RotaTouille: Rotation Equivariant Deep Learning for Contours

Fuente: arXiv
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Main Authors: Gardaa, Odin Hoff, Blaser, Nello
Format: Preprint
Published: 2025
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author Gardaa, Odin Hoff
Blaser, Nello
author_facet Gardaa, Odin Hoff
Blaser, Nello
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2508_16359
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle RotaTouille: Rotation Equivariant Deep Learning for Contours
Gardaa, Odin Hoff
Blaser, Nello
Machine Learning
Computer Vision and Pattern Recognition
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.
title RotaTouille: Rotation Equivariant Deep Learning for Contours
topic Machine Learning
Computer Vision and Pattern Recognition
url https://arxiv.org/abs/2508.16359