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Polar Transformer Networks

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arxiv 1709.01889 v3 pith:JVUNB64Z submitted 2017-09-06 cs.CV

Polar Transformer Networks

Carlos Esteves , Christine Allen-Blanchette , Xiaowei Zhou , Kostas Daniilidis This is my paper
classification cs.CV
keywords transformernetworkpolarrotationtranslationcnnsequivarianceequivariant
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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.

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