论文标题
移动框架网：SE（3） - 体积的等级网络
Moving Frame Net: SE(3)-Equivariant Network for Volumes
论文作者
论文摘要
神经网络对转换的模棱两可有助于提高其性能并减少计算机视觉任务中的概括错误，因为它们适用于呈现对称性的数据集（例如尺度，旋转，翻译）。移动框架的方法是经典的，它是为歧管中谎言组的作用而导致操作员不变的。实际上，基于移动帧方法提出了一个用于图像数据的旋转和翻译模棱两可的神经网络。在本文中，我们通过将移动帧的计算减少到输入阶段，而不是每一层重复的计算，从而显着改善了该方法。理论上证明了所得架构的均衡性，我们建立了一个旋转和翻译等效的神经网络，以处理量，即3D空间上的信号。我们训练有素的模型超出了MEDMNIST3D大多数测试数据集的医疗量分类中的基准。
Equivariance of neural networks to transformations helps to improve their performance and reduce generalization error in computer vision tasks, as they apply to datasets presenting symmetries (e.g. scalings, rotations, translations). The method of moving frames is classical for deriving operators invariant to the action of a Lie group in a manifold.Recently, a rotation and translation equivariant neural network for image data was proposed based on the moving frames approach. In this paper we significantly improve that approach by reducing the computation of moving frames to only one, at the input stage, instead of repeated computations at each layer. The equivariance of the resulting architecture is proved theoretically and we build a rotation and translation equivariant neural network to process volumes, i.e. signals on the 3D space. Our trained model overperforms the benchmarks in the medical volume classification of most of the tested datasets from MedMNIST3D.
