RotaTouille: Rotation Equivariant Deep Learning for Contours

Odin Hoff Gardaa, Nello Blaser

Keywords: contours, deep learning, planar curves, rotational equivariance, circular convolution, complex-valued neural networks

TL;DR: A deep learning framework for planar curves equivariant with respect to rotations and cyclic shifts.

Abstract: 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.

Software: https://github.com/odinhg/rotation-equivariant-contour-learning

Submission Type: Full paper proceedings track submission (max 9 main pages).

Submission Number: 35