and B3 (represent “High”, “Medium”and “Low” respectively) be defined for LV . The GaussianMFs are

µB1(x2)=exp

(−(x2− x(1)2

σ(1)2

)2),

µB2(x2)=exp

(−(x2− x(2)2

σ(2)2

)2)

and

µB3(x2)=exp

(−(x2− x(3)2

σ(3)2

)2)

where x1,x2 ∈ [0,1]. The means x(i1)1 , x(i2)2 and vari-ances σ

(i1)1 , σ

(i2)2 (for i1, i2 ∈ 1,2,3) of fuzzy sets are

calculated using K-means algorithm [16]. LE is clusteredinto three classes based on histogram (similar procedure isadopted for LV ). The means and variances of each clusterare used as centers x(i1)1 , x(i2)2 and spreads σ

(i1)1 , σ

(i2)2 of MFs

respectively.

The TS rule base for computing weights is:

IF LE(u,v) is A(i1) AND LV (u,v) is B(i2) THEN

z(i1+i2−1)(u,v)=(

11+e−η1LE (u,v)+e−η2LV (u,v)

)i1+i2−1

where η1 and η2 are constants used to control the contri-bution of LE(u,v) and LV (u,v). Note that when η1 < η2,the effect of LV (u,v) is dominant compared to LE(u,v) onweights (and vice versa). Further note that large i1 + i2 re-duces the output of rule-base (weight) which is desirable.The aggregated weights are

WEV (u,v) =

3

∑i1=1

3

∑i2=1

z(i1+i2−1)tµAi1 (LE),µBi2 (LV )

3

∑i1=1

3

∑i2=1

tµAi1 (LE),µBi2 (LV )(6)

where t represents the intersection operator and is chosenhere as an algebraic product.

4. Results and DiscussionThe results of proposed and existing RSF model are

compared by using the Probability Rand Index (PRI) andGlobal Consistency Error (GCE). This comparison is car-ried out for quantifying the consistency of simulation resultsby taking into account the pairwise label relationship. LetG represent the ground truth image and Gtest be the segmen-tation result. The PRI is defined as


(a) (b) (c) (d)

Fig. 3. Segmentation result for brain MRI (a) original image, (b) local entropy image, (c) local variation image and (d) segmentation by proposedtechnique.

(a) (b) (c) (d)

Fig. 4. Segmentation result for brain MRI (a) original image, (b) local entropy image, (c) local variation image and (d) segmentation by proposedtechnique.

PRI(Gtest ,G)=2

M(M−1)∑a,b[αa,bβa,b +(1−αa,b)(1−βa,b)]

(7)

where a 6= b and M(M−1) denotes the possible unique pixelpairs out of total M data points. αa,b represents the casewhen same labels exist in Gtest and βa,b is the probabilityof having the same labels across G. The function shows thesimilarity between Gtest and G. PRI ∈ [0,1] with 0 and 1representing no similarity and total similarity, respectively.

Another evaluation measure GCE is utilized for eval-uating the consistency between image segmentations. Letξ(Gtest ,ζ) and ξ(G,ζ) be the sets of pixels belonging to seg-ment Gtest and G, respectively. GCE is used to combine thevalues for the entire image in terms of an error measure, andis defined as

GCE(Gtest ,G) =1M

min| ξ(Gtest ,ζ)∩ξ(G,ζ) || ξ(Gtest ,ζ) |

,| ξ(G,ζ)∩ξ(Gtest ,ζ) |

| ξ(G,ζ) |

. (8)

This measure is tolerant of refinement and works forsegmentations being compared with the similar number of

segments. The range of GCE lies in between 0 and 1, where0 indicates perfect image segmentation.

The proposed technique is implemented in Matlab(7.13, Release 2011b) and experiments were carried out on aDell Inspiron, Intel Core i5 CPU, 2.1 GHz Processor, 4 GBram. The results of existing and proposed schemes are an-alyzed on 15 X-ray blood vessels [9], [13] and 86 MRIreal medical images. The accuracy of these results is com-pared with manual segmentation results similar to [22]-[24].MRI datasets contains T1 and T2-weighted brain imagesfrom Harvard Medical School [20] and National Centerfor Biotechnology Information [21]. The parameters usedduring experiments are given in Tab. 1, η is initialized as0.001× (255)2 [9], unless otherwise specified. For imageswhich contain higher intensity inhomogeneities, small ker-nel size is preferable and vice versa.

Parameters λ1 λ2 µ κ ρ ∆t u1×v1Values 1 1 1 2 3 0.1 3×3

Tab. 1. Simulation parameters.

In Fig. 2, the performance comparison of the existingRSF (Fig. 2(a - e)) and proposed scheme (Fig. 2(f - i)) forsegmenting the X-ray blood vessel image is shown. Eachimage has a spatial resolution of 103× 131. The final seg-


(a) (b)

(c)

Fig. 5. PRI and GCE graphs for existing RSF model and proposed technique: (a) PRI distribution of percent images, (b) GCE distribution ofpercent images and (c) PRI and GCE values.

mentation results of the proposed method and weighted RSFmodel are shown in Fig. 2(e) and Fig. 2(i), respectively.Blood vessel boundaries are very weak in most of the im-age. This increases the difficulty of segmenting the vesselfrom the background. The results show that despite weakvessel boundaries in an original image, the proposed schemeprovide faster convergence and gives more accurate segmen-tation results than the existing RSF model [9].

