Abstract
We introduce a family of fast spherical registration algorithms: a spherical fluid model and several modifications of the spherical demons algorithm introduced in [1]. Our algorithms are based on fast convolution of tangential spherical vector fields in the spectral domain. Using the vector harmonic representation of spherical fields, we derive a more principled approach for kernel smoothing via Mercer’s theorem and the diffusion equation. This is a non-trivial extension of scalar spherical convolution, as the vector harmonics do not generalize directly from scalar harmonics on the sphere, as in the Euclidean case. The fluid algorithm is optimized in the Eulerian frame, leading to a very efficient optimization. Several new adaptations of the demons algorithm are presented, including compositive and diffeomorphic demons, as well as fluid-like and diffusion-like regularization. The resulting algorithms are all significantly faster than [1], while also retaining greater flexibility. Our algorithms are validated and compared using cortical surface models.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Yeo, B.T.T., Sabuncu, M.R., Vercauteren, T., Ayache, N., Fischl, B., Golland, P.: Spherical Demons: Fast Diffeomorphic Landmark-Free Surface Registration. IEEE T. Med. Imaging 29, 650–668 (2010)
Wang, Y., Chan, T.F., Toga, A.W., Thompson, P.M.: Multivariate tensor-based brain anatomical surface morphometry via holomorphic one-forms. In: Yang, G.-Z., Hawkes, D., Rueckert, D., Noble, A., Taylor, C. (eds.) MICCAI 2009, Part I. LNCS, vol. 5761, pp. 337–344. Springer, Heidelberg (2009)
Shi, Y., Morra, J.H., Thompson, P.M., Toga, A.W.: Inverse-consistent surface mapping with Laplace-Beltrami eigen-features. In: Prince, J.L., Pham, D.L., Myers, K.J. (eds.) IPMI 2009. LNCS, vol. 5636, pp. 467–478. Springer, Heidelberg (2009)
Glaunes, J., Vaillant, M., Miller, M.I.: Landmark matching via large deformation diffeomorphisms on the sphere. Journal of Mathematical Imaging and Vision 20, 179–200 (2004)
Shi, J., Thompson, P.M., Gutman, B., Wang, Y.: Surface fluid registration of conformal representation: Application to detect disease burden and genetic influence on hippocampus. Neuroimage 78, 111–134 (2013)
Christensen, G.E., Rabbitt, R.D., Miller, M.I.: Deformable templates using large deformation kinematics. IEEE Transactions on Image Processing 5, 1435–1447 (1996)
Thompson, P.M., Woods, R.P., Mega, M.S., Toga, A.W.: Mathematical/computational challenges in creating deformable and probabilistic atlases of the human brain. Human Brain Mapping 9, 81–92 (2000)
Lepore, N., Leow, A., Thompson, P.: Landmark matching on the sphere using distance functions. In: 3rd IEEE International Symposium on Biomedical Imaging: Nano to Macro, pp. 450–453 (2006)
Miller, M.I., Younes, L.: Group Actions, Homeomorphisms, and Matching: A General Framework. Int. J. Comput. Vision 41, 61–84 (2001)
Tosun, D., Prince, J.L.: Cortical surface alignment using geometry driven multispectral optical flow. In: Christensen, G.E., Sonka, M. (eds.) IPMI 2005. LNCS, vol. 3565, pp. 480–492. Springer, Heidelberg (2005)
Fischl, B., Sereno, M., Tootell, R., Dale, A.: High-resolution intersubject averaging and a coordinate system for the cortical surface. Human Brain Mapping 8, 272–284 (1999)
Thirion, J.P.: Image matching as a diffusion process: an analogy with Maxwell’s demons. Medical Image Analysis 2, 243–260 (1998)
Vercauteren, T., Pennec, X., Perchant, A., Ayache, N.: Diffeomorphic demons: Efficient non-parametric image registration. Neuroimage 45, S61–S72 (2009)
D’Agostino, E., Maes, F., Vandermeulen, D., Suetens, P.: A viscous fluid model for multimodal non-rigid image registration using mutual information. Medical Image Analysis 7, 565–575 (2003)
Bro-Nielsen, M., Gramkow, C.: Fast Fluid Registration of Medical Images. In: Höhne, K.H., Kikinis, R. (eds.) VBC 1996. LNCS, vol. 1131, pp. 267–276. Springer, Heidelberg (1996)
Kostelec, P.J., Maslen, D.K., Healy, D.M., Rockmore, D.N.: Computational harmonic analysis for tensor fields on the two-sphere. J. Comput. Phys. 162, 514–535 (2000)
Courant, R., Hilbert, D.: Methods of mathematical physics. Interscience Publishers, New York (1953)
Chung, M.K., Hartley, R., Dalton, K.M., Davidson, R.J.: Encoding Cortical Surface by Spherical Harmonics. Stat. Sinica 18, 1269–1291 (2008)
Cachier, P., Ayache, N.: Isotropic Energies, Filters and Splines for Vector Field Regularization. J. Math. Imaging Vis. 20, 251–265 (2004)
Healy, D.M., Rockmore, D.N., Kostelec, P.J., Moore, S.: FFTs for the 2-sphere-improvements and variations. J. Fourier Anal. Appl. 9, 341–385 (2003)
Friedel, I., Schroeder, P., Desbrun, M.: Unconstrained spherical parameterization. In: ACM SIGGRAPH 2005 Sketches, p. 134. ACM, Los Angeles (2005)
Gutman, B., Wang, Y., Lui, L.M., Chan, T.F., Thompson, P.M., Toga, A.W.: Shape Registration with Spherical Cross Correlation. In: MICCAI Workshop on Mathematical Foundations in Computational Anatomy, MFCA 2008 (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer International Publishing Switzerland
About this paper
Cite this paper
Gutman, B.A., Madsen, S.K., Toga, A.W., Thompson, P.M. (2013). A Family of Fast Spherical Registration Algorithms for Cortical Shapes. In: Shen, L., Liu, T., Yap, PT., Huang, H., Shen, D., Westin, CF. (eds) Multimodal Brain Image Analysis. MBIA 2013. Lecture Notes in Computer Science, vol 8159. Springer, Cham. https://doi.org/10.1007/978-3-319-02126-3_24
Download citation
DOI: https://doi.org/10.1007/978-3-319-02126-3_24
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-02125-6
Online ISBN: 978-3-319-02126-3
eBook Packages: Computer ScienceComputer Science (R0)