Abstract
First Order Locally Orderless Registration (FLOR) is a scale-space framework for image density estimation used for defining image similarity, mainly for Image Registration. The Locally Orderless Registration framework was designed in principle to use zeroth-order information, providing image density estimates over three scales: image scale, intensity scale, and integration scale. We extend it to take first-order information into account and hint at higher-order information. We show how standard similarity measures extend into the framework. We study especially Sum of Squared Differences (SSD) and Normalized Cross-Correlation (NCC) but present the theory of how Normalised Mutual Information (NMI) can be included.
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References
Avants, B.B., Epstein, C.L., Grossman, M., Gee, J.C.: Symmetric diffeomorphic image registration with cross-correlation: evaluating automated labeling of elderly and neurodegenerative brain. Med. Image Anal. 12(1), 26–41 (2008)
Darkner, S., Pai, A., Liptrot, M., Sporring, J.: Collocation for diffeomorphic deformations in medical image registration. IEEE Trans. Pattern Anal. Mach. Intell. 40(7), 1570–1583 (2018). https://doi.org/10.1109/TPAMI.2017.2730205
Darkner, S., Sporring, J.: Generalized partial volume: an inferior density estimator to Parzen windows for normalized mutual information. In: Székely, G., Hahn, H.K. (eds.) IPMI 2011. LNCS, vol. 6801, pp. 436–447. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22092-0_36
Darkner, S., Sporring, J.: Locally orderless registration. IEEE Trans. Pattern Anal. Mach. Intell. 35(6), 1437–1450 (2013)
Haber, E., Modersitzki, J.: Intensity gradient based registration and fusion of multi-modal images. In: Larsen, R., Nielsen, M., Sporring, J. (eds.) MICCAI 2006. LNCS, vol. 4191, pp. 726–733. Springer, Heidelberg (2006). https://doi.org/10.1007/11866763_89
Hermosillo, G., Chefd’Hotel, C., Faugeras, O.: Variational methods for multimodal image matching. Int. J. Comput. Vision 50(3), 329–343 (2002)
Janssen, M.H., Janssen, A.J., Bekkers, E.J., Bescos, J.O., Duits, R.: Design and processing of 3D invertible orientation scores of 3D images. J. Math. Imaging Vis. 60, 1427–1458 (2018)
Jensen, H.G., Lauze, F., Nielsen, M., Darkner, S.: Locally orderless registration for diffusion weighted images. In: Navab, N., Hornegger, J., Wells, W.M., Frangi, A.F. (eds.) MICCAI 2015. LNCS, vol. 9350, pp. 305–312. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-24571-3_37
Klein, A., et al.: Evaluation of 14 nonlinear deformation algorithms applied to human brain MRI registration. Neuroimage 46(3), 786–802 (2009)
Koenderink, J.J., Van Doorn, A.J.: The structure of locally orderless images. Int. J. Comput. Vision 31(2), 159–168 (1999)
König, L., Derksen, A., Papenberg, N., Haas, B.: Deformable image registration for adaptive radiotherapy with guaranteed local rigidity constraints. Radiat. Oncol. 11(1), 1–9 (2016)
König, L., Rühaak, J.: A fast and accurate parallel algorithm for non-linear image registration using normalized gradient fields. In: 2014 IEEE 11th International Symposium on Biomedical Imaging (ISBI), pp. 580–583. IEEE (2014)
Rueckert, D., Sonoda, L.I., Hayes, C., Hill, D.L., Leach, M.O., Hawkes, D.J.: Nonrigid registration using free-form deformations: application to breast MR images. IEEE Trans. Med. Imaging 18(8), 712–721 (1999)
Sommer, S., Nielsen, M., Darkner, S., Pennec, X.: Higher-order momentum distributions and locally affine LDDMM registration. SIAM J. Imag. Sci. 6(1), 341–367 (2013)
Theljani, A., Chen, K.: An augmented lagrangian method for solving a new variational model based on gradients similarity measures and high order regularization for multimodality registration. Inverse Probl. Imaging 13(2), 309–335 (2019)
Acknowledgements
This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 764644. This paper only contains the author’s views and the Research Executive Agency and the Commission are not responsible for any use that may be made of the information it.
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Darkner, S., Vidarte, J.D.T., Lauze, F. (2021). First Order Locally Orderless Registration. In: Elmoataz, A., Fadili, J., Quéau, Y., Rabin, J., Simon, L. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2021. Lecture Notes in Computer Science(), vol 12679. Springer, Cham. https://doi.org/10.1007/978-3-030-75549-2_15
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