RotaTouille：面向轮廓的旋转等变深度学习

摘要

轮廓或闭合平面曲线在众多领域中普遍存在。例如，在计算机视觉中它们表现为物体边界，在气象学中作为等值线出现，在旋转机械中则代表运行轨迹。在处理轮廓数据进行学习时，平面旋转的输入往往会导致输出相应地旋转。因此，深度学习模型具备旋转等变性显得尤为重要。此外，轮廓通常被表示为一系列有序的边缘点，而起始点的选择是任意的。因此，深度学习方法还需对循环位移保持等变性。我们提出了RotaTouille，一个专为轮廓数据学习设计的深度学习框架，它通过复数值的循环卷积实现了旋转与循环位移的等变性。进一步地，我们引入并描述了等变非线性层、粗化层以及全局池化层，以获取适用于下游任务的不变表示。最后，我们通过形状分类、重建及轮廓回归实验，验证了RotaTouille的有效性。

English

Contours or closed planar curves are common in many domains. For example, they appear as object boundaries in computer vision, isolines in meteorology, and the orbits of rotating machinery. In many cases when learning from contour data, planar rotations of the input will result in correspondingly rotated outputs. It is therefore desirable that deep learning models be rotationally equivariant. In addition, contours are typically represented as an ordered sequence of edge points, where the choice of starting point is arbitrary. It is therefore also desirable for deep learning methods to be equivariant under cyclic shifts. We present RotaTouille, a deep learning framework for learning from contour data that achieves both rotation and cyclic shift equivariance through complex-valued circular convolution. We further introduce and characterize equivariant non-linearities, coarsening layers, and global pooling layers to obtain invariant representations for downstream tasks. Finally, we demonstrate the effectiveness of RotaTouille through experiments in shape classification, reconstruction, and contour regression.

RotaTouille：面向轮廓的旋转等变深度学习

RotaTouille: Rotation Equivariant Deep Learning for Contours

摘要

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