A Large Deformation Diffeomorphic Framework for Fast Brain Image Registration via Parallel Computing and Optimization

  • Jiong Wu
  • Xiaoying TangEmail author
Original Article


In this paper, we proposed an efficient approach for large deformation diffeomorphic metric mapping (LDDMM) for brain images by utilizing GPU-based parallel computing and a mixture automatic step size estimation method for gradient descent (MAS-GD). We systematically evaluated the proposed approach in terms of two matching cost functions, including the Sum of Squared Differences (SSD) and the Cross-Correlation (CC). The registration accuracy and computational efficiency on two datasets inducing respective 120 and 1,560 registration maps were evaluated and compared between CPU-based LDDMM-SSD and GPU-based LDDMM-SSD both utilizing backtracking line search for gradient descent (BLS-GD), GPU-based LDDMM (BLS-GD) and GPU-based LDDMM (MAS-GD) with each of the two matching cost functions being used. In addition, we compared our GPU-based LDDMM-CC (MAS-GD) with another widely-used state-of-the-art image registration algorithm, the symmetric diffeomorphic image registration with CC (SyN-CC). The GPU-based LDDMM-SSD was about 94 times faster than the CPU-based version (8.78 mins versus 828.35 mins) without sacrificing the Dice accuracy (0.8608 versus 0.8609). The computational time of LDDMM with MAS-GD for SSD and CC were shorter than that of LDDMM with BLS-GD (5.29 mins versus 8.78 mins for SSD and 6.69 mins versus 65.87 mins for CC), and the corresponding Dice scores were higher, especially for CC (0.8672 versus 0.8633). Compared with SyN-CC, the proposed algorithm, GPU-based LDDMM-CC (MAS-GD) had a higher registration accuracy (0.8672 versus 0.8612 and 0.7585 versus 0.7537 for the two datasets) and less computational time (6.80 mins versus 25.97 mins and 6.58 mins versus 26.23 mins for the two datasets).


LDDMM Brain image registration Parallelization Cross-Correlation Gradient descent optimization Automatic step-size estimation 



This study was supported by the National Key R&D Program of China (2017YFC0112404) and the National Natural Science Foundation of China (NSFC 81501546).


