Spherical Deformable U-Net: Application to Cortical Surface Parcellation and Development Prediction

Fenqiang Zhao, Zhengwang Wu, Li Wang, Weili Lin, John H. Gilmore, Shunren Xia, DInggang Shen, Gang Li

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)


Convolutional Neural Networks (CNNs) have achieved overwhelming success in learning-related problems for 2D/3D images in the Euclidean space. However, unlike in the Euclidean space, the shapes of many structures in medical imaging have an inherent spherical topology in a manifold space, e.g., the convoluted brain cortical surfaces represented by triangular meshes. There is no consistent neighborhood definition and thus no straightforward convolution/pooling operations for such cortical surface data. In this paper, leveraging the regular and hierarchical geometric structure of the resampled spherical cortical surfaces, we create the 1-ring filter on spherical cortical triangular meshes and accordingly develop convolution/pooling operations for constructing Spherical U-Net for cortical surface data. However, the regular nature of the 1-ring filter makes it inherently limited to model fixed geometric transformations. To further enhance the transformation modeling capability of Spherical U-Net, we introduce the deformable convolution and deformable pooling to cortical surface data and accordingly propose the Spherical Deformable U-Net (SDU-Net). Specifically, spherical offsets are learned to freely deform the 1-ring filter on the sphere to adaptively localize cortical structures with different sizes and shapes. We then apply the SDU-Net to two challenging and scientifically important tasks in neuroimaging: cortical surface parcellation and cortical attribute map prediction. Both applications validate the competitive performance of our approach in accuracy and computational efficiency in comparison with state-of-the-art methods.

Original languageEnglish
Article number9316936
Pages (from-to)1217-1228
Number of pages12
JournalIEEE Transactions on Medical Imaging
Issue number4
Publication statusPublished - 2021 Apr


  • Convolutional neural network
  • U-Net
  • cortical surface
  • deformable networks
  • parcellation
  • triangular mesh

ASJC Scopus subject areas

  • Software
  • Radiological and Ultrasound Technology
  • Computer Science Applications
  • Electrical and Electronic Engineering


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