Abstract. This report describes and evaluates the steps needed to perform modern model-based interpretation of the corpus callosum in MRI. The process is discussed from the initial landmark-free contours to fullfledged statistical models based on the Active Appearance Models framework. Topics treated include landmark placement, background modelling and multi-resolution analysis. Preliminary quantitative and qualitative validation in a cross-sectional study show that fully automated analysis and segmentation of the corpus callosum are feasible. 

Davies, Rhodri H.

Stegmann, Mikkel Bille

Mikkel B. Stegmann

Rhodri H. Davies

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Automated analysis of corpora callosa

This report describes and evaluates the steps needed to perform modern model-based interpretation of the corpus callosum in MRI. The process is discussed from the initial landmark-free contours to full-fledged statistical models based on the Active Appearance Models framework. Topics treated include landmark placement, background modelling and multi-resolution analysis. Preliminary quantitative and qualitative validation in a cross-sectional study show that fully automated analysis and segmentation of the corpus callosum are feasible

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Automated Analysis of Corpora CallosaMikkel B. Stegmann1, Rhodri H. Davies21Informatics and Mathematical Modelling – IMM, Technical University of Denmark,Richard Petersens Plads, Building 321, DK-2800 Kgs. Lyngby, DenmarkCorresponding author: mbs@imm.dtu.dk, http://www.imm.dtu.dk/∼mbs/2Division of Imaging Science and Biomedical Engineering – ISBE,University of Manchester, Manchester, M13 9PT, EnglandIMM Technical Report, IMM-REP-2003-02, March 2003Abstract. This report describes and evaluates the steps needed to per-form modern model-based interpretation of the corpus callosum in MRI.The process is discussed from the initial landmark-free contours to full-fledged statistical models based on the Active Appearance Models frame-work. Topics treated include landmark placement, background modellingand multi-resolution analysis. Preliminary quantitative and qualitativevalidation in a cross-sectional study show that fully automated analysisand segmentation of the corpus callosum are feasible.1 IntroductionMany neurological studies indicate that the size and shape of the corpus callo-sum are related to various human characteristics, dysfunctions et cetera [9]. Inshort, corpus callosum is the nervous tissue that connects the two cerebral hemi-spheres of the human brain. The gold standard for such morphometry studiesis magnetic resonance imaging, which allows acquisition of accurate images ofthe anatomy (and function) of the brain. However, doing manual tracings of thecorpus callosum is both time-consuming, error-prone and operator dependent.Instead, medical image analysis should aim at replacing this task with automatedand efficient methods eliminating all subjectivity. In this report we demonstratethat the generic Active Appearance Models (AAMs) [7, 2] can be adapted to thisproblem and proceed by performing a quantitative and qualitative assessmentof the method. Earlier quantitative segmentation studies of the corpus callosuminclude the work of Lundervold et al. [9], Brejl and Sonka [1] and van Ginnekenet al. [8].In addition to being a truly generic approach to corpus callosum segmenta-tion, AAMs provide a reference coordinate system for every new example. Thismakes propagation of reference areas such as the rostrum, genu, truncus, isth-mus and splenium a trivial matter. Further, regression analyses against gender,age, motor abilities, lifestyle et cetera can be carried out directly since shapevariation and size are both sensibly and compactly encoded.To supplement to this report, a continuation of our work is presented in [11]using a slightly different version of the data set and evolved versions of the AAMand MDL implementation described below.2 Data MaterialThe data material comprises 17 cross-sectional, mid-sagittal magnetic resonanceimages (MRI) of the brain. The corpus callosum was manually annotated by anexpert drawing one closed, landmark-free contour in each image. Figure 1 showsall shapes in Procrustes aligned form. The corresponding MR images are shownin Appendix A.Fig. 1: 17 corpus callosum annotations (row-wise) and the mean shape (lower right).3 Methods3.1 Active Appearance