  1. Armijo, L. (1966). Minimization of functions having Lipschitz continuous first partial derivatives. Pacific Journal of Mathematics, 16(1), 1–3.CrossRefGoogle Scholar
  2. Ashburner, J., & Friston, K.J. (2011). Diffeomorphic registration using geodesic shooting and Gauss–Newton optimisation. NeuroImage, 55(3-3), 954–967.CrossRefGoogle Scholar
  3. Avants, B.B., Epstein, C.L., Grossman, M., Gee, J.C. (2008). Symmetric diffeomorphic image registration with cross-correlation: evaluating automated labeling of elderly and neurodegenerative brain. Medical Image Analysis, 12(1), 26–41.CrossRefGoogle Scholar
  4. Avants, B.B., Tustison, N.J., Song, G., Cook, P.A., Klein, A., Gee, J.C. (2011a). A reproducible evaluation of ants similarity metric performance in brain image registration. NeuroImage, 54(3), 2033–2044.CrossRefGoogle Scholar
  5. Avants, B.B., Tustison, N.J., Song, G., Cook, P.A., Klein, A., Gee, J.C. (2011b). A reproducible evaluation of ants similarity metric performance in brain image registration. NeuroImage, 54(3), 2033–2044.CrossRefGoogle Scholar
  6. Beg, M.F., Miller, M.I., Trouvé, A, Younes, L. (2005). Computing large deformation metric mappings via geodesic flows of diffeomorphisms. International Journal of Computer Vision, 61(2), 139–157.CrossRefGoogle Scholar
  7. Bengio, Y., Simard, P., Frasconi, P. (1994). Learning long-term dependencies with gradient descent is difficult. IEEE Transactions on Neural Networks, 5(2), 157–166.CrossRefGoogle Scholar
  8. Bottou, L. (1991). Stochastic gradient learning in neural networks. Proceedings of Neuro-Nımes, 91, 8.Google Scholar
  9. Brennan, R.W., & Rogers, P. (1995). Stochastic optimization applied to a manufacturing system operation problem. In Simulation conference proceedings (pp. 857–864).Google Scholar
  10. Ceritoglu, C., Tang, X., Chow, M., Hadjiabadi, D., Shah, D., Brown, T., Burhanullah, M.H., Trinh, H., Hsu, J.T., Ament, K.A., et al. (2013). Computational analysis of lddmm for brain mapping. Frontiers in Neuroscience, 7.Google Scholar
  11. Cole-Rhodes, A.A., Johnson, K.L., LeMoigne, J., Zavorin, I. (2003). Multiresolution registration of remote sensing imagery by optimization of mutual information using a stochastic gradient. IEEE Transactions on Image Processing, 12(12), 1495–1511.CrossRefGoogle Scholar
  12. Dice, L.R. (1945). Measures of the amount of ecologic association between species. Ecology, 26(3), 297–302.CrossRefGoogle Scholar
  13. Fonov, V., Evans, A.C., Botteron, K., Almli, C.R., McKinstry, R.C., Collins, D.L., Group, B.D.C., et al. (2011). Unbiased average age-appropriate atlases for pediatric studies. NeuroImage, 54(1), 313–327.CrossRefGoogle Scholar
  14. Gennatas, E.D., Avants, B.B., Wolf, D.H., Satterthwaite, T.D., Ruparel, K., Ciric, R., Hakonarson, H., Gur, R.E., Gur, R.C. (2017). Age-related effects and sex differences in gray matter density, volume, mass, and cortical thickness from childhood to young adulthood. Journal of Neuroscience, 37(20), 5065–5073.CrossRefGoogle Scholar
  15. George, A.P., & Powell, W.B. (2006). Adaptive stepsizes for recursive estimation with applications in approximate dynamic programming. Machine learning, 65(1), 167–198.CrossRefGoogle Scholar
  16. Glaunès, J., Qiu, A., Miller, M.I., Younes, L. (2008). Large deformation diffeomorphic metric curve mapping. International Journal of Computer Vision, 80(3), 317.CrossRefGoogle Scholar
  17. Ha, L, Krüger, J., Joshi, S, Silva, C.T. (2011). Multiscale unbiased diffeomorphic atlas construction on multi-gpus. In GPU computing gems emerald edition. Elsevier (pp. 771–791).Google Scholar
  18. Hardie, R.C., Barnard, K.J., Armstrong, E.E. (1997). Joint map registration and high-resolution image estimation using a sequence of undersampled images. IEEE Transactions on Image Processing, 6(12), 1621–1633.CrossRefGoogle Scholar
  19. Harold, J., Kushner, G., Yin, G. (1997). Stochastic approximation and recursive algorithm and applications. Application of Mathematics, 35.Google Scholar
  20. Hernandez, M. (2014). Gauss–newton inspired preconditioned optimization in large deformation diffeomorphic metric mapping. Physics in Medicine & Biology, 59(20), 6085.CrossRefGoogle Scholar
  21. Joshi, S.C., & Miller, M.I. (2000). Landmark matching via large deformation diffeomorphisms. IEEE Transactions on Image Processing, 9(8), 1357–1370.CrossRefGoogle Scholar
  22. Klein, S., Staring, M., Pluim, J.P.W. (2007). Evaluation of optimization methods for nonrigid medical image registration using mutual information and b-splines. IEEE Transactions on Image Processing, 16(12), 2879.CrossRefGoogle Scholar
  23. Klein, A., Andersson, J., Ardekani, B.A., Ashburner, J., Avants, B., Chiang, M.C., Christensen, G.E., Collins, D.L., Gee, J., Hellier, P., et al. (2009a). Evaluation of 14 nonlinear deformation algorithms applied to human brain mri registration. NeuroImage, 46(3), 786–802.CrossRefGoogle Scholar
  24. Klein, S., Pluim, J.P.W., Staring, M., Viergever, M.A. (2009b). Adaptive stochastic gradient descent optimisation for image registration. International Journal of Computer Vision, 81(3), 227.CrossRefGoogle Scholar
  25. Kutten, K.S., Charon, N., Miller, M.I., Ratnanather, J.T., Matelsky, J., Baden, A.D., Lillaney, K., Deisseroth, K., Ye, L., Vogelstein, J.T. (2017). A large deformation diffeomorphic approach to registration of CLARITY images via mutual information (pp. 275–282). Cham: Springer International Publishing.Google Scholar
