RotDCF: Decomposition of Convolutional Filters for Rotation-Equivariant Deep Networks.
Abstract
Explicit encoding of group actions in deep features makes it possible for
convolutional neural networks (CNNs) to handle global deformations of images,
which is critical to success in many vision tasks. This paper proposes to
decompose the convolutional filters over joint steerable bases across the space
and the group geometry simultaneously, namely a rotation-equivariant CNN with
decomposed convolutional filters (RotDCF). This decomposition facilitates
computing the joint convolution, which is proved to be necessary for the group
equivariance. It significantly reduces the model size and computational
complexity while preserving performance, and truncation of the bases expansion
serves implicitly to regularize the filters. On datasets involving in-plane and
out-of-plane object rotations, RotDCF deep features demonstrate greater
robustness and interpretability than regular CNNs. The stability of the
equivariant representation to input variations is also proved theoretically
under generic assumptions on the filters in the decomposed form. The RotDCF
framework can be extended to groups other than rotations, providing a general
approach which achieves both group equivariance and representation stability at
a reduced model size.
Type
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https://hdl.handle.net/10161/17836Collections
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Guillermo Sapiro
James B. Duke Distinguished Professor of Electrical and Computer Engineering
Guillermo Sapiro received his B.Sc. (summa cum laude), M.Sc., and Ph.D. from the Department
of Electrical Engineering at the Technion, Israel Institute of Technology, in 1989,
1991, and 1993 respectively. After post-doctoral research at MIT, Dr. Sapiro became
Member of Technical Staff at the research facilities of HP Labs in Palo Alto, California.
He was with the Department of Electrical and Computer Engineering at the University
of Minnesota, where he held the position of Distinguished McKni

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