Allal, A.

Duay, V.

Houhou, N.

Thiran, J.

Infoscience - École polytechnique fédérale de Lausanne

MEDICAL IMAGES REGISTRATION WITH A HIERARCHICAL ATLASNawal Houhou, Vale´rie Duay, Abdelkarim S. Allal∗, Jean-Philippe ThiranSignal Processing Institute (ITS),Ecole Polytechnique Fe´de´rale de Lausanne (EPFL)CH-1015 Lausanne, Switzerland∗ Divisions of Radiation Oncology, University Hospital, Geneva, Switzerland{Nawal.Houhou, Valerie.Duay, JP.Thiran}@epfl.ch, Abdelkarim.Allal@hcuge.chABSTRACTAtlas-based medical image segmentation is a well knownmethod for including prior knowledge in medical imageanalysis. It requires as basic component the registration of anatlas with the image. In this paper, we introduce the conceptof hierarchical atlas and show how to efficiently include itin a state-of-the-art non-rigid registration algorithm. We firstpresent how to build a hierarchical atlas. Then we presentthe extension of a non-rigid registration algorithm, namelythe B-spline Free Form Deformation (FFD), to a hierarchicalversion. The procedure includes first an affine registrationto bring the atlas and the patient image in global correspon-dence. Then the non-rigid registration is performed layer bylayer, i.e. registering the image with each layer of the hierar-chical atlas, using the result of the registration of the previouslayer as initial condition for the registration of the next layer.We show on 2D CT images that this approach gives better re-sults than the non-rigid registration algorithm alone, in termsof registration accuracy.1. INTRODUCTIONIn this paper, we want to explore the integration of a registra-tion method in segmentation of the neck structures in Com-puted Tomography (CT) images. The clinical aim is radio-therapy of the neck cancer. In a radiotherapy treatment, asource emits radiations which penetrate through the skin inthe tumoral volume to be irradiated. To be both effective incancerous tissues and respectful to healthy ones, the dose ofradiation should vary according to the area. In the neck, 7distinct spaces are counted out by specialists; for each spacea specific intensity is required. In the traditional approach aalloy cover is constructed for each patient in order to protectsome regions and thus minimize the destruction of healthycells. Obviously, this technique is too restrictive in term oftime and cost. According to the current state of the tech-nique, the ultimate ”high precision” technique is the Inten-sity Modulated Radiotherapy (IMRT) where the intensity ofthe radiation is modulated depending on the region. This re-quires thus a precise definition of the region of interest, i.e.a segmentation of the target image. Nevertheless, for tumorsof the Head and Neck (H&N), the implementation in routinepractice is facing significant obstacles. Indeed, besides theprecise contouring of primary H&N tumors that is often diffi-cult, the accurate, reproducible and time-efficient contouringof elective nodal risk regions represents an even greater chal-lenge that is making the use of this technique uncommon.To cope with this problem, we propose to use an atlas of theneck area and to exploit it to segment the different regions ofinterest. Several atlas-based segmentation techniques havebeen proposed for medical applications. Their review is outof the scope of this paper. Let us only mention two of themdirectly related to this paper. In [1], Bach et al. present anatlas-based segmentation for pathological brain images andin a hierarchical point of view, Kapur et al. ([7]) adapt a reg-istration algorithm for each level of a multi-level knee atlas.In the case of the neck, we must take into account the highlocal variability and complexity of the region, and thereforea localized registration is required. In the literature, we canfind a large panel of registration methods. A general formu-lation of the problem that is often encountered consists inoptimizing a functional F :argminTF(Image1, Image2,T )where T is the geometric transformation used to register oneimage with the other one.The resolution of the formulation depends on one side onthe choice of T and on the other side of the