Zhao Fenqiang, Xia Shunren, Wu Zhengwang, Duan Dingna, Wang Li, Lin Weili, Gilmore John H, Shen Dinggang, Li Gang
Key Laboratory of Biomedical Engineering of Ministry of Education, Zhejiang University, Hangzhou, China.
Department of Radiology and BRIC, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA.
Inf Process Med Imaging. 2019 Jun;11492:855-866. doi: 10.1007/978-3-030-20351-1_67. Epub 2019 May 22.
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.
卷积神经网络（CNNs）在涉及欧几里得空间中二维/三维图像的学习相关问题上一直提供着最先进的性能。然而，与欧几里得空间不同，医学成像中许多结构的形状在流形空间中具有球形拓扑结构，例如由三角网格表示的大脑皮质或皮质下表面，在顶点数量和局部连通性方面存在较大的个体间和个体内差异。因此，对于皮质/皮质下表面数据，没有一致的邻域定义，也就没有直接的卷积/转置卷积操作。在本文中，通过利用重新采样到球形空间的皮质表面的规则且一致的几何结构，我们提出了一种类似于图像网格上标准卷积的新型卷积滤波器。相应地，我们为球形表面数据开发了卷积、池化和转置卷积的相应操作，从而构建了球形卷积神经网络。具体而言，我们通过将标准U-Net中的所有操作替换为其球形操作对应物，提出了球形U-Net架构。然后，我们将球形U-Net应用于婴儿大脑中的两个具有挑战性且在神经科学上重要的任务：皮质表面分割和皮质属性图发育预测。与最先进的方法相比，这两个应用都展示了我们提出的球形U-Net在准确性、计算效率和有效性方面的竞争性能。
