Abstract
Current spherical surface registration methods achieve good performance on alignment and spatial normalization of cortical surfaces across individuals in neuroimaging analysis. However, they are computationally intensive, since they have to optimize an objective function independently for each pair of surfaces. In this paper, we present a fast learning-based algorithm that makes use of the recent development in spherical Convolutional Neural Networks (CNNs) for spherical cortical surface registration. Given a set of surface pairs without supervised information such as ground truth deformation fields or anatomical landmarks, we formulate the registration as a parametric function and learn its parameters by enforcing the feature similarity between one surface and the other one warped by the estimated deformation field using the function. Then, given a new pair of surfaces, we can quickly infer the spherical deformation field registering one surface to the other one. We model this parametric function using three orthogonal Spherical U-Nets and use spherical transform layers to warp the spherical surfaces, while imposing smoothness constraints on the deformation field. All the layers in the network are well-defined and differentiable, thus the parameters can be effectively learned. We show that our method achieves accurate cortical alignment results on 102 subjects, comparable to two state-of-the-art methods: Spherical Demons and MSM, while runs much faster.
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We used the MSM algorithm in fsl/6.0.0.
References
Balakrishnan, G., Zhao, A., Sabuncu, M.R., Guttag, J., Dalca, A.V.: An unsupervised learning model for deformable medical image registration. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 9252–9260 (2018)
Dalca, A.V., Balakrishnan, G., Guttag, J., Sabuncu, M.R.: Unsupervised Learning for Fast Probabilistic Diffeomorphic Registration. In: Frangi, A.F., Schnabel, J.A., Davatzikos, C., Alberola-López, C., Fichtinger, G. (eds.) MICCAI 2018. LNCS, vol. 11070, pp. 729–738. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-00928-1_82
Fischl, B., Sereno, M.I., Tootell, R.B., Dale, A.M.: High-resolution intersubject averaging and a coordinate system for the cortical surface. Hum. Brain Mapp. 8(4), 272–284 (1999)
Gahm, J.K., Shi, Y., Initiative, A.D.N., et al.: Riemannian metric optimization on surfaces (RMOS) for intrinsic brain mapping in the Laplace-Beltrami embedding space. Med. Image Anal. 46, 189–201 (2018)
Kingma, D.P., Ba, J.: Adam: a method for stochastic optimization. arXiv preprint arXiv:1412.6980 (2014)
Li, G., et al.: Measuring the dynamic longitudinal cortex development in infants by reconstruction of temporally consistent cortical surfaces. Neuroimage 90, 266–279 (2014)
Li, G., Wang, L., Shi, F., Gilmore, J.H., Lin, W., Shen, D.: Construction of 4D high-definition cortical surface atlases of infants: methods and applications. Med. Image Anal. 25(1), 22–36 (2015)
Li, G., et al.: Computational neuroanatomy of baby brains: a review. NeuroImage 185, 906–925 (2019)
Lombaert, H., Sporring, J., Siddiqi, K.: Diffeomorphic Spectral Matching of Cortical Surfaces. In: Gee, J.C., Joshi, S., Pohl, K.M., Wells, W.M., Zöllei, L. (eds.) IPMI 2013. LNCS, vol. 7917, pp. 376–389. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38868-2_32
Möller, T.: A fast triangle-triangle intersection test. J. Graph. Tools 2(2), 25–30 (1997)
Nenning, K.H., Liu, H., Ghosh, S.S., Sabuncu, M.R., Schwartz, E., Langs, G.: Diffeomorphic functional brain surface alignment: functional demons. NeuroImage 156, 456–465 (2017)
Niethammer, M., Kwitt, R., Vialard, F.X.: Metric learning for image registration. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 8463–8472 (2019)
Robinson, E.C., et al.: Multimodal surface matching with higher-order smoothness constraints. NeuroImage 167, 453–465 (2018)
Robinson, E.C., et al.: MSM: a new flexible framework for multimodal surface matching. Neuroimage 100, 414–426 (2014)
Ronneberger, O., Fischer, P., Brox, T.: U-Net: Convolutional Networks for Biomedical Image Segmentation. In: Navab, N., Hornegger, J., Wells, W.M., Frangi, A.F. (eds.) MICCAI 2015. LNCS, vol. 9351, pp. 234–241. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-24574-4_28
Vercauteren, T., Pennec, X., Perchant, A., Ayache, N.: Diffeomorphic demons: efficient non-parametric image registration. NeuroImage 45(1), S61–S72 (2009)
Wang, L., Li, G., Shi, F., Cao, X., Lian, C., Nie, D., Liu, M., Zhang, H., Li, G., Wu, Z., Lin, W., Shen, D.: Volume-Based Analysis of 6-Month-Old Infant Brain MRI for Autism Biomarker Identification and Early Diagnosis. In: Frangi, A.F., Schnabel, J.A., Davatzikos, C., Alberola-López, C., Fichtinger, G. (eds.) MICCAI 2018. LNCS, vol. 11072, pp. 411–419. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-00931-1_47
Wang, Q., Kim, M., Shi, Y., Wu, G., Shen, D., Initiative, A.D.N., et al.: Predict brain MR image registration via sparse learning of appearance and transformation. Med. Image Anal. 20(1), 61–75 (2015)
Yeo, B.T., Sabuncu, M.R., Vercauteren, T., Ayache, N., Fischl, B., Golland, P.: Spherical demons: fast diffeomorphic landmark-free surface registration. IEEE Trans. Med. Imaging 29(3), 650–668 (2009)
Zhao, F., Xia, S., Wu, Z., Duan, D., Wang, L., Lin, W., Gilmore, J.H., Shen, D., Li, G.: Spherical U-Net on Cortical Surfaces: Methods and Applications. In: Chung, A.C.S., Gee, J.C., Yushkevich, P.A., Bao, S. (eds.) IPMI 2019. LNCS, vol. 11492, pp. 855–866. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-20351-1_67
Acknowledgements
This work was partially supported by NIH grants (MH116225, MH117943, MH109773). This work also utilizes approaches developed by an NIH grant (1U01MH110274) and the efforts of the UNC/UMN Baby Connectome Project Consortium.
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Zhao, F. et al. (2020). Unsupervised Learning for Spherical Surface Registration. In: Liu, M., Yan, P., Lian, C., Cao, X. (eds) Machine Learning in Medical Imaging. MLMI 2020. Lecture Notes in Computer Science(), vol 12436. Springer, Cham. https://doi.org/10.1007/978-3-030-59861-7_38
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