choice of F .Firstly, the choice of T determines the nature of the transfor-mation and the number of degrees of freedom associated. Formore local result, a non-rigid approach must be used. Sev-eral methods have been developed. Christensen and Miller[4] proposed for T a free deformation on the model of vis-cous fluid (similar to the Navier Stokes equations). By anal-ogy with Maxwell’s Demons, Thirion [13] has developed adiffusion model. Meyer et al. [9] have proposed an algo-rithm based on thin plates spline deformation. Following thisidea, Rueckert [12] et al. have used B-splines associated to amulti-scale framework. Finally, in a similar scheme, Rhodeet al. [11] apply radially symmetric basis functions whichcan be spatially adapted. In most of the methods, the para-meters of T are iteratively computed such a way that the sim-ilarity measure F between both images is maximized. Differ-ent techniques for measuring this similarity have been devel-oped. A widely used measure is the mutual information, orits derived form the normalized mutual information, whichmodel the statistical relationship between the target imageand the transformed image. The mutual information measurehas been introduced in parallel by Collignon [5] and Viola[14]. [2], [3], [11], [12] and [9] take this criterion as the sim-ilarity measure (see [10] for a review on this topic). In thispaper, we propose a variation of the atlas-based segmentationtechnique, by defining a hierarchical procedure to progres-sively register the atlas with the target image. As a demon-stration, we will consider Computed Tomography(CT) im-ages of the neck.2. METHOD2.1 Construction of the AtlasGiven a CT image of the neck, we define an atlas of this re-gion (figure 1) by manual extraction of some structures of in-terest in a reference image. Next, we establish a hierarchicalFigure 1: Left: Source image. Right: The atlas deduced fromthe source imageconstruction of our atlas, related to the degree of easiness ofthe segmentation problem. The first layer will be composedof the most visible structures and the last layer, obviously, ofthe less visible. Figure 2 illustrates the construction of themask.Figure 2: Left: Source image. Right: Successive atlas layer2.2 Registration TechniqueIn order to find the best matching between the target imageand the mask, we need to know the transformation that re-lates the coordinate space in an image A with the correspond-ing coordinate space in the other image B. Let us call T thisregistration transformation:T : B 7→ AT (uB) = uAIn the following, A will denote the target image and B thesource image.2.2.1 Global partAs a pre-processing, we apply an affine transformation to thesource image to put it in global correspondence with the tar-get one. In 2D, this leads to the optimization of 6 parameters,describing the translation, rotation, scaling and shearing ofthe source image.[xy1]= Trigid[xByB1]=[a11 a12 a13a21 a22 a230 0 1][xy1](1)2.2.2 Nonrigid registration using B-splinesFor this part, we have chosen to use a state-of-the-art non-rigid registration techniques, based on B-Splines, followingan approach similar to [12]. We want to remind the readerthat the actual algorithm used here is not central in thispaper. We just use it to illustrate our hierarchical approach,which is the main point that we want to present. Any goodnon-rigid algorithm can fit in this framework. For this type ofregistration, a control points grid is constructed in the sourceimage. The goal is to find the best displacement of thosecontrol points which maps the source image landmark pointsto the target image using spline interpolation. B-Splinesbelong to the Free Form Deformations (FFD) class and area powerful tool for modelling deformable model. Unlike theclassical radial basis functions such as thin-plate Splines,B-Spline have finite support. It means that we will have onlya local influence for each control point.Let now define our B-Spline-based FFD.