High-dimensional Convolutional Networks for Geometric Pattern Recognition

TL;DR

This paper introduces high-dimensional convolutional networks designed for geometric pattern recognition in high-dimensional spaces, demonstrating their effectiveness in tasks like 3D registration and outperforming previous methods.

Contribution

The paper develops and evaluates high-dimensional ConvNets for geometric pattern recognition, extending their application to spaces up to 32 dimensions and complex tasks like 3D registration.

Findings

High-dimensional ConvNets effectively detect linear subspaces in up to 32 dimensions.

They outperform prior global pooling-based deep networks in geometric registration tasks.

Experiments show superior accuracy in 3D registration and image correspondence estimation.

Abstract

Many problems in science and engineering can be formulated in terms of geometric patterns in high-dimensional spaces. We present high-dimensional convolutional networks (ConvNets) for pattern recognition problems that arise in the context of geometric registration. We first study the effectiveness of convolutional networks in detecting linear subspaces in high-dimensional spaces with up to 32 dimensions: much higher dimensionality than prior applications of ConvNets. We then apply high-dimensional ConvNets to 3D registration under rigid motions and image correspondence estimation. Experiments indicate that our high-dimensional ConvNets outperform prior approaches that relied on deep networks based on global pooling operators.