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A New Shape-Based Segmentation Approach for the DCE-MRI Kidney Images

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A New Shape-Based Segmentation Approach for the DCE-MRI Kidney Images
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  2007 IEEE International Symposium on Signal Processing and Information Technology A NEW SHAPE-BASED SEGMENTATION APPROACH FOR THE DCE-MRI KIDNEYIMAGES Hossam Abd EL Munim1, Aly A. Farag1, Mohamed Abo El-Ghar2, and Tarek El-Diasty2 1CVIP Laboratory, University of Louisville,Louisville, KY, USA 2The UrologyandNephrology Center, Schoolof Medicine, Mansoura University, Egypt {faraggcvip.uofl.edu} ABSTRACT or underestimation of the extent ofinflammation in theen- Acute rejection is the most common reason of graftfailure tire graft [3]. Therefore, a noninvasive and repeatable tech- after kidney transplantation, and early detection is crucial to nique is notonly helpful but also needed in the diagnosis of survivethe transplanted kidney function. Automatic classi- acuterenal rejection. In DCE-MRI, a contrast agent called fication of normaland acute rejectiontransplants from Dy- Gd-DTPA is injected into the bloodstream, and as it perfuses namic Contrast Enhanced Magnetic Resonance Imaging into the organ, the kidneys are imaged rapidly and repeatedly.  DCEMRI) is considered. The algorithm is based onsegmen- During the perfusion, Gd-DTPA causes a change in the relax-tation to isolate the kidney from the surroundinganatomi- ation times of the tissue and creates a contrast change in the cal structures viaa shape-based segmentation approach us- images. As a result, the patterns of the contrast change gives ing level sets. So the main focus of this paper is the shape functional information, while MRI provides good anatomical based segmentation. Training shapes are collected from dif- information which helps in distinguishing thediseases that ferent real data sets to representthe shape variations. Signed affectdifferent parts of the kidneys. However, even withan distancefunctions are used to representtheseshapes. The imaging technique like DCE-MRI, there are several problemsmethodology incorporate the image information with the shape such as, (i) thespatialresolution of the dynamic MR images prior in a variational framework. The shape registration isis low due to fast scanning, (ii) the images suffer from the mo- considered the backbone of the approach where more gen- tion induced by the patient breathing which necessitatesad- eral transformations can beused to handle the process. Thevanced registration techniques, (iii) the intensity of the kidney perfusion curves that show thetransportation of thecontrast changes non-uniformly as the contrast agent perfuses into the agent into the tissue are obtained fromsegmented kidneys and cortex which complicates the segmentation procedures. To used in the classification of normaland acute rejection trans- thebest of our knowledge, there has been limited work on plants. Applications of the proposed approach yield promis- the dynamic MRI to overcome the problems of registration ing resultsthat would, in the near future, replace the useof and segmentation. For theregistration problem, Gerig et al. current technologies such as nuclear imagingand ultrasonog- [4] proposed,using Hough transform, to register the edges in raphy, which are not specific enough to determine the type of an image to the edges of a mask and Giele et al. [5] intro- kidney dysfunction. duced a phase difference movement detection method tocor- rect for kidney displacements. Both of these studies required Ievel Sets,Enerms- Shape Repreentbuilding a mask manually by drawing the kidney contour on a Level Sets, Energy Minimization. 2DDCE-MRI image,followed by the registration of the time frames tothis mask. Most of these efforts used healthy trans- I. INTRODUCTION plants in the image analysis, and edge detection algorithms were sufficient. However; in thecase of acute rejection pa- In the United States, approximately 12000 renaltransplants tients, the uptakeof the contrast agent is decreased,so edge are performed annually [1], and considering thelimited sup- detection fails in giving connected contours. For this reason, ply ofdonor organs, every effort is made to salvage the trans- we consider the combined usageof gray level and prior shape planted kidney [2]. Currently, the diagnosis of rejection is information to give better results. done via biopsy which has the downside effect of subjecting the patients torisks such as bleeding and infections. More- II. SHAPE MODELING BY LEVEL SETS Over, th1e relatively smal needl-e biopsies may lead to over Shp-ersnaini h ai akonlsso hps ' ~~~~~~~~~~~~~~~The election ofsuch representation is very important in sev- THIS RESEARCH HAS BEEN SUPPORTED IN PART BY THE NSF eral computer vision and medical applications