ModelsActive Appearance Models are generative models capable of synthesising im-ages of a given object class. By estimating a compact and specific basis from atraining set, model parameters can be adjusted to fit unseen images and henceperform image interpretation. The modelled object properties are shape andpixel intensities (called texture). Training objects are defined by marking upeach example image with points of correspondence. Variability is modelled bymeans of principal component analyses (PCA). Prior to PCA modelling shapesare Procrustes aligned and textures are warped into a shape-free reference frameand sampled. Let there be given P training examples, and let each example berepresented by a set of N landmark points and M texture samples. Let s and tdenote a synthesised shape and texture and let s and t denote the correspondingmeans. New instances can be generated by adjusting the PC scores, bs and btin s = s + Φsbs and t = t + Φtbt where Φs and Φt are eigenvectors of theshape and texture dispersions estimated from the training set. To recover anycorrelation between shape and texture and obtain a combined parameterisation,c, the values of bs and bt over the training set are combined in a third PCA,[WsΦTs (s− s)ΦTt (t− t)]=[Wsbsbt]=[Φc,sΦc,t]c = Φcc. (1)Here, Ws is a diagonal matrix weighting pixel distances against intensities.Synthetic examples, parameterised by c, are generated by s = s+ΦsW−1s Φc,scand t = t+ΦtΦc,tc and rendered into an image by warping the pixel intensitiesof t into the geometry of the shape s. Using an iterative updating scheme themodel can be fitted to an unseen image. See [2, 3] for the details.3.2 Landmark PlacementEstablishing points of correspondence, the so-called landmarks, on training ex-amples by hand can not only be time-consuming, tedious and error-prone, butin some cases directly impossible when no good anatomical points are available.We have tried to manually identify two landmarks on the corpus callosum;one at the rostrum (left ”tip”) and one at the splenium (right ”tip”). Further, 78semi-landmarks were interpolated along the contour using a uniform arc-lengthparameterisation.To supplement this, a method for automatic landmarking in 2D and 3D wasalso applied. This was the MDL-framework proposed by Davies et al. [5, 6] that– in the spirit of Occam’s razor – seeks to minimise the total description lengthof the resulting PCA shape model. As a starting point, the method requiresthe shapes to be Procrustes aligned, which was obtained from our manuallylandmarked shapes. Then landmarks with a minimal description length werecalculated for all shapes and the alignment was inverted so that the MDL-basedlandmarks were given in image coordinates.3.3 Background AwarenessBy modelling the full appearance of objects, AAMs achieve an impressive degreeof robustness, e.g. when compared to its predecessor the Active Shape Mod-els (ASMs) [4]. However, one widely recognised advantage of the ASMs is thatthey also model the appearance of the background variation. In fact, the typicalASM implementation has equal weights on appearance of the object and back-ground. Obviously, this is good when the background is fairly constant or, moreimportantly, when the object has a rather homogeneous appearance. On theother hand, modelling object appearance only is preferred when the backgroundis highly varying. However, this requires that the object modelled have internalfeatures that can constrain the outer border, e.g. mouth, nose and eyes in faceimages.In medical images, organs and structures typically have a very homogenousappearance. Since AAMs only model the object appearance the cost functioncan easily have perfectly fine minimum inside the object, where both a plausibleshape and good texture fit can be obtained. Corpora callosa are no exceptionto this. One typical fix is to model the convex hull of the shape points. How-ever, this only helps at the concave parts of the modelled contour. Therefore, wepropose a simple scheme for modelling background variation by adding normalsoutwards from the shape, which we call whiskers, at all contour points. Theseare implicitly added during texture sampling and scaled according to the cur-rent shape size. Texture samples obtained from whiskers can now be weightedagainst the normal AAM samples. As in Active Shape Models (ASMs) [4] thisunfortunately introduces the need for one more parameter setting, namely thelength of the whiskers.3.4 