Abstract
We present a novel variational framework for image registration with explicit modeling of sliding motion, as it occurs, e.g., in the medical context at organ boundaries. The key of our method is a piecewise smooth deformation model that allows for discontinuities at the sliding interfaces while keeping the sliding domain in contact with its surrounding. The presented approach is generic and can be used with a large class of both image similarity measures and regularizers for the deformations. A useful byproduct of the proposed method is an automatic propagation of a given segmentation from one image to the other. We proof existence of minimizers under rather mild assumptions and present an efficient scheme for computing a numerical solution. The minimization is based on a splitting approach with alternating derivative based Gauss-Newton and fast first order convex optimization. Finally, we evaluate the proposed method on synthetic and real data.
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References
Zitová, B., Flusser, J.: Image registration methods: a survey. Image and Vision Computing 21, 977–1000 (2003)
Delmon, V., Rit, S., Pinho, R., Sarrut, D.: Direction dependent B-splines decomposition for the registration of sliding objects. In: Proceedings of the Fourth International Workshop on Pulmonary Image Analysis, pp. 45–55 (2011)
Schmidt-Richberg, A., Werner, R., Handels, H., Ehrhardt, J.: Estimation of slipping organ motion by registration with direction-dependent regularization. Medical Image Analysis 16, 150–159 (2012)
Pace, D., Aylward, S., Niethammer, M.: A locally adaptive regularization based on anisotropic diffusion for deformable image registration of sliding organs. IEEE Transactions on Medical Imaging 32, 2114–2126 (2013)
Baluwala, H.Y., Risser, L., Schnabel, J.A., Saddi, K.A.: Toward physiologically motivated registration of diagnostic CT and PET/CT of lung volumes. Medical Physics 40(2), 021 903-1–021 903-13 (2013)
Han, L., Hawkes, D., Barratt, D.: A hybrid biomechanical model-based image registration method for sliding objects. In: SPIE Medical Imaging, pp. 90 340G-1-6 (2014)
Derksen, A., Heldmann, S., Polzin, T., Berkels, B.: Image registration with sliding motion constraints for 4D CT motion correction. In: Bildverarbeitung für die Medizin 2015 (2015)
Vemuri, B., Chen, Y.: Joint image registration and segmentation. In: Vemuri, B., Chen, Y. (eds.) Geometric Level Set Methods in Imaging, Vision, and Graphics, pp. 251–269. Springer, New York (2003)
Yezzi, A., Zöllei, L., Kapur, T.: A variational framework for integrating segmentation and registration through active contours. Medical Image Analysis 7(2), 171–185 (2003)
Amiaz, T., Kiryati, N.: Piecewise-smooth dense optical flow via level sets. International Journal of Computer Vision 68(2), 111–124 (2006)
Modersitzki, J.: FAIR: Flexible Algorithms for Image Registration. SIAM (2009)
Ambrosio, L., Fusco, N., Pallara, D.: Functions of bounded variation and free discontinuity problems, ser. The Clarendon Press, Oxford Mathematical Monographs, New York (2000)
Evans, L.C.: Partial Differential Equations. American Math. Soc. (1998)
Nikolova, M., Esedoḡlu, S., Chan, T.F.: Algorithms for finding global minimizers of image segmentation and denoising models. SIAM Journal on Applied Mathematics 66(5), 1632–1648 (2006)
Berkels, B.: An unconstrained multiphase thresholding approach for image segmentation. In: Tai, X.-C., Mørken, K., Lysaker, M., Lie, K.-A. (eds.) SSVM 2009. LNCS, vol. 5567, pp. 26–37. Springer, Heidelberg (2009)
Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, New York (2006)
Chambolle, A., Pock, T.: A first-order primal-dual algorithm for convex problems with applications to imaging. Journal of Mathematical Imaging and Vision 40(1), 120–145 (2011)
Castillo, R., Castillo, E., Guerra, R., Johnson, V.E., McPhail, T., Garg, A.K., Guerrero, T.: A framework for evaluation of deformable image registration spatial accuracy using large landmark point sets. Physics in Medicine and Biology 54, 1849–1870 (2009)
Fischer, B., Modersitzki, J.: Curvature based image registration. Journal of Mathematical Imaging and Vision 18(1), 81–85 (2003)
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Heldmann, S., Polzin, T., Derksen, A., Berkels, B. (2015). An image registration framework for sliding motion with piecewise smooth deformations. In: Aujol, JF., Nikolova, M., Papadakis, N. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2015. Lecture Notes in Computer Science(), vol 9087. Springer, Cham. https://doi.org/10.1007/978-3-319-18461-6_27
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DOI: https://doi.org/10.1007/978-3-319-18461-6_27
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