such as regis- GRANT OISE-06 10528 AND THE UNIVERSITY OF LOUISVILLE. tration and segmentation. There are several ways described 978-1 -4244-1 835-0/07/ 25.00 ©C2007 IEEE 1 186  in [6]. Although some of these ways are powerful enough a Gaussian distribution with adaptiveparameters. Expres- to capture local deformations,they require a large number sions for the prior probability and the Gaussian parameters of parameters to deal with important shapedeformations and are found in [9]. have problems withchanging topology. An emerging way to represent shapes can be derived using level sets [7]. This IV. ALIGNMENT OFTHE TRAININGSHAPES representation is invariant to translation and rotation. Given a curve V that represent boundariesof a certain shape, we Let thetraining set consist of a set of training shapes can definethe following level set function 0 to be the mini- V1,...,VN, withsigned distance level set functions defined as mum Euclidean distance between the point X and the shape above , The goal is to calculate the set of pose pa- boundary. It is positive inside, negative outside, and zero on rameters used to jointly align theseshapes, and hence remove the shape boundary. Such representation canaccount for lo- any variations in shape due to pose differences. The objective cal deformations thatare not visiblefor iso-contours that far is to finda set of transformations A1, ..., AN that register an away from the srcinal shape and geometrical features of the evolving mean shape represented by XOM to the given train- shapecan also be derived naturally from this representation. ing shapes respectively. We assume that each transformation has scaling components sx, sy, rotation angle 0 (with a rota- tion matrix defined by R), and translations T = [Tx, Ty]T. SEGMENTATION The scale matrix will be S = diag{sx, sy}. Globalalignment details will come in the following sections. Within the level set formalism [7], the evolving curve is a propagating front embedded as the zero level of a 3D scalar function  (x, y, t). The continuous change of X can be de- scribed by the partialdifferential equation: Given two shapes a and / represented by signed distance functions s, and /a, we need to calculate a transformation &(4X, t) + F VO(X, t) 0  : (1) (A) defined as above to move the first shape to its target. The At signed distance function is invariant to rotation and translation where F is a scalar velocity function depending on the local butunfortunately variant toscaling. Now we are going to geometric properties (local curvature) of the front and theex- formulate a dissimilarity measure to overcome this problem. temal parameters related to the inputdata e.g, image gradient. Assume that the vector distancefunction can be expressed in The function X deforms iteratively according to F,and the terms of its projections in the coordinates directions as d a = position of the 2D front is given at each iteration by solving [dxdy]T at any point in the domain of the shape a. Applying the equation 0(X, t) = 0. The design of the velocity functionaglobal transformation A on the given function X resultsin F plays the major role in the evolutionary process. We have a changeof its distanceprojections as d, SRd,. This chosen the form F   V   K, where v   1 or-I for the vector is directly having a magnitude:   Sdc, which contracting or expanding front respectively, c is a smoothing implies that , . max(s-, sy) , A dissimilarity measure coefficient which is always small with respect to 1, and K is can be directly formulated as r(X) Sdc, (X) - (A) the local curvature of the front. The latter parameter actsas a to measure thedifference between the transformed shape and regularizationterm. its target representation. A natural energy function can be The term (vg = ± 1) in the PDE specifies thedirection formulated by summing up the squared difference betweenof the front propagation either moving inward or outward (g the two representations as follows: is used to refer to the intensity gray level model associated with a function Og which will evolve according to the above E1   X08: r2 dQ (3) PDE). The problem can be reformulated asclassification ofeach point at the evolving front (points of the narrowbandwhere 6' is added to reduce the complexity of the problem region). If the point belongs to the associated object, the frontas shown in [9] where E is the widthparameterof the band expands, otherwise (the background) it contracts. around the shape contour. Itis straightforward to show that The point classification is based on the Bayesian decision the given measure r satisfies the relation: r < (sOb'(X) - [8] at point X. The term (vg) for each point is replaced by the /a (A)) where s = max(sx, sy). Hence another energycan function vg (X) defined as follows: be obtained which is always less than or equal to El: 7 1 Y f -1if woPo(I(X)) ._ wbPb(I(X)) V 'AC)-A )2,7 A 9g X) { +i1 