Abstract
A technique is presented for elastic alignment applicable to human brains. The transformation which minimizes the distance measure D(u) between template and reference is determined, thereby simultaneously satisfying smoothness constraints derived from an elastic potential known from the theory of kontinuum mechanics. The resulting partial differential equations, with up to 3·220 unknowns are directly solved for each voxel, that is, without interpolation, by an adapted full multigrid-method (FMG) providing a perfect alignment. For further increases of resolution, the full advantages of the FMG are maintained, that is, parallelization and linear effort with O(N), N being the number of grid-points.
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Bajcsy, R., Kovacic, S.: Multiresolution elastic matching. Comput. Vision. Graph. Im. Proc. 46 (1989) 1–21
Miller, M.I., Christensen, G.E., Amit, Y., Grenander, U.: Mathematical textbook of deformable neuroanatomies. Proc. Nat. Acad. Sci. 90 (1993) 11944–11948
Christensen, G.E., Rabbitt, R.D., Miller, M.I.: 3D brain mapping using deformable neuroanatomy. Phys. Med. Biol. 39 (1994) 609–618
Budó A.: Theoretische Mechanik. Verlag der Wissenschaften, Berlin (1980)
Landau, L.D., Lifshitz, E.M.: Theory of Elasticity. Pergamon Press, London (1959)
Stüben, K., Trottenberg, U.: Multigrid methods: fundamental algorithms, model problem analysis and applications. In “Multigrid methods” (Hackbusch, W., Trottenberg, U., eds.), Lecture Notes in Mathematics 960, Springer-Verlag, Berlin (1982).
Schormann, T., Matthey, M.v., Dabringhaus, A., Zilles, K.: Alignment of 3-D brain data sets originating from MR and histology. Bioimaging 1 (1993) 119–128
Schormann, T., Dabringhaus, A., Zilles, K.: Statistics of deformations in histology and improved alignment with MRI. IEEE Trans. Med. Imaging 14 (1995) 25–35
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© 1996 Springer-Verlag Berlin Heidelberg
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Schormann, T., Henn, S., Zilles, K. (1996). A new approach to fast elastic alignment with applications to human brains. In: Höhne, K.H., Kikinis, R. (eds) Visualization in Biomedical Computing. VBC 1996. Lecture Notes in Computer Science, vol 1131. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0046971
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DOI: https://doi.org/10.1007/BFb0046971
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