Spherical U-Net on Cortical Surfaces: Methods and Applications

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11492)


Convolutional Neural Networks (CNNs) have been providing the state-of-the-art performance for learning-related problems involving 2D/3D images in Euclidean space. However, unlike in the Euclidean space, the shapes of many structures in medical imaging have a spherical topology in a manifold space, e.g., brain cortical or subcortical surfaces represented by triangular meshes, with large inter-subject and intra-subject variations in vertex number and local connectivity. Hence, there is no consistent neighborhood definition and thus no straightforward convolution/transposed convolution operations for cortical/subcortical surface data. In this paper, by leveraging the regular and consistent geometric structure of the resampled cortical surface mapped onto the spherical space, we propose a novel convolution filter analogous to the standard convolution on the image grid. Accordingly, we develop corresponding operations for convolution, pooling, and transposed convolution for spherical surface data and thus construct spherical CNNs. Specifically, we propose the Spherical U-Net architecture by replacing all operations in the standard U-Net with their spherical operation counterparts. We then apply the Spherical U-Net to two challenging and neuroscientifically important tasks in infant brains: cortical surface parcellation and cortical attribute map development prediction. Both applications demonstrate the competitive performance in the accuracy, computational efficiency, and effectiveness of our proposed Spherical U-Net, in comparison with the state-of-the-art methods.


Spherical U-Net Convolutional Neural Network Cortical surface Parcellation Prediction 



This work was partially supported by NIH grants (MH107815, MH108914, MH109773, MH116225, and MH117943) and China Scholarship Council.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Key Laboratory of Biomedical Engineering of Ministry of EducationZhejiang UniversityHangzhouChina
  2. 2.Department of Radiology and BRICUniversity of North Carolina at Chapel HillChapel HillUSA
  3. 3.Department of PsychiatryUniversity of North Carolina at Chapel HillChapel HillUSA

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