otherwise (2) F =]6d(q5c,q5j) (sqc(X) - q1(A))2dQ (4) where wr is the region prior probability and p(.) is the cor- The above energy functionhas a big advantage since it allows responding probabilitydensity function (pdf) for theobject the use of inhomogeneous scales. Alsoadding theindicator (o) and the background (b). We characterize each region by function 6' makes the comparison limited to a band around the 1187  shapes contours. This is very important to make the perfect where q S1 bi (Ai) represents the transformed signed alignment with almost zero energy when E -+ 0. Then we distance map marked by t. We define w   [wl ... wN]T to be will obtain identical optimization parameters for both E1 and the weighting coefficient vector. By varying these weights, E. Gradient descent is used to handle the optimization to (P can cover all values of the training distance maps and estimate the transformation parameters. Unfortunately, the hence the shape model changes according to all the given function s(sz, sy) = max(sz, sy) is not differentiable at the shapes. In [10], principal component analysis is used to get line (s, = sy). So we use a smeared version of that function eigenshapes and a limited number of them is used to build based on its srcinal definition: the model. The shape variability is restricted to theselected eigen shapes while in the proposedapproach all the training s(sz, sy) = max(sx, sy) = sxH(sx-sy)+b(1-H,(s-sy)) shapes are taken into consideration to enhance the results. (5) Basedon the above formulation, the functionreturns s x if s sy > 0, otherwise it resultsin sy. The smeared heaviside MODELS step function H (defined in [9]) is used to get a smooth transi- tion around the line sx = sy and hence the function is differ- The shape model is fittedto the image volume by means entiable everywhere. The function derivativeswill be directly of registration using a transformation A (defined as before) calculated as follows aS = HE (sx-sy) ± (sY-sy) E (s - registeringtheintensity model Og to the shape model Op. As sy) and as = HE (sy - s) + (sy - sx)& (sy - sm). stated in section IV, the registration is formulated as an energy minimization problem as follows: IV-B. Mean Shape Estimation E(5g, qOp) 6 q5g,qp)r2dQ. (9) Registering the mean shape OM with the shapei repre- Q sented by Xi~ means sjq5M q Xi(Ai) where i - 1..N and sent(dby i as show above So ther transforatn where r =sg   qp(A) is the dissimilarity measure. The par=ameters shou minimize b the n eneg .fu tion: transformation A and the weight vector w should minimize the objective function E: using the gradient descent flow. A N closed form solution for the weight vector is used as shown E(qM, X   qN) Sf 6 (qM, qi)r 2dQ (6) in [1 1]. The shape parameters and the transfornation give the i=l steady state shape as the segmentation results. where ri = siM - i(Ai), is the dissimilarity measure. Rotation and translation do not have any effect on the valueVII. EXPERIMENTAL RESULTS of the signed distance map but scaling will result in increas- A 39 data sets are used to builda kidneyshape contours ing/decreasing projections in each direction which motivates (Fig. 1. (a)). The alignment and mean shape calculations the use of the smeared max function. are carried out to remove thedifferences between thetraining The minimizationof the energy with respect to the transfor- instances (Fig. 1. (b) and (c)). Image statistics are used to ini- mations parameters is done through the gradient descent. The tialize the intensity segmentation level set function Og using mean level set function OM evolves according its calculus of the well known stochastic expectation maximization (SEM). variation using the following PDE: Automatic seed initialization is usedbased on the region pa- rameters estimated by the SEM. A similar approach to that in N N [9] but the contour seeds are decided basedon the Bayesian =-2 EXdi siridQ- [ 0 ',rfdQ. (7) decision rule. The contour evolves and reaches the steady at Oml 2 state to mark the object region.This results in segmenting some parts of the background as kidney or at the same time V. THE SHAPE MODEL LEVEL SET FUNCTION missing kidney tissues. This motivates the incorporation of VThe hape model SA MOquired LEE capture the variationsinthe the shape model Op by estimating the weight and the global The shape model is required to capture the variations in the transformationparameters. Some examples of the shape seg- training set. For this purpose, Each curve/surface is trans- mentation results are illustratedin Fig. 2. The approach pro- formed to the domain of the mean function b M by its cor- videssuccessful results since it can handle different scales, responding transformation. Themodel is considered to be a rotations, and translations in the process.   