RotaTouille: Rotation Equivariant Deep Learning for Contours
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.
68ac400686b21a0e2e358be8
Odin Hoff Gardaa
claimed_verified
2025-08-25T12:37:29.662Z
65e0a09f5cc7e39aba11eb21
/avatars/297775c57d820a40f762ace9456abcd4.svg
Odin HG
user
odinhg
68ac400686b21a0e2e358be9
Nello Blaser
RotaTouille: Rotation Equivariant Deep Learning for Contours
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.
RotaTouille is a deep learning framework that achieves rotation and cyclic shift equivariance for contour data using complex-valued circular convolution, enabling effective performance in shape classification, reconstruction, and contour regression.
rotationally equivariant cyclic shift equivariance complex-valued circular convolution equivariant non-linearities coarsening layers global pooling layers invariant representations