[Paper Review] CyCNN: A Rotation Invariant CNN using Polar Mapping and Cylindrical Convolution Layers

Jin-Pyo Kim, Wooekun Jung+2 more|arXiv (Cornell University)|Jul 21, 2020

Advanced Neural Network ApplicationsComputer Science35 references32 citations

TL;DR

CyCNN converts rotation to translation via polar mapping and uses cylindrical convolution layers to achieve rotation invariance, improving rotated-image classification without data augmentation.

ABSTRACT

Deep Convolutional Neural Networks (CNNs) are empirically known to be invariant to moderate translation but not to rotation in image classification. This paper proposes a deep CNN model, called CyCNN, which exploits polar mapping of input images to convert rotation to translation. To deal with the cylindrical property of the polar coordinates, we replace convolution layers in conventional CNNs to cylindrical convolutional (CyConv) layers. A CyConv layer exploits the cylindrically sliding windows (CSW) mechanism that vertically extends the input-image receptive fields of boundary units in a convolutional layer. We evaluate CyCNN and conventional CNN models for classification tasks on rotated MNIST, CIFAR-10, and SVHN datasets. We show that if there is no data augmentation during training, CyCNN significantly improves classification accuracies when compared to conventional CNN models. Our implementation of CyCNN is publicly available on https://github.com/mcrl/CyCNN.

Motivation & Objective

• Motivate the need for rotation-invariant image classification in CNNs.
• Propose a pipeline that maps inputs to polar coordinates to convert rotation into translation.
• Introduce Cylindrical Convolution (CyConv) layers with cylindrically sliding windows.
• Show that CyCNN improves rotated-image classification without data augmentation while preserving parameter count.

Proposed method

• Map input images from Cartesian to polar (or log-polar) coordinates to convert rotation into translation.
• Replace standard convolutional layers with Cylindrical Convolution (CyConv) layers that use cylindrically sliding windows (CSW).
• Wrap boundary rows to create a cylindrical input enabling full cylindrical scanning by filters.
• Optionally implement a Cylindrical Winograd (CyWino) convolution for faster training.
• Maintain equal parameter count to the original CNN by only changing representations and layer types.

Experimental results

Research questions

• RQ1 Can polar coordinate transformation convert rotation variations into translation variations for CNNs?
• RQ2 Do Cylindrical Convolution (CyConv) layers improve rotation invariance without increasing model size?
• RQ3 How does CyCNN perform on rotated versions of standard datasets (MNIST, SVHN, CIFAR-10, CIFAR-100) compared to conventional CNNs?
• RQ4 What is the impact of data augmentation (rotation, translation) on CyCNN versus baseline CNNs?

Key findings

• Polar mapping improves baseline CNN accuracy on rotated data over original CNNs.
• CyCNN with CyConv layers significantly improves rotated-image accuracy over corresponding baseline CNNs when trained without augmentation.
• With rotation+translation augmentation, CyCNN achieves competitive accuracies to baselines across several datasets.
• CyCNN maintains the same number of learnable parameters as the original CNN, with slower training times due to less optimized kernels (CyWino) which can be later sped up.