球谐函数
计算机科学
卷积(计算机科学)
卷积神经网络
滤波器(信号处理)
旋转(数学)
人工智能
算法
集合(抽象数据类型)
模式识别(心理学)
核(代数)
计算机视觉
数学
人工神经网络
数学分析
组合数学
程序设计语言
出处
期刊:IEEE Transactions on Medical Imaging
[Institute of Electrical and Electronics Engineers]
日期:2022-10-01
卷期号:41 (10): 2739-2751
被引量:4
标识
DOI:10.1109/tmi.2022.3168670
摘要
We present a spherical harmonics-based convolutional neural network (CNN) for cortical parcellation, which we call SPHARM-Net. Recent advances in CNNs offer cortical parcellation on a fine-grained triangle mesh of the cortex. Yet, most CNNs designed for cortical parcellation employ spatial convolution that depends on extensive data augmentation and allows only predefined neighborhoods of specific spherical tessellation. On the other hand, a rotation-equivariant convolutional filter avoids data augmentation, and rotational equivariance can be achieved in spectral convolution independent of a neighborhood definition. Nevertheless, the limited resources of a modern machine enable only a finite set of spectral components that might lose geometric details. In this paper, we propose (1) a constrained spherical convolutional filter that supports an infinite set of spectral components and (2) an end-to-end framework without data augmentation. The proposed filter encodes all the spectral components without the full expansion of spherical harmonics. We show that rotational equivariance drastically reduces the training time while achieving accurate cortical parcellation. Furthermore, the proposed convolution is fully composed of matrix transformations, which offers efficient and fast spectral processing. In the experiments, we validate SPHARM-Net on two public datasets with manual labels: Mindboggle-101 (N=101) and NAMIC (N=39). The experimental results show that the proposed method outperforms the state-of-the-art methods on both datasets even with fewer learnable parameters without rigid alignment and data augmentation. Our code is publicly available at https://github.com/Shape-Lab/SPHARM-Net.
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