Abstract
Learning surface data is fundamental to neuroscience. Recent advances has enabled the use of graph convolution filters directly within neural network frameworks. These filters are, however, constrained to a single fixed-graph structure. A pooling strategy remains yet to be defined for learning graph-node data in non-predefined graph structures. This lack of flexibility in graph convolutional architectures currently limits applications on brain surfaces. Graph structures and number of mesh nodes, indeed, highly vary across brain geometries. This paper proposes a new general graph-based pooling method for processing full-sized surface-valued data, as input layers of graph neural networks, towards predicting subject-based variables, as output information. This novel method learns an intrinsic aggregation of input graph nodes based on the geometry of the input graph. This is leveraged using recent advances in spectral graph alignment where the surface parameterization becomes common across multiple brain geometries. These novel adaptive intrinsic pooling layers enable the exploration of entirely new architectures of graph neural networks, which were previously constrained to one single fixed structure in a dataset. We demonstrate the flexibility of the new pooling strategy in two proof-of-concept applications, namely, the classification of disease stages and regression of subject’s ages using directly the surface data from varying mesh geometries.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Arbabshirani, M.R., Plis, S., Sui, J., Calhoun, V.D.: Single subject prediction of brain disorders in neuroimaging: promises and pitfalls. NeuroImage 145, 137–165 (2017)
Hua, X., et al.: Unbiased tensor-based morphometry: improved robustness and sample size estimates for Alzheimer’s disease clinical trials. NeuroImage 66, 648–661 (2013)
Fischl, B., et al.: Automatically parcellating the cortex. Cereb. Cortex 14, 11–22 (2004)
Yeo, B.T., Sabuncu, M.R., Vercauteren, T., Ayache, N., Fischl, B., Golland, P.: Spherical demons: fast diffeomorphic surface registration. TMI 29, 650–668 (2010)
Styner, M., et al.: Framework for the statistical shape analysis of brain structures using SPHARM-PDM. Insight J. (2006)
Lecun, Y., Bottou, L., Bengio, Y., Haffner, P.: Gradient-based learning applied to document recognition. ISP 86, 2278–2324 (1998)
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
Kamnitsas, K., et al.: Efficient multi-scale 3D CNN with fully connected CRF for accurate brain lesion segmentation. MedIA 36, 61–78 (2017)
Bruna, J., Zaremba, W., Szlam, A., LeCun, Y.: Spectral networks and locally connected networks on graphs. In: ICLR (2014)
Kipf, T.N., Welling, M.: Semi-Supervised classification with graph convolutional networks. In: ICLR (2017)
Defferrard, M., Bresson, X., Vandergheynst, P.: Convolutional neural networks on graphs with fast localized spectral filtering. In: NIPS (2016)
Monti, F., Boscaini, D., Masci, J., Rodolà, E., Svoboda, J., Bronstein, M.M.: Geometric deep learning on graphs and manifolds using CNNs. In: CVPR (2017)
Xu, Y., Fan, T., Xu, M., Zeng, L., Qia, Y.: SpiderCNN: deep learning on point sets with parameterized convolutional filters. In: ECCV (2018)
Levie, R., Monti, F., Bresson, X., Bronstein, M.M.: CayleyNets: graph convolutional neural networks with complex rational spectral filters. In: ICLR (2018)
Fey, M., Lenssen, J.E., Weichert, F., Müller, H.: SplineCNN: fast geometric deep learning with continuous B-Spline kernels. In: CVPR (2018)
Ovsjanikov, M., Ben-Chen, M., Solomon, J., Butscher, A., Guibas, L.: Functional maps: a flexible representation of maps between shapes. In: SIGGRAPH (2012)
Yi, L., Su, H., Guo, X., Guibas, L.J.: SyncSpecCNN: synchronized spectral CNN for 3D shape segmentation. In: CVPR (2017)
Lombaert, H., Arcaro, M., Ayache, N.: Brain transfer: spectral analysis of cortical surfaces and functional maps. In: Ourselin, S., Alexander, D.C., Westin, C.-F., Cardoso, M.J. (eds.) IPMI 2015. LNCS, vol. 9123, pp. 474–487. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-19992-4_37
Gopinath, K., Desrosiers, C., Lombaert, H.: Graph convolutions on spectral embeddings: learning of cortical surface data. In: arXiv preprint arXiv:1803.10336 (2018)
Dhillon, I.S., Guan, Y., Kulis, B.: Weighted graph cuts without eigenvectors a multilevel approach. PAMI 29, 1944–1957 (2007)
Parisot, S., et al.: Spectral graph convolutions for population-based disease prediction. In: Descoteaux, M., Maier-Hein, L., Franz, A., Jannin, P., Collins, D.L., Duchesne, S. (eds.) MICCAI 2017. LNCS, vol. 10435, pp. 177–185. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-66179-7_21
Ying, R., et al.: Hierarchical graph representation learning with differentiable pooling. arXiv arXiv:1806.08804 (2018)
Bron, E., et al.: The CADDementia challenge. Neuroimage (2015)
Lombaert, H., Criminisi, A., Ayache, N.: Spectral forests: learning of surface data, application to cortical parcellation. In: Navab, N., Hornegger, J., Wells, W.M., Frangi, A.F. (eds.) MICCAI 2015. LNCS, vol. 9349, pp. 547–555. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-24553-9_67
Wang, C., Samari, B., Siddiqi, K.: Local spectral graph convolution for point set feature learning. In: ECCV (2018)
Destrieux, C., et al.: A sulcal depth parcellation of the cortex. NeuroImage (2009)
Sowell, E.R., et al.: Longitudinal mapping of cortical thickness and brain growth in normal children. J. Neurosci. 24, 8223–8231 (2004)
Lerch, J.P., et al.: Focal decline of cortical thickness in Alzheimer’s disease identified by computational neuroanatomy. Cereb. Cortex 15, 995–1001 (2004)
Jack, C.R., et al.: ADNI: MRI methods. JMRI 27, 685–691 (2008)
Ledig, C., et al.: Alzheimer’s state classification using volumetry, thickness and intensity. In: MICCAI (2014)
Acknowledgment
This work is supported by the Research Council of Canada (NSERC), NVIDIA Corp. with the donation of a Titan Xp GPU. Data were obtained from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) database.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Gopinath, K., Desrosiers, C., Lombaert, H. (2019). Adaptive Graph Convolution Pooling for Brain Surface Analysis. In: Chung, A., Gee, J., Yushkevich, P., Bao, S. (eds) Information Processing in Medical Imaging. IPMI 2019. Lecture Notes in Computer Science(), vol 11492. Springer, Cham. https://doi.org/10.1007/978-3-030-20351-1_7
Download citation
DOI: https://doi.org/10.1007/978-3-030-20351-1_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-20350-4
Online ISBN: 978-3-030-20351-1
eBook Packages: Computer ScienceComputer Science (R0)