High-Dimensional Convolutional Networks for Geometric Pattern Recognition

High-dimensional geometric patterns appear in many computer vision problems. In this work, we present high-dimensional convolutional networks for geometric pattern recognition problems that arise in 2D and 3D registration problems. We first propose high-dimensional convolutional networks from 4 to 32 dimensions and analyze the geometric pattern recognition capacity in high-dimensional linear regression problems. Next, we show that the 3D correspondences form hyper-surface in a 6-dimensional space and validate our network on 3D registration problems. Finally, we use image correspondences, which form a 4-dimensional hyper-conic section, and show that the high-dimensional convolutional networks are on par with many state-of-the-art multi-layered perceptrons.