The segmentation result for T1 weighted brain MRI im-age containing a primitive neuroepithelial tumor of 256×256 resolution, is shown in Fig. 3. η is set as 0.04× 2552

whereas λ1 and λ2 are initialized as 1.0 and 2.0, respectively.The output of local entropy and variance is given in Fig. 3(b)and Fig. 3(c), respectively. Medical images have intensityinhomogeneity due to which the segmentation of all the ob-jects becomes a non trivial task. The proposed techniquehas successfully segmented the objects present inside an im-age in 45 iterations, shown in Fig. 3(d). This illustrates theadvantage of the proposed model, its ability to handle weakboundaries, complex background and intensity inhomogene-ity.

A right frontal glioblastoma in T1 weighted brain MRIimage is given in Fig. 4. The output of local entropy andvariance is given in Fig. 4(b) and Fig. 4(c), respectively. InFig. 4(d), the final segmentation of the proposed method isshown. This technique has successfully segmented the ob-jects present inside the image in 55 iterations. This indicates

that by assigning weights, based on LE and LV , the proposedscheme performs accurate segmentation.

For quantitative analysis, the results of the proposedand existing RSF models are shown by using a ProbabilityRand Index (PRI) and Global Consistency Error (GCE) [17].Fig. 5 shows the PRI and GCE graphs for 45 different im-ages. These images belong to the above mentioned reputablemedical image databases. Fig. 5(a) and Fig. 5(b) use percentimages for computing PRI and GCE respectively. Note thatPRI lies between 0.8 and 0.9 for most of the images usingthe proposed technique whereas for existing RSF model, PRIlies between 0.5 and 0.7. The GCE lies between 0.1 and 0.2for most of the images using the proposed technique whereasfor existing RSF model, GCE lies between 0.2 and 0.4. InFig. 5(c), results are plotted for 100 iterations, since pro-posed technique, (in general), successfully segmented theROI within these iterations. Note that soon after 70 itera-tions our proposed technique show no further improvementin PRI and GCE values. This indicates that the algorithm hasreached its desired segmentation result. On the other handRSF model keeps on converging even after 70 iterations. Af-ter several experiments the behavior shows that existing RSFmodel converges to proposed model’s PRI and GCE valuesbut after more iterations.

The average convergence analysis of existing RSF andproposed model, for blood vessel and brain images is givenin Tab. 2. The spatial resolution of all images is also listed.


Techniques Images RSF Proposed

Blood vesselIterations 220 130Computation time 8.58 5.15

BrainIterations 150 85Computation time 34.19 20.37

Tab. 2. Iterations and CPU time (in seconds) by RSF and pro-posed model.

The maximum iteration value for an experiment is achievedwhen the difference between two consecutive PRI samplesis less than an arbitrary number τ. The suitable value of τ

is based upon error tolerance criteria. The value of τ is ini-tialized as 0.05 for experiments. Note that proposed methodconverges to desired result much faster then the existing RSFmodel. Our proposed model also offers lesser number of it-erations than the existing technique. This indicates that as-signing fuzzy weights to local descriptors not only reducesthe computation time but converges faster than the standardRSF model.

5. ConclusionThis paper presents an improved RSF model that uses

fuzzy weighted local features and active contour model formedical image segmentation. Local variance is used withlocal entropy to extract the regional information from theimage which is then processed with the TS fuzzy system tocompute weights. Higher weights are assigned to pixels hav-ing less local entropy and less local variance, and vice versa.The use of regional descriptors enables this model to seg-ment the inhomogeneous intensity images. The proposedobjective function is minimized by using level set function.Several experiments are conducted on real blood vessel andMRI brain images. The extensive experiments show the pro-posed technique offers better PRI and GCE values in lessernumber of iterations and computation time.

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About Authors . . .Umer JAVED received the BS and MS (Electronic Engi-neering) in 2007 and 2009, respectively. He is currently pur-suing PhD in Electronic Engineering from Isra University,Pakistan. His research interests include fuzzy logic, neuralnetworks and evolutionary computing.

Muhammad Mohsin RIAZ has completed PhD (ElectricalEngineering) in 2013 from National University of Sciencesand Technology (NUST), Pakistan. His research interestsinclude signal processing, fuzzy logic, neural networks andevolutionary computing.

Abdul GHAFOOR completed his BE in 1994, MS in 2003

and PhD in 2007. Since 2008, he is with the Departmentof Electrical Engineering, College of Signals, National Uni-versity of Sciences and Technology, Pakistan. His researchinterests include Control, Communication and Signal Pro-cessing. He has contributed over 100 research publicationswhich include 40 papers in well reputed international jour-nals.

Tanveer Ahmed CHEEMA received his PhD (ElectronicEngineering) from Muhammad Ali Jinnah University, Pak-istan in 2005. He is currently Associate Professor in Depart-ment of Electronic Engineering, Isra University, Pakistan.His research interests include image processing, templatematching and neural networks.

local features and takagi-sugeno fuzzy logic based medical

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