This paper presents a new approach to higher dimensional segmentation. We present an extended Active Shape Model (ASM) formulation for the segmentation of multi-contour anatomical structures. We employ coupling and weighting schemes to improve the robustness of ASM segmentation. 3D segmentation is achieved through propagation of a 2D ASM using a learned non-rigid spatial model. This approach does not suffer from the training and aligning difficulties faced by direct 3D model-based methods used today. Experimental results are encouraging at this early stage, and future directions of research are provided

Ghita, Ovidiu

O'Brien, Stephen

Whelan, Paul F.

DCU Online Research Access Service

Segmenting the Left Ventricle in 3D Using aCoupled ASM and a Learned Non-Rigid SpatialModelStephen O’Brien, Ovidiu Ghita, and Paul F. WhelanCentre for Image Processing and Analysis,Dublin City University, Dublin 9, Irelandstephen.obrien@eeng.dcu.ieAbstract. This paper presents a new approach to higher dimensionalsegmentation. We present an extended Active Shape Model (ASM) for-mulation for the segmentation of multi-contour anatomical structures.We employ coupling and weighting schemes to improve the robustness ofASM segmentation. 3D segmentation is achieved through propagation ofa 2D ASM using a learned non-rigid spatial model. This approach doesnot suffer from the training and aligning difficulties faced by direct 3Dmodel-based methods used today. Experimental results are encouragingat this early stage, and future directions of research are provided.Keywords: segmentation, coupled ASM, adaptive weighting, active shapemodel, left-ventricle, non-rigid model.1 IntroductionCardiovascular disease (CVD) accounted for 17.5 million deaths worldwide in2005. If trends continue, CVD will claim 20 million lives, annually, by 2015 [1].In 2008 CVD was responsible for approximately half of all deaths in Europe.Today, modern MRI scanners produce 3D+time images of the heart for diag-nosis of CVD. Deriving quantitative measurements of the left ventricle fromthese images, such as ejection fraction, cardiac output and myocardial thicken-ing, provides crucial indicators of cardiac health and therefore plays a centralrole in CVD diagnosis. However, manual extraction of left ventricle contours isan especially difficult task due to intensity variations, poor contrast betweenthe epicardium and surrounding thoracic cavity and the presence of papillarymuscles which can cause diffuse endocardium borders in 2D images. Automatedimage segmentation techniques are a promising alternative to traditional man-ual methods that avoid: operator fatigue, inter/intra observer variability andproviding repeatable results, crucial in long-term patient monitoring.In recent years, it has become widely recognised that automatic segmenta-tion methods need to maximise a priori knowledge of the segmentation target to2be effective[2]. Model-based methods have been shown to perform well in noisymedical images, where anatomical structures are often poorly defined. The Ac-tive Shape Model (ASM), introduced by Cootes et al.[3], is one such popularmodel-based approach, where shape variation is captured in linear models usingPrincipal Component Analysis (PCA). ASMs, and their later extension to in-clude texture variation Active Appearance Models (AAM), have been applied toa range of medical applications, including the brain[4], lung [5] and cardiac[6, 7]segmentation. Early ASM and AAM implementations were primarily developedto address the segmentation of 2D data. In recent years there has been a growingtrend towards 3D and 3D+time medical image segmentation[8–10].However, generalising the ASM to 3D (and 3D+time) faces many problems.Specifically, to capture the full variation of a 3D shape requires significantly moretraining samples and landmarks than the 2D case. Aligning the training set posesa difficult challenge since one has to deal with more degrees of freedom. Finally,3D ASM initialisation and optimisation are computationally intensive and oftenbecome trapped in local minima. Many publications have dealt with the issueswith direct 3D ASM implementations, especially constructing 3D ASMs in thepresence of small training sets [4]. We propose a new approach to higher di-mensional modelling and segmentation that avoids the problems outlined above.The main contributions of this work lies in combining a learned non-rigid spatialmodel and an extended 2D ASM formulation to achieve 