Ω = {(x,y) | 0≤ x < X ,0≤ y < Y} is the rectangulardomain containing the region to be transformed and Φ anx × ny mesh of control points φi, j. Using the B-splineinterpolation, we define the local transformation by :Tlocal(x,y) =3∑l=03∑m=0θl(u)θm(v)φi+l, j+m (2)where i= b xnxc−1, j= b ynyc−1, u= xnx−b xnxc, v= yny−b ynycand θl represents the l-th basis function of the B-splines:θ0(s) = (1− s)3/6θ1(s) = (3s3−6s2+4)/6θ2(s) = (−3s3+3s2+3s+1)/6θ3(s) = s3/6(3)where 0≤ s < 1.After the affine and the B-spline transformation, the final de-formation field is given by:u′ = u+Tlocal(u) (4)where u = (x,y) is issued from the affine transformation.With the basis functions, the weight of the contribution ofeach control point in Tlocal(x,y) is estimated. Thus, the con-trol points displacement determines the local transformation.The next step is to find this displacement by optimizing asimilarity measure.Figure 3: Summary of our hierarchical atlas based registra-tion algorithm2.2.3 Similarity criterion: Mutual InformationIn the registration process, the choice of the metric systemof similarity has significant effects. The similarity criterionwill measure the quality of the alignment between the tar-get and the source image. As it has been said, since in ourapplication the target image come form a CT scanner andthe source image is a binary image, the similarity criterionmust take in account the multimodal nature of those images.Therefore we have chosen to use Mutual Information (MI),which measures statistical dependance between two images.Mutual information is defined in terms of entropy:H(A) =−∑apA(a) log pA(a) (5)One form of mutual information is:MI(A,B) = H(A)+H(B)−H(A,B) (6)where H(A), H(B) denote the marginal entropies of A, B andH(A,B) denotes the joint entropy of two random variables.The joint entropy measured from the joint histogram must beminimized in order to maximize the mutual information. Wehave used the Mattes et al. [8] implementation for the MIcomputation.2.3 Hierarchical atlas-based registrationUsing the algorithm described previously, we wish to registersuccessively each layer of our atlas with the target image. Inthis aim, the FFD registration is applied for each layer. Ourstrategy is to treat each layer’s registration as a sequentialprocess. Concretely, the deformation field of the layer i willinitialize the deformation field of layer i+1. Thus, each de-formation field is a part of the hierarchical scheme where thehighest level corresponds to the last transformation. Figure3 describes the steps of the hierarchical registration. Fur-thermore, the hierarchical scheme allows a coarse-to-fine ap-proach for the registration.3. RESULTSUsing 2D images CT scans of the two patients neck region,we first apply a global registration using an affine transforma-tion. From this result, we perform our tests. In this section,we compare the results of our algorithm with a state-of-the-art approach. In this case, we use the B-Spline multiresolu-tion framework of Rueckert et al.[12] in which the resolutionof the grid control points increases with the image resolution.Figure 4 gives the different results of registration. The firstimage in the left side is the superposition of the target imageand the contour of the initial mask. The image on the mid-dle shows the result after the registration in a multiresolutionframework and the last image shows the results obtained withour algorithm. We note a difference of the registration in theexternal structure and in the smaller structures. In particularythe jaw has better registration results with our technique.We assess the registration quality by measuring the distancebetween a set of landmark points of the source image trans-formed and the correspondent set in the target image. First,7 points of interest are pointed manually on the target imageand second the corresponded points are marked on the sourceimage (figure 5). The Euclidean distance (equation 7) is used12 3456712 34 567Figure 5: Corresponding landmarks on the target and sourceimagesas the error estimator between the landmark point u′i and themanually selected point uBi in the source image.d = ‖uBi −u′i‖ (7)This estimation error is applied to the two registrationsmodality. Table 1 presents results of our measures. dinit isthe error before the registration, dNRM the error