Harmonic Networks: Deep Translation and Rotation Equivariance

Worrall, Daniel E.; Garbin, Stephan J.; Turmukhambetov, Daniyar; Brostow, Gabriel J.

doi:10.48550/arxiv.1612.04642

Cited by 14 publications

(22 citation statements)

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“…This approach to training the deep neural network is not absolutely rotationally invariant, however the numerical error experienced due to a rotation was on the same order as the error of the method itself. Recent proposals to modify the network architecture itself to make it rotationally invariant are promising, as the additional training cost incurred with using an augmented dataset could be avoided [59,60].…”

Section: Discussionmentioning

confidence: 99%

Deep learning and the Schrödinger equation

Mills¹,

Spanner²,

Tamblyn³

2017

Phys. Rev. A

159

125

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We have trained a deep (convolutional) neural network to predict the ground-state energy of an electron in four classes of confining two-dimensional electrostatic potentials. On randomly generated potentials, for which there is no analytic form for either the potential or the ground-state energy, the model was able to predict the ground-state energy to within chemical accuracy, with a median absolute error of 1.49 mHa. We also investigate the performance of the model in predicting other quantities such as the kinetic energy and the first excited-state energy. arXiv:1702.01361v3 [cond-mat.mtrl-sci]

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Section: Discussionmentioning

confidence: 99%

Deep learning and the Schrödinger equation

Mills¹,

Spanner²,

Tamblyn³

2017

Phys. Rev. A

159

125

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“…A lot of recent works are aimed at CNNs. Some works learn invariant CNN representations with respect to specific transformations such as symmetry [11], scale [21] and rotation [52]. However, these works assume the transformations are fixed and known, which restricts their generalization to new tasks with unknown transformations.…”

Section: Related Workmentioning

confidence: 99%

Interaction-And-Aggregation Network for Person Re-Identification

Hou

Chang

et al. 2019

2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)

341

141

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Person re-identification (reID) benefits greatly from deep convolutional neural networks (CNNs) which learn robust feature embeddings. However, CNNs are inherently limited in modeling the large variations in person pose and scale due to their fixed geometric structures. In this paper, we propose a novel network structure, Interaction-and-Aggregation (IA), to enhance the feature representation capability of CNNs. Firstly, Spatial IA (SIA) module is introduced. It models the interdependencies between spatial features and then aggregates the correlated features corresponding to the same body parts. Unlike CNNs which extract features from fixed rectangle regions, SIA can adaptively determine the receptive fields according to the input person pose and scale. Secondly, we introduce Channel IA (CIA) module which selectively aggregates channel features to enhance the feature representation, especially for smallscale visual cues. Further, IA network can be constructed by inserting IA blocks into CNNs at any depth. We validate the effectiveness of our model for person reID by demonstrating its superiority over state-of-the-art methods on three benchmark datasets. ID Conv Block Conv Block …. Conv Block Conv Block …. Conv Block Conv Block …. Conv Block Conv Block

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“…RotEqNet obtains an error of 1.09%, a small improvement with respect to the state-of-the-art TI-pooling [16], but with almost 100× less parameters. Test-time data augmentation further reduces the error to 1.01%, thus improving significantly over TI-Pooling and over the more recent H-Net [29] and ORN [31].…”

Section: Methodsmentioning

confidence: 97%

“…Error rate (in %) SVM [17] 10.38±0.27 TIRBM [26] 4.2 H-Net [29] 1.69 ORN [31] 1.54 TI-pooling [16] 1. Results: We first studied the behavior of RotEqNet with respect to the total number of parameters and compared it to the state-of-the-art TI-pooling [16].…”

Section: Methodsmentioning

confidence: 99%

“…The most similar approaches to RotEqNet are the recently proposed Harmonic Networks (H-Nets) [29] and Oriented Response Networks (ORN) [31], both of which use an enriched feature map explicitly capturing the underlying orientations. They do so by using either complex circular harmonics (H-Nets) or the full vector of oriented responses (ORN).…”

Section: Related Workmentioning

confidence: 99%

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Rotation Equivariant Vector Field Networks

Marcos

Volpi

Komodakis

et al. 2017

2017 IEEE International Conference on Computer Vision (ICCV)

206

201

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In many computer vision tasks, we expect a particular behavior of the output with respect to rotations of the input image. If this relationship is explicitly encoded, instead of treated as any other variation, the complexity of the problem is decreased, leading to a reduction in the size of the required model.In this paper, we propose the Rotation Equivariant Vector Field Networks (RotEqNet), a Convolutional Neural Network (CNN) architecture encoding rotation equivariance, invariance and covariance. Each convolutional filter is applied at multiple orientations and returns a vector field representing magnitude and angle of the highest scoring orientation at every spatial location. We develop a modified convolution operator relying on this representation to obtain deep architectures. We test RotEqNet on several problems requiring different responses with respect to the inputs' rotation: image classification, biomedical image segmentation, orientation estimation and patch matching. In all cases, we show that RotEqNet offers extremely compact models in terms of number of parameters and provides results in line to those of networks orders of magnitude larger.

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Harmonic Networks: Deep Translation and Rotation Equivariance

Cited by 14 publications

References 0 publications

Deep learning and the Schrödinger equation

Deep learning and the Schrödinger equation

Interaction-And-Aggregation Network for Person Re-Identification

Rotation Equivariant Vector Field Networks

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