3D segmentation.2 Method2.1 ASM TheoryWhen building an ASM from a set of training shapes, the segmentation tar-get must be descretised into N landmarks. A shape vector, x, containing Nlandmarks is described as:x = [x0, x1, . . . , xN ] (1)where xi is the ith landmark. The training set containing M training shapes isdefined as:T = [x0,x1, . . .xM] (2)After the training set (T ) has been aligned (T ′), PCA is applied to extract theeigenvectors which describe the shape variation of T ′. To align the shapes in thetraining set, only translation effects need to be removed as we wish to capturethe scale variation of the training samples. Rotational effects are negligible sincethe contours are all taken from a specific short axis slice and temporal volume.Therefore, the training set can be aligned without applying Procrustes analysis[3]. The most significant eigenvectors Φ are chosen to capture 95% of the variationin the training set [3]. New shapes can be synthesised using Φ and the mean-shape of T ′, x, according to:x ≈ x + Φβ (3)3where β represents the model parameters and x is the shape vector (1). Thelimits on the ith component of the β vector is constrained by ±3√Φi, where Φidescribes the variance of the ith element of β in T ′ [3].Fitting the trained ASM to an unseen image is achieved with an iterativetwo-stage process. First, the energy of each landmark is minimised according tothe local image information (usually image gradient or local texture). This isa data-driven process where the search space for each landmark is constrainedalong a 1D profile, normal to the direction of the contour. For example, the ithlandmark xi has a corresponding grey-scale profile L(xi):L(xi) = {I(xi − j−→n ) , −k ≤ j ≤ k} (4)where 2k is the length of the profile, −→n is the normal direction of the contour atthe landmark xi and I(xi) is the grey-scale value in the image at the landmarkxi. In the standard ASM formulation, the minimised landmark x′i is chosenaccording to the maximum of the gradient profile:x′i = max(OL(xi)) (5)where OL(xi) is the gradient profile of L(xi). Then, the ASM approximates theset of minimised landmarks, x′, by synthesising a new shape, x′′, which is thebest fit between the captured variation of the ASM and x′. This is described by:x′′ ≈ x+ Φβ′ (6)where β′ = ΦT (x′ − x) (7)This process continues until convergence is reached.2.2 Single Shape Multi-contour ASMWhen building an ASM of the left ventricle, the variations of the endo- and epi-cardium need to be captured. These two contours are strongly related anatom-ically, and so are treated as a single shape (as opposed to creating a separateASM for each contour). This is achieved by extending the shape vector (1) todescribe both contours as one shape. All subsequent calculations to derive Φ, xetc. are similar to the single contour ASM case, described in Section 2.1.During landmark optimisation, energy is minimised on an individual basis -i.e. no contextual knowledge is used from surrounding landmarks. This is nota limitation when dealing with a single contour ASM where searching is con-strained along contour normals so there can be no overlapping between landmarkprofiles.However, when two contours are treated as a single shape landmark pro-files can overlap. This compromises the stability of the ASM in the case of leftventricle segmentation, due to the proximity of the endo- and epi-cardium asillustrated in Figure 2.2(a). The endocardium is generally the stronger featureof the two due to the contrast between the bright blood pool and the darkermyocardium. Therefore, landmarks for both contours tend to converge on the4endocardium in the image (Figure 2.2(b)). The ASM will be unable to approx-imate the set of landmarks x′, since such a case will never arise in the trainingset. The resulting ASM approximation, x′′, will have little correspondence to theminimised landmarks x′ and, in fact, can go someway to hiding the underlyingproblem (Figure 2.2(c)).