comparison be- weighted sum of the transformed signed distance maps devi- tween the proposed technique and that given in [11] is illus- ated from the mean as follows: trated in 3. The homogeneous scales do notallow the shape N model to correctly deform to mark the correct boundaries of qs= M ±7E WiV  t-X (8) the kidney while this problem is already solved by the pro- =l posed methodology. 1188  (a) (b) (c) Fig. 1. Trainingcontours of 39 differentpatients' kidneys are given in (a). Alignment results are visualized in (b) after removing the pose differences between the subjects. Averageshape is given in (c). figure The ultimate goal of the proposed algorithms is to suc- network: transplant data: 1990-1999. BureauofHealth cessfully constructa renogram (mean intensity signal curves) Resources Department, Richmond, VA; 2000. from the DCE-MRI sequences, showing the behavior of the [2] M. Neimatallah, Q Dong, S. Schoenberg, K. Cho, and kidney as the contrast agent perfuses into the transplant. In M. Prince, Magnetic resonance imaging in renal trans- acute rejection patients, the DCE-MRI images show a delayed plantation, Journal of Magnetic Resonance Imaging, perfusion pattern and a reduced cortical enhancement. We vol. 10(3), pp. 357-368, Sep  999 tested the above algorithms on thirty patients, three of which [3] D. Yang, Q. Ye, M. Williams, Y. Sun, T. C.C. Hu, D. S. are shown in Fig. 3.d (1 and 2 are normal but 3 is acute rejec- Williams, J. M. F. Moura, and C. Ho., USPIO-Enhanced tion). The normal patient shows the expected abrupt increase Dynamic MRI: Evaluation of Normal and Transplanted to the higher signal intensities and the valley with a small Rat Kidneys, Magnetic Resonance in Medicine, vol. 46, slope. The acute rejectionpatients show a delay in reach- 1152-1163,2001. ing their peak signal intensities. From these observations, we [4] G. Gerig, R. Kikinis, W. Kuoni, G.K. van Schulthess, have been able to conclude that the relative peak signal inten- and 0. Kubler, Semiautomated ROI analysis in dynamic sity, time to peak signal intensity, the slope between the peak MRI studies:Part I: image analysis toolsfor automatic and the first minimum, and the slope between the peak and thecorrection of organ displacements, IEEE Transactionssignal measuredfrom the last image in the sequence are the Image Processing, vol. 11:(2),pp. 221-232, 1992. major four features in the renograms of the segmented kidney [5]E. Giele, Computer methods for semi-automatic MR for classification. renogram determination, Ph.D. dissertation, Depart- ment of Electrical Engineering, Eindhoven University VIII. CONCLUSIONS AND DISCUSSIONS ofTechnology, Eindhoven, 2002. In this paper, we presented a framework for thedetection [6] K. Siddiqi, A.Shokoufandeh, S. Dickinson, and S. of acute renalrejection from DCE-MRI which includes seg- Zucker.  Shocks graphs and shape matching, IEEE In- mentationof the kidneys from the abdomen images. The seg- ternational Journal of Computer Vision, 35:1332, 1999. mentation includesprior shape modeling by level sets. The [7] S. Osherand J. Sethian.  Fronts Propagatingwith model is embedded into the imagedomain by means of regis- Curvature-Dependent Speed: Algorithms Based on tration which allows the use of inhomogeneous scales. This is the Hamilton-JacobiFormulation, Journal of Computa- considered an advantage over existing techniques which fails tional Physics, 79:12-49, 1988. in many cases. Our future work will include testing on more [8] R. Duda, P. Hart, and D. Stork.  Pattern Classification , patients;the results of the proposed framework are promis- John Wiley and Sons Inc., 2001. ing andmight replace the current nuclear imaging tests or the [9] H. E. Abd El Munim and A.A. Farag,  A Shape-Based invasive biopsy techniques. Segmentation Approach: An Improved Technique Us- IX. REFERENCES ~~~~~ing Level Sets , Tenth IEEE International Conference * ~~~~~~~~~~on omputer Vision UICCV), Beijing, China, Oct.17- [1] U. S. Department ofHealth and Human Services . An- 20,2005, pp. 930-935. nual report of the U.S. scientific registry of transplant re- [10] A.Tsai, W. Wells,C. Tempany, E. Grimson,and A. cipients and the organ procurement and transplantation 1189  (1) (2) (3) (a)(b) (c) Fig. 2. Segmentation results(I-3): (a) level set initialization using the automaticseed initialization. Two classes are supposed to have Gaussian distributions with parameters estimated using the EM algorithm, (b) steady state resultfor the intensity model Og (c) steady state results for the shape model Op1. figure Willsky.  Mutual information in coupled multi-shape model for medical image segmentation, In Medical Im- age Analysis, vol. 8, pp 429-445, December 2004. [11] M. Rousson, N. Paragios and R. Deriche.  Implicit Ac- tive Shape Models for 3D Segmentation in MRI Imag- ing, Medical ImageComputing and Computer Assisted Intervention (MICCAI), Part 1, pp 209-216, Saint-Malo,France, September 26-29, 2004. 1190
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