Spherical CNNs

WORK IN PROGRESS********************************************************************************************************************

Introduction

Convolutional Neural Networks (CNNs), or network architectures involving CNNs, are the current state of the art for learning 2D image processing tasks such as semantic segmentation and object detection. CNNs work well in large part due to the property of being translationally invariant when combined with max pooling. This property allows a network trained to detect a certain type of object to still detect the object even if it is translated to another position in the image.

Notation

Below are listed several important terms:

• [math]\displaystyle{ S^2 }[/math] Sphere - The two dimensional surface from an ordinary 3D sphere
• SO(3) - A three-dimensional manifold which consists of 3D rotations

Experiments

The authors provide several experiments. The first set of experiments are designed to show the numerical stability and accuracy of the outlined methods. The second groups of experiments shows how the algorithms can be applied to current problem domains.

Equivariance Error

In this experiment the authors try to show experimentally that their theory of equivariance holds. They express doubts that they had that the equivariance would hold due to discretization potentially introducing artifacts. The experiment is set up by

Source Code

Source code is available at: https://github.com/jonas-koehler/s2cnn