(a) (b) (c)Fig. 1: Sub-figure (a) shows how landmark profiles overlap when minimising the energyof a single shape multi-contour ASM. (b) shows the resulting energy minimisation(assuming the endocardium is the stronger feature in the image). (c) shows the modelapproximation.2.3 Proposed ASM Contour Coupling ApproachTo address this weakness in the standard ASM (when applied to multi-contourstructures) we propose to extend the standard ASM formulation to enforce apriori structure during segmentation. Specifically, we enforce biological integritythat forces the epicardium to be outside the endocardium. In the standard ap-proach, each landmark (xi) is minimised according to the maximum of it’s gra-dient profile OL(xi) (5). In order to couple the contours, i.e. to enforce a prioriconstraints, we extend (5) as follows:x′endoi = max(OL(xendoi )) (8)x′epii = max(OL(xepii ) \Ωendo′) (9)where A\B = {x ∈ A |x /∈ B} and Ωendo′ is the region defined by the minimisedendocardium landmarks x′endo. Here, we minimise the energy of the endo- andepi-cardium landmarks differently. We give preference to the endocardium land-marks, which are minimised first, as the endocardium contour is the strongerfeature in the image. The profile for each epicardium landmark is excluded fromΩendo′ , ensuring structural consistency is maintained during segmentation. Thisis the central concept of the proposed contour coupling approach and is illus-trated in Figure 2.5Fig. 2: Contour Coupling. Landmark profiles for xj and xk are truncated by Ωendo′ asdescribed in Equation (9)2.4 Contour WeightingSections of the epicardium contour are often poorly defined due to low contrastwith surrounding tissues in the thoracic cavity. To improve epicardium segmenta-tion robustness we introduce an adaptive weighting term which reinforces weakedge information. We exploit the knowledge that the endo- and epi-cardiumare approximately concentric. Before landmark minimisation, an edge frequencyhistogram is generated from each epicardium gradient profile, OL(xepii ). Thehistogram is defined as:H =1NN∑j=1OL(xepij ) (10)where the epicardium is described by N landmarks. This histogram is usedas a weighting term during epicardium landmark minimisation which extendsEquation (8) and (9) to:x′endoi = max(OL(xendoi )) (11)x′epii = max((OL(xepii ) \Ωendo′)H) (12)Here, the epicardium gradient profiles are weighted using the dynamic histogram.The histogram gives weighting to common edges outside Ωendo′ region, thusbringing global context into the local landmark minimisation process.2.5 Propagation to 3DThe common approach to modelling a 3D structure involves the construction ofdirect 3D shape models [6, 11–13]. Despite the popularity of this approach - itsuffers from several flaws. Most importantly, direct modelling of 3D structuresis not scalable. This is primarily due to the large increase of degrees of freedomwhen moving from the 2D to the 3D domain, and further from the 3D to the3D+time domain. Moreover, large training databases are needed to train 3D,and especially 3D+time models. Finally, the difficulty with aligning the data6Fig. 3: Flowchart for 3D segmentation algorithm.during training, as well as the increase of local minima also add to the problemsassociated with direct 3D and 3D+time modelling.In this paper, a new scalable method of higher dimensional modelling andsegmentation is detailed, when applied to the segmentation of the endo- andepi-cardium in 3D data. This approach does not rely on large databases anddoes not suffer from aligning or local minima problems. A model is trained thatcaptures the scale variation of the left ventricle over the z axis (Figure 3 (iii)).Scale variations are derived from the manual annotations of the systolic anddiastolic cardiac phases from the training set. Scale samples are normalised andused to create a probability density function describing mean scale variations onthe z axis.The initial 2D ASM segmentation of the basal-most slice of the left ventricle(Figure 3 (i)) interacts with the statistically estimated scale model to producean estimation of the scale of the shape in the next slice. The ASM is initialisedwith this estimated scale and constrained during segmentation according to thelearned variance for that slice from the scale model. Segmentation is propagatedin this manner (Figure 3 (ii)) to achieve 3D segmentation (Figure 3 (iv)).3 ResultsThe proposed 3D segmentation technique requires two seed points. The firstgives both the initial spatial slice of the left ventricle in the dataset and theinitialisation for the ASM. The second point defines the final spatial slice of theleft ventricle in the volume at the apex. The method is evaluated against 30 3Dcine-MRI cardiac images. Both systolic and diastolic cardiac phases are includedin the testing database. The 3D scale model is trained from the manual anno-tations of 30 different 3D cine-MRI cardiac images, containing both normal andpathological patients. Full details of the data