Multi-Resolution AnalysisTo improve both convergence and robustness AAM analysis can be performed atdifferent resolutions. A widely used scheme is to recursively decimate an inputimage thereby creating a scale pyramid representation. This can be carried outon the training set, thus producing one model for each level of the pyramid.In our formulation, model optimisations are initialised at the smallest leveland propagated toward the full image resolution. Let ci denote the convergedmodel configuration at level i. The corresponding shape, si is trivially propagatedto level i + 1 = j by sj = 2si and the texture is sampled into tj . Assumingthat the optimisation at level i produced a match up to the accuracy givenby image resolution, cj can now be estimated by projecting sj and tj into thecorresponding combined eigenspacecˆj = ΦTc,j[Ws,jΦTs,j(sj − sj)ΦTt,j(tj − tj)](2)and model optimisation can continue at level j. If Φs,i = Φs,j ∀ i, j then bs,ican be used to ease the calculation of cˆj , but more importantly; sj and tj wouldlie in (or at least be very close to) the space spanned by Φc,j . This means thattj can be used directly to calculate the first update of cˆj .4 Experimental ResultsTo assess the applicability of AAMs a set of test scenarios were set up. Westarted by inspecting the quality of the two different shape models provided bythe manual and the MDL annotation. Figure 2 shows the three first principalmodes of shape variation for both shape sets. As these are ordered in terms ofdecreasing variance it might surprise that the first mode in the manual case seemsto deliver less shape change than the second. The cause is clearly illustrated inFigure 3, which shows that variation in the manual case almost solely stems fromlandmark movements along the contour. However, in the MDL case deformationsare, by design, much closer to being orthogonal to the tangent of the contour.−2.5σi mean 2.5σi −2.5σi mean 2.5σiFig. 2: Shape deformation using the three largest principal modes (top-down). Left:Manual annotation. Right: MDL annotation.Fig. 3: The first principal shape mode shown as displacements from the mean shape.Left: Manual annotation. Right: MDL annotation.Table 1: Segmentation Results in Units of PixelsWhiskers MDL Scale Pt.pt. Pt.crv. Lower bound (pt.pt.)added shapes pyramid Mean Median Mean Median Leave-all-in Shape modelA - - - 3.64 2.70 0.90 0.88 1.61 1.06B - - Yes 2.54 2.36 0.91 0.93 n/a n/aC - Yes - 6.98 2.29 3.85 0.91 1.74 0.93D - Yes Yes 2.24 1.97 0.94 0.89 n/a n/aE Yes - - 2.92 2.33 0.80 0.76 0.72 1.06F Yes - Yes 2.40 2.12 0.89 0.81 n/a n/aG Yes Yes - 3.01 1.93 0.85 0.77 1.51 0.93H Yes Yes Yes 1.85 1.80 0.86 0.77 n/a n/aE F G H24681012Pt.pt. error [pixels]E F G H0.40.60.811.21.41.61.8Pt.crv. error [pixels]−0.1 −0.06 −0.02 0.02 0.06 0.1−0.08−0.0400.040.08 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17MDS1MDS 2Fig. 4: Left: Boxplots of the segmentation accuracy for models built with whiskers.Right: Multidimensional scaling (MDS) of the MDL-based principal shape scores.But how much does this affect the segmentation accuracy? Trying to answerthis, we also tested the effects of the multi-resolution analysis and the additionof whiskers. Each test was carried out using cross-validation in leave-one-outscheme. Used performance measures were the average distance between i) modeland ground truth landmarks (pt.pt.), and ii) model and ground truth contour(pt.crv.). Further, two lower bounds on the segmentation error were calculated.The first is the error obtained from a leave-all-in segmentation test. This meansthat the optimisation process had knowledge of the image being optimised onand the shape, texture and combined models should – apart from the truncation– span the space of the test example. The second lower bound is obtained fromdiscarding any error introduced from the lack of span from the combined modeland the error introduced by an erroneous optimisation. Fitting the independentleave-one-out shape model directly to the ground truth carried this out. Allresults are shown in Table 1 and a subset is shown as boxplots in Figure 4 (left).All models were automatically initialised using a method we have describedin [10]. Texture samples from whiskers influenced the texture model by onethird. The convex hull was retained and the whisker length was three times thedistance between landmark 1 and 2 on the mean shape sized to mean size.A qualitative impression of the average segmentation result is given in Fig-ure 5 (middle) and an example of failure is shown in Figure 5 (right). In this casethe pt.pt. error was 11.6 pixels but the pt.crv. error was only 1.3 pixels. Thisstems from the non-symmetry of the latter measure. Hence, the vanilla pt.crv.formulation is clearly misleading in cases with search failures. A simple patch tothis is to use Esym.pt.crv.