卷积神经网络(CNN)一直在为涉及欧几里得空间中的2D/3D图像的学习相关问题提供最先进的性能。然而,与欧几里得空间不同,医学成像中的许多结构的形状在歧管空间中具有球形拓扑,例如,由三角形网格表示的大脑皮层或皮层下表面,在顶点数和局部连通性方面具有较大的主体间和主体内变化。因此,没有一致的邻域定义,因此对于皮质/皮质下表面数据没有直接的卷积/转置卷积操作。在本文中,通过利用映射到球形空间的重采样皮质表面的规则和一致的几何结构,我们提出了一种新的卷积滤波器,类似于图像网格上的标准卷积。因此,我们开发相应的卷积运算,池化,和球面数据的转置卷积,从而构造球面CNN。具体来说,我们通过用球形操作对应物替换标准U-Net中的所有操作来提出球形U-Net架构。然后,我们将球形U-Net应用于婴儿大脑中两个具有挑战性且具有神经科学意义的任务:皮质表面分裂和皮质属性图发育预测。这两种应用程序都在准确性方面表现出竞争优势,计算效率,以及我们提出的球形U网的有效性,与最先进的方法相比。
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.