and evaluation procedures can befound in Radau et al. [14]. Average segmentation errors are measured at 3.73 mmand 3.16 mm for the endocardium and epicardium, respectively. The Dice mea-sure was also used to detect percentage error in overlap between the segmentedregion and the manually annotated region. Dice error is measured at 80.9% and791.3% for the endocardium and epicardium, respectively. The results show thatthe accuracy of the epicardium is higher than that of the endocardium. Thisis due, in part, to the effect of the papillary muscles obscuring the true endo-cardium border during endocardium landmark minimisation. Figure 4 shows asample volume segmentation using the proposed method.(a) Z0 (b) Z2 (c) Z4(d) Z5 (e) Z7 (f) Z8Fig. 4: Sample volume segmentation result using the proposed method. Note: only apartial volume is shown due to space restrictions.4 ConclusionThis paper describes the implementation and evaluation of a new 3D segmen-tation technique using a coupled and weighted ASM formulation in conjunctionwith a learned non-rigid spatial model. The proposed approach addresses thesegmentation of the endo- and epi-cardial interfaces in 3D+time cardiac MRIdata. This approach is evaluated on real 3D+time cardiac MRI datasets. Ex-perimental results are encouraging at this stage of research. Future directions ofresearch include: improved segmentation accuracy of the 2D ASM, especially inthe presence of papillary muscles, and extension of this approach to 3D+timesegmentation.8Acknowledgements This work is supported by the Irish Research Councilfor Science, Engineering and Technology (IRCSET), with additional supportprovided by the National Biophotonics and Imaging Platform Ireland (NBIP).References1. (WHO), W.H.O.: Cardiovascular disease statistics. (2004)2. Frangi, A., Niessen, W., Viergever, M.: Three-dimensional modeling for functionalanalysis of cardiacimages, a review. IEEE Transactions on Medical Imaging 20(1)(2001) 2–53. Cootes, T., Taylor, C., Cooper, D., Graham, J., et al.: Active Shape Models-Their Training and Application. Computer Vision and Image Understanding 61(1)(1995) 38–594. Zhao, Z., Aylward, S., Teoh, E.: A Novel 3D Partitioned Active Shape Modelfor Segmentation of Brain MR Images. Lecture Notes in Computer Science 3749(2005) 2215. Shi, Y., Shen, D.: Hierarchical Shape Statistical Model for Segmentation of LungFields in Chest Radiographs. Springer (2008)6. Andreopoulos, A., Tsotsos, J.: Efficient and generalizable statistical models ofshape and appearance for analysis of cardiac MRI. Medical Image Analysis (2008)7. Casero, R., Noble, J.: A novel explicit 2D+ t cyclic shape model applied to echocar-diography. In: Medical image computing and computer-assisted intervention:MICCAI International Conference on Medical Image Computing and Computer-Assisted Intervention. Volume 11., Springer (2008) 5278. Lynch, M., Ghita, O., Whelan, P.: Segmentation of the Left Ventricle of theHeart in 3-D+ t MRI Data Using an Optimized Nonrigid Temporal Model. IEEETransactions on Medical Imaging 27(2) (2008) 195–2039. Montagnat, J., Delingette, H.: 4D deformable models with temporal constraints:application to 4D cardiac image segmentation. Medical Image Analysis 9(1) (2005)87–10010. Stegmann, M., Pedersen, D.: Bi-temporal 3D active appearance models with ap-plications to unsupervised ejection fraction estimation. In: Proc. SPIE. Volume5747.11. Frangi, A., Rueckert, D., Schnabel, J., Niessen, W.: Automatic construction ofmultiple-object three-dimensional statistical shape models: application to cardiacmodeling. IEEE Transactions on Medical Imaging 21(9) (2002) 1151–116612. Fritz, D., Rinck, D., Dillmann, R., Scheuering, M.: Segmentation of the left andright cardiac ventricle using a combined bi-temporal statistical model. MedicalImaging 2006: Visualization, Image-Guided Procedures, and Display. Edited byCleary, Kevin R.; Galloway, Robert L., Jr. Proceedings of the SPIE, 6141 (2006)605–61413. Zambal, S., Hladuvka, J., Buhler, K.: Improving Segmentation of the Left VentricleUsing a Two-Component Statistical Model. Lecture Notes In Computer Science4190 (2006) 15114. 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Segmenting the left ventricle in 3D using a coupled ASM and a learned non-rigid spatial model

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Segmenting the left ventricle in 3D using a coupled ASM and a learned non-rigid spatial model

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