(a, b) = max( Ept.crv.(a, b) + Ept.crv.(b, a) ) instead.Fig. 5: Left: Corpus callosum annotation using 80 landmarks. Middle: Average pt.pt.segmentation result (case H). Right: Segmentation failure (case E).Finally, a multidimensional scaling (MDS) map of the principal shape scoresis shown in Figure 4 (right), which gives a planar approximation to the Euclideandistances between shapes in the high-dimensional space of bs.5 Discussion and ConclusionWe observe that the addition of the multi-resolution representation, the whiskersand the MDL-based landmarking consistently lead to better models. This wasachieved by a combination of eliminating initialisation and search failures andimproving the general accuracy. Further, the validity of Occam’s razor is con-firmed by the last column of Table 1.To the best of our knowledge, this is the first work documenting the feasi-bility of applying Active Appearance Models for fully automated shape analysisand segmentation of the corpus callosum. We have evaluated three differentimprovements, which all lead to better models. The three combined lead to alandmark error median of 1.80 pixels pt.pt. and 0.77 pixels pt.crv. We considerthis acceptable considering the rather small training set.We conclude that AAMs are feasible as a tool for automated analysis of thecorpus callosum in MRI images. Future work should aim at a clinical validationperformed on a larger data set.AcknowledgementsEdward Ho, ISBE provided the MDL annotations. M.D., M.Sc. Egill Rostrup,Danish Research Centre for Magnetic Resonance (DRCMR) initiated this project.M.D., Charlotte Ryberg (DRCMR) provided the annotations. M. B. Stegmannwas funded by the Danish Medical Research Council, grant no. 52-00-0767.References1. M. Brejl and M. Sonka. Object localization and border detection criteria designin edge-based image segmentation: automated learning from examples. MedicalImaging, IEEE Transactions on, 19(10):973–985, 2000.2. T. F. Cootes, G. J. Edwards, and C. J. Taylor. Active appearance models. In Proc.European Conf. on Computer Vision, volume 2, pages 484–498. Springer, 1998.3. T. F. Cootes and C. J. Taylor. Statistical Models of Appearance for ComputerVision. Tech. Report. Feb 2000, University of Manchester, 2000.4. T. F. Cootes, C. J. Taylor, D. H. Cooper, and J. Graham. Active shape mod-els – their training and application. Computer Vision and Image Understanding,61(1):38–59, 1995.5. R. H. Davies. Learning Shape: Optimal Models for Analysing Natural Variability.PhD thesis, Department of Imaging Science and Biomedical Engineering, Univer-sity of Manchester, Stopford building, University of Manchester, 2002.6. R. H. Davies, C. J. Twining, T. F. Cootes, J. C. Waterton, and C. J. Taylor.A minimum description length approach to statistical shape modeling. MedicalImaging, IEEE Transactions on, 21(5):525–537, 2002.7. G. J. Edwards, C. J. Taylor, and T. F. Cootes. Interpreting face images usingactive appearance models. In Proc. 3rd IEEE Int. Conf. on Automatic Face andGesture Recognition, pages 300–5. IEEE Comput. Soc, 1998.8. B. van Ginneken, A. F. Frangi, J. J. Staal, B. M. Ter Haar Romeny, and M. A.Viergever. Active shape model segmentation with optimal features. IEEE Trans-actions on Medical Imaging, 21(8):924–933, 2002.9. A. Lundervold, N. Duta, T. Taxt, and A. K. Jain. Model-guided segmentation ofcorpus callosum in MR images. Computer Vision and Pattern Recognition, 1999.10. M. B. Stegmann. Object tracking using active appearance models. In Proc. 10thDanish Conference on Pattern Recognition and Image Analysis, Copenhagen, Den-mark, volume 1, pages 54–60. DIKU, 2001.11. M. B. Stegmann and R. H. Davies. Corpus callosum analysis using MDL-basedsequential models of shape and appearance. In preparation, 2003.A Corpus Callosum MRIsImages are presented row-wise in same ordering as the corresponding annotationsin Figure 1.

Automated Analysis of Corpora Callosa

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Automated Analysis of Corpora Callosa

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