Abstract
Registration of image-time series has so far been accomplished (i) by concatenating registrations between image pairs, (ii) by solving a joint estimation problem resulting in piecewise geodesic paths between image pairs, (iii) by kernel based local averaging or (iv) by augmenting the joint estimation with additional temporal irregularity penalties. Here, we propose a generative model extending least squares linear regression to the space of images by using a second-order dynamic formulation for image registration. Unlike previous approaches, the formulation allows for a compact representation of an approximation to the full spatio-temporal trajectory through its initial values. The method also opens up possibilities to design image-based approximation algorithms. The resulting optimization problem is solved using an adjoint method.
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References
Ashburner, J., Friston, K.J.: Diffeomorphic registration using geodesic shooting and Gauss-Newton optimisation. Neuroimage 55(3), 954–967 (2011)
Beg, M., Miller, M., Trouvé, A., Younes, L.: Computing large deformation metric mappings via geodesic flows of diffeomorphisms. IJCV 61(2), 139–157 (2005)
Davis, B., Fletcher, P., Bullitt, E., Joshi, S.: Population shape regression from random design data. In: ICCV, pp. 1–7 (2007)
Durrleman, S., Pennec, X., Trouvé, A., Gerig, G., Ayache, N.: Spatiotemporal atlas estimation for developmental delay detection in longitudinal datasets. In: Yang, G.Z., Hawkes, D., Rueckert, D., Noble, A., Taylor, C. (eds.) MICCAI 2009. LNCS, vol. 5761, pp. 297–304. Springer, Heidelberg (2009)
Fan, J.: Local linear regression smoothers and their minimax efficiencies. The Annals of Statistics 21(1), 196–216 (1993)
Joshi, S., Davis, B., Jomier, M., Gerig, G.: Unbiased diffeomorphic atlas construction for computational anatomy. Neuroimage 23, S151–S160 (2004)
Miller, M.I., Trouve, A., Younes, L.: Geodesic shooting for computational anatomy. Journal of Mathematical Imaging and Vision 24, 209–228 (2006)
Niethammer, M., Hart, G., Zach, C.: An optimal control approach for the registration of image time series. In: Conference on Decision and Control (CDC), pp. 2427–2434. IEEE, Los Alamitos (2009)
Qiu, A., Albert, M., Younes, L., Miller, M.I.: Time sequence diffeomorphic metric mapping and parallel transport track time-dependent shape changes. NeuroImage 45(1), S51–S60 (2009)
Vaillant, M., Miller, M.I., Younes, L., Trouvé, A.: Statistics on diffeomorphisms via tangent space representations. Neuroimage 23, S161–S169 (2004)
Vialard, F.X., Risser, L., Rueckert, D., Cotter, C.J.: Diffeomorphic 3D image registration via geodesic shooting using an efficient adjoint calculation (2011) (preprint)
Younes, L., Qiu, A., Winslow, R.L., Miller, M.I.: Transport of relational structures in groups of diffeomorphisms. Journal of Mathematical Imaging and Vision 32, 41–56 (2008)
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Niethammer, M., Huang, Y., Vialard, FX. (2011). Geodesic Regression for Image Time-Series. In: Fichtinger, G., Martel, A., Peters, T. (eds) Medical Image Computing and Computer-Assisted Intervention – MICCAI 2011. MICCAI 2011. Lecture Notes in Computer Science, vol 6892. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23629-7_80
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DOI: https://doi.org/10.1007/978-3-642-23629-7_80
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