Abstract
We present a novel method for building an optimal statistical deformable model from a set of surfaces whose topological realization is homeomorphic to a compact 2D manifold with boundary. The optimal parameterization of each shape is recursively refined by using hierarchical PBMs and tensor product B-spline representation of the surface. A criterion based on MDL is used to define the internal correspondence of the training data. The strength of the proposed technique is demonstrated by deriving a concise statistical model of the human left ventricle which has principal modes of variation that correspond to intrinsic cardiac motions. We demonstrate how the derived model can be used for 3D dynamic volume segmentation of the left ventricle, with its accuracy assessed by comparing results obtained from manual delineation of 3D cine MR data of 8 asymptomatic subjects. The extension of the technique to shapes with complex topology is also discussed.
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References
McInerney, T., Terzopoulos, D.: Deformable models in medical image analysis: A survey. Medical Image Analysis 1, 91–108 (1996)
Cohen, L.D., Cohen, I.: Finite-Element Methods for Active Contour Models and Balloons for 2-D and 3-D Images. IEEE Transactions on Pattern Analysis and Machine Intelligence 15(11), 1131–1147 (1993)
Coots, T.F., Taylor, C.J., Cooper, D.H., Graham, J.: Active Shape Models – Their Training and Application. Computer Vision and Image Understanding 61(1), 38–59 (1995)
Coots, T.F., Hill, A., Taylor, C.J., Haslam, J.: The Use of Active Shape Models for Locating Structures in Medical Images. Image and Vision Computing 12(6), 355–366 (1994)
Duta, N., Sonka, M.: Segmentation and Interpretation of MR Brain Images: an Improved Active Shape Model. IEEE Trans. Med. Imag. 17, 1049–1062 (1998)
Wang, Y., Staib, L.H.: Boundary Finding with Correspondence using Statistical Shape Models. In: Proc. Conf. Computer Vision and Pattern Recognition, Santa Barbara, California, pp. 338–345 (1998)
Wolberg, G.: Image morphing: a survey. The Visual Computer 14(8/9), 360–372 (1998)
Lazarus, F., Verroust, A.: Three-dimensional Metamorphosis: a Survey. The Visual Computer 14(8/9), 373–389 (1998)
DeCarlo, D., Gallier, J.: Topological Evolution of Surfaces, In: Graphic Interface. Canadian Human-Computer Communications Society, Toronto, Canada, pp. 194–203 (1996)
Kanai, T., Suzuki, H., Kimura, F.: Metamorphosis of Arbitrary Triangular Meshes. IEEE Computer Graphics and Applications 20(2), 62–75 (2000)
Eggert, D.W., Fitzgibbon, A.W., Fisher, R.B.: Note: Simultaneous Registration of Multiple Range Views for Use in Reverse Engineering of CAD Models. Computer Vision and Image Understanding 69(3), 253–272 (1998)
Rueckert, D., Frangi, F., Schnabel, J.A.: Automatic construction of 3D statistical deformable models using non-rigid registration. In: Niessen, W.J., Viergever, M.A. (eds.) MICCAI 2001. LNCS, vol. 2208, pp. 77–84. Springer, Heidelberg (2001)
Praun, E., Sweldens, W., Schroder, P.: Consistent Mesh Parameterizations. In: Computer Graphics Proceedings (SIGGRAPH 2001 ), pp. 179–184 (2001)
Kotcheff, A.C.W., Taylor, C.J.: Automatic construction of of eigenshape models by direct optimisation. Medical Image Analysis 2(4), 303–314 (1998)
Davies, R.H., Twinig, C.J., Coots, T.F., Waterton, J.C., Taylor, C.J.: A Minimum Description Length Approach to Statistical Shape Modelling. TMI (2002)
Hansen, M.H., Yu, B.: Model Selection and the Principle of Minimum Description Length. Technical Memorandum, Bell Labs, Murray Hill, N.J. (1998)
Floater, M.S.: Meshless Parameterization and B-spline Surface Approximation. In: Cipolla, R., Martin, R. (eds.) The Mathematics of Surfaces IX, pp. 1–18. Springer, Heidelberg (2000)
Duchamp, T., Certain, A., DeRose, A., Stuetzle, W.: Hierarchical Computation of PL Harmonic Embedding, Technical Report, University of Washington, pp. 1–21 (1997)
Eck, M., DeRose, T., Dutchamp, T., Hoppe, H., Lounsbery, M., Stuetzle, W.: Multiresolution Analysis of Arbitrary Meshes. In: Computer Graphics Proceedings (SIGGRAPH 1995), pp. 173–182 (1995)
Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes in C, 2nd edn. Cambridge University Press, Cambridge (1996)
Eck, M., Hope, H.: Automatic Reconstruction of B-Spline Surfaces of Arbitrary Topological Type. In: Computer Graphics Proceedings (SIGGRAPH 1996), pp. 325–334 (1996)
Moore, C.C., Lugo-Olivieri, C.H., McVeigh, E.R., Zerhouni, E.A.: Three-Dimensional Systolic Strain Patterns in the Normal Human Left Ventricle: Characterization with Tagged MR Imaging. Radiology 214(2), 453–466 (2000)
Fleute, M., Lavallee, S., Desbat, L.: Integrated Approach for Matching Statistical Shape Models with Intra-operative 2D and 3D Data. In: Dohi, T., Kikinis, R. (eds.) MICCAI 2002. LNCS, vol. 2489, pp. 364–372. Springer, Heidelberg (2002)
Lamecker, H., Lange, T., Sebass, M.: A Statistical Shape Model for Liver. In: Dohi, T., Kikinis, R. (eds.) MICCAI 2002. LNCS, vol. 2489, pp. 421–427. Springer, Heidelberg (2002)
Fordy, A.P., Wood, J.C.: Harmonic Maps and Integrable Systems. Aspects of Mathematics, vol. E23, Vieweg, Braunschweig/Wiesbaden (1994)
Yang, G.Z., Burger, P., Firmin, D.N., Underwood, S.R.: Structural Adaptive Anisotropic Image Filtering. Image and Vision Computing 14(2), 135–145 (1996)
Bishop, R.L., Goldberg, S.I.: Tensor Analysis on Manifolds. Dover Publications, Mineola (1981)
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Horkaew, P., Yang, G.Z. (2003). Optimal Deformable Surface Models for 3D Medical Image Analysis. In: Taylor, C., Noble, J.A. (eds) Information Processing in Medical Imaging. IPMI 2003. Lecture Notes in Computer Science, vol 2732. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45087-0_2
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DOI: https://doi.org/10.1007/978-3-540-45087-0_2
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