Abstract
In this paper, we develop a variational method for the computation of average images of biological organs in three-dimensional Euclidean space. The average of three-dimensional biological organs is an essential feature to discriminate abnormal organs from normal organs. We combine the diffusion registration technique and optical flow computation for the computation of spatial deformation field between the averages and each input organ. We define the average as the shape which minimises the total deformation.
This research was supported by “Computational anatomy for computer-aided diagnosis and therapy: Frontiers of medical image sciences” funded by the Grant-in-Aid for Scientific Research on Innovative Areas, MEXT, Japan, the Grants-in-Aid for Scientific Research funded by Japan Society of the Promotion of Sciences and the Grant-in-Aid for Young Scientists (A), JSPS, Japan.
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References
Grigorescu, C., Petkov, N.: Distance Sets for Shape Filters and Shape Recognition. IEEE Trans. IP 12, 1274–1286 (2003)
Hajnal, J.V., Hill, D.L.G., Hawkes, D.J.: Medical Image Registration. Phys. Med. Bio.l 46, R1–R45 (2001)
Fischer, B., Modersitzki, J.: Ill-posed Medicine - An Introduction to Image Registration. Inverse Prob. 24, 1–17 (2008)
Rumpf, M., Wirth, B.: A Nonlinear Elastic Shape Averaging Approach. SIAM J. Imaging Sci. 2, 800–833 (2009)
Sebastian, T.B., Klein, P.N., Kimia, B.B.: On Aligning Curves. IEEE Trans. PAMI 25, 116–125 (2003)
Baeza-Yates, R., Valiente, G.: An Image Similarity Measure Based on Graph Matching. In: Proc. SPIRE 2000, pp. 8–38 (2000)
Riesen, K., Bunke, H.: Approximate Graph Edit Distance Computation by Means of Bipartite Graph Matching. Image and Vision Comput. 27, 950–959 (2009)
Arrate, F., Ratnanather, J.T., Younes, L.: Diffeomorphic Active Contours. SIAM J. Imaging Sci. 3, 176–198 (2010)
Sharon, E., Mumford, D.: 2D-Shape Analysis using Conformal Mapping. IJCV 70, 55–75 (2006)
Najman, L.: The 4D heart database, http://www.laurentnajman.org/heart/
Tănase, M., Veltkamp, R.C., Haverkort, H.J.: Multiple Polyline to Polygon Matching. In: Deng, X., Du, D.-Z. (eds.) ISAAC 2005. LNCS, vol. 3827, pp. 60–70. Springer, Heidelberg (2005)
Arkin, E.M., Chew, L.P., Huttenlocher, D.P., Kedem, K., Mitchell, J.S.B.: An Efficiently Computable Metric for Comparing Polygonal Shapes. IEEE Trans. PAMI 13, 209–216 (1991)
Stegmann, M.B., Gomez, D.D.: A Brief Introduction to Statistical Shape Analysis. Informatics and Mathematical Modelling, Technical University of Denmark 15 (2002)
Srivastava, A., Joshi, S.H., Mio, W., Liu, X.: Statistical Shape Analysis: Clustering, Learning, and Testing. IEEE Trans. PAMI 27, 590–602 (2005)
Horn, B.K.P., Schunck, B.G.: Determining Optical Flow. Artif. Intell. 17, 185–204 (1981)
Modersitzki, J.: Numerical Methods for Image Registration, OUP (2004)
Rumpf, M., Wirth, B.: An Elasticity-Based Covariance Analysis of Shapes. IJCV 92, 281–295 (2011)
Wirth, B., Bar, L., Rumpf, M., Sapiro, G.: A Continuum Mechanical Approach to Geodesics in Shape Space. IJCV 93, 293–318 (2011)
Berkels, B., Linkmann, G., Rumpf, M.: An SL(2) Invariant Shape Median. JMIV 37, 85–97 (2010)
Strang, G., Nguyen, T.: Wavelets and Filter Banks. Wellesley-Cambridge Press (1996)
Beg, M.F., Miller, M.I., Trouvé, A., Younes, L.: Computing Large Deformation Metric Mappings via Geodesic Flows of Diffeomorphisms. IJCV 61(2), 139–157 (2005)
Garcin, L., Rangarajan, A., Younes, L.: Non Rigid Registration of Shapes via Diffeomorphic Point Matching and Clustering. In: Proc. ICIP 2004, pp. 3299–3302. IEEE (2004)
Strang, G.: Computational Science and Engineering. Wellesley-Cambridge Press (2007)
Demmel, J.W.: Applied Numerical Linear Algebra. SIAM (1997)
Varga, R.S.: Matrix Iteration Analysis, 2nd edn. Springer (2000)
Vialard, F., Risser, L., Rueckert, D., Cotter, C.J.: Diffeomorphic 3D Image Registration via Geodesic Shooting using an Efficient Adjoint Calculation. IJCV 97, 229–241 (2012)
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Inagaki, S., Imiya, A., Hontani, H., Hanaoka, S., Masutani, Y. (2013). Variational Method for Computing Average Images of Biological Organs. In: Kuijper, A., Bredies, K., Pock, T., Bischof, H. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2013. Lecture Notes in Computer Science, vol 7893. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38267-3_37
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DOI: https://doi.org/10.1007/978-3-642-38267-3_37
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