Polar Transformer Networks

TL;DR

The Polar Transformer Network (PTN) enhances CNNs by achieving invariance to translation and equivariance to rotation and scale, improving performance on rotated and cluttered digit datasets.

Contribution

PTN introduces a novel polar transformer module that extends CNN equivariance to include scale, building on spatial transformer concepts.

Findings

State-of-the-art on rotated MNIST

Effective on SIM2MNIST with clutter and transformations

Extensible to 3D with Cylindrical Transformer Network

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.