RotaTouille: Rotation Equivariant Deep Learning for Contours
This addresses the need for rotation and cyclic shift equivariance in deep learning for contour data, which is incremental as it builds on existing equivariance concepts but applies them specifically to contours.
The paper tackled the problem of learning from contour data, where deep learning models need to be equivariant to rotations and cyclic shifts, and introduced RotaTouille, a framework using complex-valued circular convolution to achieve this, demonstrating effectiveness in tasks like shape classification and reconstruction.
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.