Polar transformer networks

Carlos Esteves; Christine Allen-Blanchette; Xiaowei Zhou; Kostas Daniilidis

Polar transformer networks

Carlos Esteves, Christine Allen-Blanchette, Xiaowei Zhou, Kostas Daniilidis

Research output: Contribution to conference › Paper › peer-review

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.

Original language	American English
State	Published - 2018
Externally published	Yes
Event	6th International Conference on Learning Representations, ICLR 2018 - Vancouver, Canada Duration: Apr 30 2018 → May 3 2018

Conference

Conference	6th International Conference on Learning Representations, ICLR 2018
Country/Territory	Canada
City	Vancouver
Period	4/30/18 → 5/3/18

ASJC Scopus subject areas

Language and Linguistics
Education
Computer Science Applications
Linguistics and Language

Cite this

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title = "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.",

author = "Carlos Esteves and Christine Allen-Blanchette and Xiaowei Zhou and Kostas Daniilidis",

note = "Publisher Copyright: {\textcopyright} Learning Representations, ICLR 2018 - Conference Track Proceedings.All right reserved.; 6th International Conference on Learning Representations, ICLR 2018 ; Conference date: 30-04-2018 Through 03-05-2018",

year = "2018",

language = "American English",

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TY - CONF

T1 - Polar transformer networks

AU - Esteves, Carlos

AU - Allen-Blanchette, Christine

AU - Zhou, Xiaowei

AU - Daniilidis, Kostas

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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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M3 - Paper

T2 - 6th International Conference on Learning Representations, ICLR 2018

Y2 - 30 April 2018 through 3 May 2018

ER -

Polar transformer networks

Abstract

Conference

ASJC Scopus subject areas

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