提出可同时处理旋转与循环位移的轮廓数据深度学习框架
RotaTouille: Rotation Equivariant Deep Learning for Contours
- 用复数域循环卷积实现旋转与循环位移等变性
- 在形状分类、重构和轮廓回归任务中表现优于基线方法
- 适合处理图像边界、气象等高线等具有对称性的数据
轮廓或闭合平面曲线在多个领域普遍存在，如计算机视觉中的物体边界、气象学中的等值线以及旋转机械的轨迹。在从轮廓数据学习时，输入的平面旋转会导致输出相应旋转，因此理想模型应具备旋转等变性。此外，轮廓通常以边缘点的有序序列表示，起始点选择是任意的，故模型也应具备循环位移等变性。本文提出 RotaTouille 框架，通过复数域循环卷积实现旋转与循环位移双重等变性，并引入等变非线性、下采样层及全局池化层，获得下游任务所需的不变表示。实验验证了该框架在形状分类、轮廓重建与轮廓回归任务中的有效性。
原文摘要 · Abstract (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.
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