Abstract
Image registration, especially the quantification of image similarity, is an important task in image processing. Various approaches for the comparison of two images are discussed in the literature. However, although most of these approaches perform very well in a two image scenario, an extension to a multiple images scenario deserves attention. In this article, we discuss and compare registration methods for multiple images. Our key assumption is, that information about the singular values of a feature matrix of images can be used for alignment. We introduce, discuss and relate three recent approaches from the literature: the Schatten q-norm based \(\mathrm {S}q\mathrm {N}\) distance measure, a rank based approach, and a feature volume based approach. We also present results for typical applications such as dynamic image sequences or stacks of histological sections. Our results indicate that the \(\mathrm {S}q\mathrm {N}\) approach is in fact a suitable distance measure for image registration. Moreover, our examples also indicate that the results obtained by \(\mathrm {S}q\mathrm {N}\) are superior to those obtained by its competitors.
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Bhatia, K.K., Hajnal, J.V., Puri, B.K., Edwards, A.D., Rueckert, D.: Consistent groupwise non-rigid registration for atlas construction. In: 2004 2nd IEEE International Symposium on Biomedical Imaging: Nano to Macro (IEEE Cat No. 04EX821), vol. 1, pp. 908–911 (2004)
Brehmer, K., Wacker, B., Modersitzki, J.: A novel similarity measure for image sequences. In: Klein, S., Staring, M., Durrleman, S., Sommer, S. (eds.) WBIR 2018. LNCS, vol. 10883, pp. 47–56. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-92258-4_5
Brehmer, K., Wacker, B., Modersitzki, J.: Simultaneous registration of image sequences - a novel singular value based images similarity measure. PAMM 18(1), e201800370 (2018)
Cootes, T.F., Marsland, S., Twining, C.J., Smith, K., Taylor, C.J.: Groupwise diffeomorphic non-rigid registration for automatic model building. In: Pajdla, T., Matas, J. (eds.) ECCV 2004. LNCS, vol. 3024, pp. 316–327. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24673-2_26
Fischler, M.A., Elschlager, R.A.: The representation and matching of pictorial structures. IEEE Tran. Comput. 22(1), 67–92 (1973)
Friedman, S., Weisberg, H.F.: Interpreting the first eigenvalue of a correlation matrix. Educ. Psychol. Measure. 41(1), 11–21 (1981)
Geng, X., Christensen, G.E., Gu, H., Ross, T.J., Yang, Y.: Implicit reference-based group-wise image registration and its application to structural and functional MRI. NeuroImage 47(4), 1341–1351 (2009)
Guyader, J.M., et al.: Groupwise image registration based on a total correlation dissimilarity measure for quantitative MRI and dynamic imaging data. Sci. Rep. 8(1), 13112 (2018)
Haber, E., Modersitzki, J.: A multilevel method for image registration. SIAM J. Sci. Comput. 27(5), 1594–1607 (2006)
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
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
Huizinga, W., et al.: PCA-based groupwise image registration for quantitative mri. Med. Image Anal. 29, 65–78 (2016)
Joshi, S., Davis, B., Jomier, M., Gerig, G.: Unbiased diffeomorphic atlas construction for computational anatomy. NeuroImage 23, S151–S160 (2004)
Marschner, H., et al.: High-resolution quantitative magnetization transfer imaging of post-mortem marmoset brain. In: 22nd Annual Meeting of the International Society for Magnetic Resonance in Medicine (2014)
Modersitzki, J.: FAIR: Flexible Algorithms for Image Registration. SIAM, Philadelphia (2009)
Nocedal, J., Wright, S.J.: Numerical Optimization. Springer Series in Operations Research, 2nd edn. Springer, Heidelberg (2006). https://doi.org/10.1007/978-3-540-35447-5
Papadopoulo, T., Lourakis, M.I.A.: Estimating the jacobian of the singular value decomposition: theory and applications. In: Vernon, D. (ed.) ECCV 2000. LNCS, vol. 1842, pp. 554–570. Springer, Heidelberg (2000). https://doi.org/10.1007/3-540-45054-8_36
Polfliet, M., Klein, S., Huizinga, W., Paulides, M.M., Niessen, W.J., Vandemeulebroucke, J.: Intrasubject multimodal groupwise registration with the conditional template entropy. Med. Image Anal. 46, 15–25 (2018)
Schmitt, O., Modersitzki, J., Heldmann, S., Wirtz, S., Fischer, B.: Image registration of sectioned brains. Int. J. Comput. Vis. 73(1), 5–39 (2006)
Sotiras, A., Davatzikos, C., Paragios, N.: Deformable medical image registration: A survey. IEEE Trans. Med. Imaging 32(7), 1153–1190 (2013)
Yigitsoy, M., Wachinger, C., Navab, N.: Temporal groupwise registration for motion modeling. Inf. Process. Med. Imaging 22, 648–59 (2011)
Zitová, B., Flusser, J.: Image registartion methods: a survey. Image Vis. Comput. 21, 977–1000 (2003)
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The authors acknowledge the financial support by the Federal Ministry of Education and Research of Germany in the framework of MED4D (project number 05M16FLA).
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Brehmer, K., Aggrawal, H.O., Heldmann, S., Modersitzki, J. (2019). Variational Registration of Multiple Images with the SVD Based \(\mathrm {S}q\mathrm {N}\) Distance Measure. In: Lellmann, J., Burger, M., Modersitzki, J. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2019. Lecture Notes in Computer Science(), vol 11603. Springer, Cham. https://doi.org/10.1007/978-3-030-22368-7_20
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DOI: https://doi.org/10.1007/978-3-030-22368-7_20
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