RotaTouille: Rotation Equivariant Deep Learning for Contours

TL;DR

RotaTouille is a deep learning framework that achieves rotation and cyclic shift equivariance for contour data using complex-valued circular convolution, improving shape classification, reconstruction, and regression tasks.

Contribution

It introduces a novel rotation and cyclic shift equivariant deep learning method for contour data using complex-valued circular convolution.

Findings

Effective in shape classification, reconstruction, and contour regression

Achieves rotation and cyclic shift equivariance in contour analysis

Demonstrates improved performance over non-equivariant models

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.