Rotation equivariant vector field networks

TL;DR

RotEqNet is a CNN architecture that encodes rotation equivariance, invariance, and covariance, leading to more compact models and competitive results across various vision tasks.

Contribution

The paper introduces RotEqNet, a novel CNN design that explicitly encodes rotation properties to improve efficiency and performance.

Findings

RotEqNet achieves comparable accuracy with significantly fewer parameters.

The architecture performs well on classification, segmentation, and orientation tasks.

RotEqNet outperforms larger models in efficiency and effectiveness.

Abstract

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.