  26. Miller, M.I., Trouve, A., Younes, L. (2002). On the metrics and euler-lagrange equations of computational anatomy. Annual Review of Biomedical Engineering, 4(1), 375.CrossRefGoogle Scholar
  27. Muyan-Ozcelik, P, Owens, J.D., Xia, J., Samant, S.S. (2008). Fast deformable registration on the gpu: a cuda implementation of demons. In International conference on computational sciences and its applications (pp. 223–233).Google Scholar
  28. Oliveira, F.P., & Tavares, J.M.R. (2014). Medical image registration: a review. Computer Methods in Biomechanics and Biomedical Engineering, 17(2), 73–93.CrossRefGoogle Scholar
  29. Polzin, T, Niethammer, M, Heinrich, M.P., Handels, H., Modersitzki, J. (2016). Memory efficient lddmm for lung ct. In International conference on medical image computing and computer-assisted intervention (pp. 28–36).Google Scholar
  30. Qiao, Y., Van, L.B., Lelieveldt, B.P., Staring, M. (2016). Fast automatic step size estimation for gradient descent optimization of image registration. IEEE Transactions on Medical Imaging, 35(2), 391.CrossRefGoogle Scholar
  31. Robbins, H., & Monro, S. (1951). A stochastic approximation method. The Annals of Mathematical Statistics, 400–407.Google Scholar
  32. Rousseau, F., Habas, P.A., Studholme, C. (2011). A supervised patch-based approach for human brain labeling. IEEE Transactions on Medical Imaging, 30(10), 1852–1862.CrossRefGoogle Scholar
  33. Shamonin, D.P., Bron, E.E., Lelieveldt, B.P.F., Smits, M., Klein, S., Staring, M. (2013). Fast parallel image registration on cpu and gpu for diagnostic classification of alzheimer’s disease. Frontiers in Neuroinformatics, 7(50), 50.PubMedGoogle Scholar
  34. Shams, R., Sadeghi, P., Kennedy, R.A., Hartley, R.I. (2010). A survey of medical image registration on multicore and the gpu. Signal Processing Magazine IEEE, 27(2), 50–60.CrossRefGoogle Scholar
  35. Shattuck, D.W., Mirza, M., Adisetiyo, V., Hojatkashani, C., Salamon, G., Narr, K.L., Poldrack, R.A., Bilder, R.M., Toga, A.W. (2008). Construction of a 3d probabilistic atlas of human cortical structures. NeuroImage, 39(3), 1064–1080.CrossRefGoogle Scholar
  36. Spall, J.C. (2005). Introduction to stochastic search and optimization: estimation, simulation, and control Vol. 65. New York: Wiley.Google Scholar
  37. Staniforth, A., & Côté, J. (1991). Semi-lagrangian integration schemes for atmospheric models—a review. Monthly Weather Review, 119(9), 2206–2223.CrossRefGoogle Scholar
  38. Suri, R, & Leung, Y.T. (1987). Single run optimization of a Siman model for closed loop flexible assembly systems. In Proceedings of the 19th conference on winter simulation. ACM (pp. 738–748).Google Scholar
  39. Thévenaz, P, & Unser, M. (2000). Optimization of mutual information for multiresolution image registration. IEEE Transactions on Image Processing A Publication of the IEEE Signal Processing Society, 9(12), 2083–99.CrossRefGoogle Scholar
  40. Tward, D.J., Kolasny, A, Sicat, C.S., Brown, T, Miller, M.I. (2016). Tools for studying populations and timeseries of neuroanatomy enabled through gpu acceleration in the computational anatomy gateway. In Xsede16 Conference on diversity, big data, and science at scale (p. 15).Google Scholar
  41. Vaillant, M, & Glaunès, J. (2005). Surface matching via currents. In Information processing in medical imaging. Springer (pp. 1–5).Google Scholar
  42. Vysochanskij, D., & Petunin, Y.I. (1980). Justification of the 3σ rule for unimodal distributions. Theory of Probability and Mathematical Statistics, 21, 25–36.Google Scholar
  43. Wang, H., Suh, J.W., Das, S.R., Pluta, J.B., Craige, C., Yushkevich, P.A. (2013). Multi-atlas segmentation with joint label fusion. IEEE Transactions on Pattern Analysis and Machine Intelligence, 35(3), 611–623.CrossRefGoogle Scholar
  44. Woods, R.P., Grafton, S.T., Holmes, C.J., Cherry, S.R., Mazziotta, J.C. (1998a). Automated image registration: I. General methods and intrasubject, intramodality validation. Journal of Computer Assisted Tomography, 22(1), 139–152.CrossRefGoogle Scholar
  45. Woods, R.P., Grafton, S.T., Watson, J.D., Sicotte, N.L., Mazziotta, J.C. (1998b). Automated image registration: II. intersubject validation of linear and nonlinear models. Journal of Computer Assisted Tomography, 22 (1), 153–165.CrossRefGoogle Scholar
  46. Wu, J, & Tang, X. (2018). Fast diffeomorphic image registration via gpu-based parallel computing: an investigation of the matching cost function. In Medical imaging 2018: image processing, international society for optics and photonics, (Vol. 10574 p. 105742S).Google Scholar
  47. Yang, X., Kwitt, R., Styner, M., Niethammer, M. (2017). Quicksilver: fast predictive image registration–a deep learning approach. NeuroImage, 158, 378–396.CrossRefGoogle Scholar
  48. Zhang, M, Liao, R, Dalca, A.V., Turk, E.A., Luo, J., Grant, P.E., Golland, P. (2017). Frequency diffeomorphisms for efficient image registration. In International conference on information processing in medical imaging (pp. 559–570).Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Electronics and Information TechnologySun Yat-sen UniversityGuangzhouChina
  2. 2.Department of Electrical and Electronic EngineeringSouthern University of Science and TechnologyShenzhenChina

Personalised recommendations