Polar Transformer Networks

Abstract

Convolutional neural networks (CNNs) are inherently equivariant to translation. Efforts to embed other forms of equivariance have concentrated solely on rotation. We expand the notion of equivariance in CNNs through the Polar Transformer Network (PTN). PTN combines ideas from the Spatial Transformer Network (STN) and canonical coordinate representations. The result is a network invariant to translation and equivariant to both rotation and scale. PTN is trained end-to-end and composed of three distinct stages: a polar origin predictor, the newly introduced polar transformer module and a classifier. PTN achieves state-of-the-art on rotated MNIST and the newly introduced SIM2MNIST dataset, an MNIST variation obtained by adding clutter and perturbing digits with translation, rotation and scaling. The ideas of PTN are extensible to 3D which we demonstrate through the Cylindrical Transformer Network.

arXiv commentAccepted as a conference paper at ICLR 2018

References in corpus (4)

• DeepPose: Human Pose Estimation via Deep Neural Networks
• Stacked Hourglass Networks for Human Pose Estimation
• Harmonic Networks: Deep Translation and Rotation Equivariance
• Warped Convolutions: Efficient Invariance to Spatial Transformations

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