after a mul-tiresolution non rigid registration and dNRHA the error afterthe non rigid hierarchical atlas-based registration.Table 1:Landmarks dinit dNRM dNRHA1 9.06 8.01 2.692 8.06 2.19 2.813 6.00 5.96 1.914 7.21 5.46 5.095 10.63 7.28 4.586 8.06 5.11 2.087 31.76 26.22 24.07Mean 11.54 8.60 3.734. CONCLUSION AND FUTURE WORKIn this paper, we have proposed a new framework for FreeForm registration, illustrated in the case of B-Splines basedregistration. The registration by successive layers allows bet-ter local deformation. We have compared our technique withFigure 4: Results. From left to right, initialization of the atlas, atlas after applying FFD multiresolution registration, atlas afterapplying our FFD hierarchical frameworkthe well know technique of free form multiresolution regis-tration. The results have shown that a hierarchical atlas cap-tures more precisely the contours of interest. The registrationmade is a preliminary step before segmenting each area asso-ciated to a label. Future works will focus first on working on3D images and on the automatization of the atlas construc-tion.5. ACKNOWLEDGEMENTSAll this registration process has been implemented in the ITKenvironment [6]. This work is partially supported by theSwiss NSF grant nbr 205320-101621.REFERENCES[1] M. Bach Cuadra, C. Pollo, A. Bardera, O. Cuisenaire,J. Villemure and J. Thiran ”Atlas-based Segmentationof Pathological MR Brain Images using a Model of Le-sion Growth ”, IEEE Transactions on Medical Imaging,23(10), (Oct 2004), 1301–1314[2] T. Butz and J. Thiran, ”Feature-space mutual informa-tion for multi-modal signal processing, with applica-tion to medical image registration, European Conferenceon Signal Processing Conference”, EUSIPCO, 1, (Sept2002), 3–10[3] T. Butz and J.-Ph. Thiran, ”From Error Probability toInformation Theoretic (Multi-Modal) Signal Process-ing”,Signal Processing, (2005), in press[4] G. E. Christensen, M. I. Miller, and M. Vannier, ”3Dbrain mapping using a deformable neuroanatomy”, Phys.Med. Biol., 39, (1994), 609–618.[5] A. Collignon, F. Maes, D. Delaere, D. Vandermeulen,P. Seutens, and G.Manal, ” Automated multimodalityimage registration using information theory”, Informa-tion Processing Medical Imaging: Proc. 14th Int.Conf.IPMI’95 , (1995), 263–274[6] See ”http://www.itk.org”[7] T. Kapur, P. A. Beardsley, S. F. Gibson. W. E. L. Grim-son, W. M. Wells III, ”Model Based Segmentation ofClinical Knee MRI”, in conjuction with ICCV, (Jan1998)[8] D. Mattes, D. R. Haynor, H. Vesselle, T. K. Lewellen,and W. Eubank, ”PET-CT Image Registration in theChest Using Free-Form Deformations”, IEEE Transac-tions on Medical Imaging., 22(1), (Jan 2003), 120–128[9] C. R. Meyer, J. L. Boes, B. Kim, P. Bland, K. R. Za-sadny, P. V. Kison, K. Koral, K. A. Frey, and R. L. Wahl,”Demonstration of accuracy and clinical versatility ofmutual information for automatic multimodality imagefusion using affine and thin plate spline warped geomet-ric deformations”, IEEE Transactions on Medical Imag-ing., 22(8), (August 2003), 609–618.[10] J.P W Pluim, M. J.B Antoine Maintz, and M. AViergever, ”Mutual Information based registration ofmedical images: a survey”, IEEE Trans Med Imaging.,22(8),(Aug 2003), 986–1004[11] G. K. Rohde, A. Aldroubi and B. M. Dawant, ”TheAdaptive Bases Algorithm for Intensity-Based NonrigidImage Registration”, IEEE Transactions on MedicalImaging, 22(11), (Nov 2003), 1470–1479.[12] D. Rueckert, L. I. Sonoda, C. Hayes, D. L. G. Hill, M.O. Leach, and D. J. Hawkes, ” Nonrigid Registration Us-ing Free-Form Deformations: Application to Breast MRImages ”, IEEE Transactions on Medical Imaging , 18(8)(1999), 712–721[13] J.-Ph. Thirion, ”Image matching as a diffusion process:An analogy with Maxwell’s demons”, Medical ImageAnalysis, 2( 3),(1998), 243–260[14] P.Viola and W.M Welles III, ”Alignment by maximiza-tion of mutual information”, International journal ofComputer Vision , 24(2), (1997), 137–154

Medical images registration with a hierarchical atlas

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MEDICAL IMAGES REGISTRATION WITH A HIERARCHICAL ATLAS

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