RotDCF: Decomposition of Convolutional Filters for Rotation-Equivariant Deep Networks

By Xiuyuan Cheng, Qiang Qiu, Robert Calderbank, Guillermo Sapiro. 2018

47 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Biomedical Engineering, Computer Vision and Pattern Recognition, Model Architectures

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Citations in the corpus

Directional Message Passing for Molecular Graphs (2020, methodology): “We can do so by generating a separate embedding m ji for each atom i and neighbor j by applying the same learned ﬁlter in the direction of each neighboring atom (in contrast to equivariant CNNs, which apply ﬁlters in ﬁxed, global directions).”
Group Equivariant Stand-Alone Self-Attention For Vision (2020, background): “The translation equivariance of CNNs has been extended to additional symmetries ranging from planar rotations (Dieleman et al., 2016; Marcos et al., 2017; Worrall et al., 2017; Weiler et al., 2018b; Li et al., 2018; Cheng et al., 2018; Hoogeboom et al., 2018; Bekkers et al., 2018; Veeling et al., 20”
Wavelet Networks: Scale Equivariant Learning From Raw Waveforms (2020, methodology): “[8] Xiuyuan Cheng, Qiang Qiu, Robert Calderbank, and Guillermo Sapiro.”
Dense Steerable Filter CNNs for Exploiting Rotational Symmetry in Histology Images (2020, unknown): “[35] propose a rotation-equivariant CNN, named”
On Learning Sets of Symmetric Elements (2020, background): “Another successful line of work took into account other image symmetries such as reflections and rotations (Dieleman et al., 2016; Cohen & Welling, 2016a;b; Worrall et al., 2017; Cheng et al., 2018), spherical symmetries (Cohen et al.”
Continual Learning with Filter Atom Swapping (2022, background): “…work further inspires other works in domain adaptation (Wang et al., 2020b), adaptive convolution (Wang et al., 2021b; 2020a), image generation (Wang et al., 2021a; 2019), video understanding (Miao et al., 2021), rotation equivariance (Cheng et al., 2018) and graph convolution (Cheng et al., 2020).”
Attentive Group Equivariant Convolutional Networks (2020, background): “, 1989), planar rotations (Dieleman et al., 2016; Marcos et al., 2017; Worrall et al., 2017; Weiler et al., 2018b; Li et al., 2018; Cheng et al., 2018; Hoogeboom et al., 2018; Bekkers et al., 2018; Veeling et al., 2018; Lenssen et al., 2018; Smets et al., 2020), spherical rotations (Cohen et al.”