RotaTouille：面向轮廓的旋转等变深度学习

RotaTouille: Rotation Equivariant Deep Learning for Contours

August 22, 2025

作者: Odin Hoff Gardaa, Nello Blaser

cs.AI

摘要

輪廓或閉合平面曲線在多個領域中普遍存在。例如，在計算機視覺中它們作為物體邊界出現，在氣象學中作為等值線，以及在旋轉機械的軌跡中。在許多從輪廓數據學習的情況下，輸入的平面旋轉將導致相應旋轉的輸出。因此，深度學習模型應具有旋轉等變性。此外，輪廓通常表示為邊緣點的有序序列，其中起始點的選擇是任意的。因此，深度學習方法在循環移位下也應具有等變性。我們提出了RotaTouille，這是一個從輪廓數據學習的深度學習框架，通過複數值圓周卷積實現了旋轉和循環移位的等變性。我們進一步引入並表徵了等變非線性、粗化層和全局池化層，以獲得用於下游任務的不變表示。最後，我們通過形狀分類、重建和輪廓回歸的實驗展示了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.