Abstract
Registering pairs or groups of images is a widely-studied problem that has seen a variety of solutions in recent years. Most of these solutions are variational, using objective functions that should satisfy several basic and desired properties. In this paper, we pursue two additional properties – (1) invariance of objective function under identical warping of input images and (2) the objective function induces a proper metric on the set of equivalence classes of images – and motivate their importance. Then, a registration framework that satisfies these properties, using the L 2-norm between a novel representation of images, is introduced. Additionally, for multiple images, the induced metric enables us to compute a mean image, or a template, and perform joint registration. We demonstrate this framework using examples from a variety of image types and compare performances with some recent methods.
Chapter PDF
Similar content being viewed by others
Keywords
References
Beg, M., Miller, M., Trouvé, A., Younes, L.: Computing large deformation metric mappings via geodesic flows of diffeomorphisms. International Journal of Computer Vision 61, 139–157 (2005)
Bookstein, F.L.: Principal warps: Thin-plate splines and the decomposition of deformations. IEEE Transactions on Pattern Analysis and Machine Intelligence 11(6), 567–585 (1989)
Christensen, G., Johnson, H.: Consistent image registration. IEEE Transactions on Medical Imaging 20(7), 568–582 (2001)
Collignon, A., Vandermeulen, D., Marchal, G., Suetens, P.: Multimodality image registration by maximization of mutual information. IEEE Transactions on Medical Imaging 16(2), 187–198 (1997)
Davies, R., Twining, C., Cootes, T., Waterton, J., Taylor, C.: A minimum description length approach to statistical shape modeling. IEEE Transactions on Medical Imaging 21(5), 525–537 (2002)
Dupuis, P., Grenander, U.: Variational problems on flows of diffeomorphisms for image matching. Journal Quarterly of Applied Mathematics LVI (3), 587–600 (1998)
Eriksson, A., Astrom, K.: Bijective image registration using thin-plate splines. In: International Conference on Pattern Recognition, vol. 3, pp. 798–801 (2006)
Joshi, S., Davis, B., Jomier, B.M., Gerig, G.: Unbiased diffeomorphic atlas construction for computational anatomy. Neuroimage 23, 151–160 (2004)
Kurtek, S., Klassen, E., Ding, Z., Jacobson, S., Jacobson, J., Avison, M., Srivastava, A.: Parameterization-invariant shape comparisons of anatomical surfaces. IEEE Transactions on Medical Imaging 30, 849–858 (2011)
Kurtek, S., Klassen, E., Ding, Z., Srivastava, A.: A novel Riemannian framework for shape analysis of 3D objects. In: 2010 IEEE Conference on Computer Vision and Pattern Recognition, pp. 1625–1632 (2010)
Kurtek, S., Srivastava, A., Klassen, E., Laga, H.: Landmark-guided elastic shape analysis of spherically-parameterized surfaces. In: Computer Graphics Forum (Proceedings of Eurographics 2013, vol. 32(2), pp. 429–438 (2013)
Lorenzen, P., Davis, B., Joshi, S.: Unbiased atlas formation via large deformations metric mapping. In: Duncan, J.S., Gerig, G. (eds.) MICCAI 2005. LNCS, vol. 3750, pp. 411–418. Springer, Heidelberg (2005)
Miller, M., Trouve, A., Younes, L.: On the metrics and Euler-Lagrange equations of computational anatomy. Annual Review of Biomedical Engineering 4, 375–405 (2002)
Modat, M., Cardoso, M., Daga, P., Cash, D., Fox, N., Ourselin, S.: Inverse-consistent symmetric free form deformation. In: Dawant, B.M., Christensen, G.E., Fitzpatrick, J.M., Rueckert, D. (eds.) WBIR 2012. LNCS, vol. 7359, pp. 79–88. Springer, Heidelberg (2012)
Modersitzki, J.: FAIR: Flexible Algorithms for Image Registration. Society for Industrial and Applied Mathematics (2009)
Szeliski, R., Coughlan, J.: Spline-based image registration. International Journal of Computer Vision 22(3), 199–218 (1997)
Tagare, H., Groisser, D., Skrinjar, O.: Symmetric non-rigid registration: A geometric theory and some numerical techniques. Journal of Mathematical Imaging and Vision 34(1), 61–88 (2009)
Taquet, M., Macq, B., Warfield, S.: A generalized correlation coefficient: application to DTI and multi-fiber DTI. In: Mathematical Methods in Biomedical Image Analysis (2012)
Thirion, J.: Image matching as a diffusion process: an analogy with Maxwell’s demons. Medical Image Analysis 2(3), 243–260 (1998)
Trouve, A.: Diffeomorphisms groups and pattern matching in image analysis. International Journal of Computer Vision 28(3), 213–221 (1998)
Twining, C., Marsland, S., Taylor, C.: Groupwise non-rigid registration: The minimum description length approach. In: Proceedings of the British Machine Vision Converence (BMVC), vol. 1, pp. 417–426 (2004)
Vercauteren, T., Pennec, X., Perchant, A., Ayache, N.: Diffeomorphic demons: Efficient non-parametric image registration. NeuroImage 45(suppl. 1), S61–S72 (2009)
Viola, P., Wells III, W.: Alignment by maximization of mutual information. In: Fifth International Conference on Computer Vision, pp. 16–23 (June 1995)
Xie, Q., Kurtek, S., Christensen, G., Ding, Z., Klassen, E., Srivastava, A.: A novel framework for metric-based image registration. In: Dawant, B.M., Christensen, G.E., Fitzpatrick, J.M., Rueckert, D. (eds.) WBIR 2012. LNCS, vol. 7359, pp. 276–285. Springer, Heidelberg (2012)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Xie, Q., Kurtek, S., Klassen, E., Christensen, G.E., Srivastava, A. (2014). Metric-Based Pairwise and Multiple Image Registration. In: Fleet, D., Pajdla, T., Schiele, B., Tuytelaars, T. (eds) Computer Vision – ECCV 2014. ECCV 2014. Lecture Notes in Computer Science, vol 8690. Springer, Cham. https://doi.org/10.1007/978-3-319-10605-2_16
Download citation
DOI: https://doi.org/10.1007/978-3-319-10605-2_16
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-10604-5
Online ISBN: 978-3-319-10605-2
eBook Packages: Computer ScienceComputer Science (R0)