High-Dimensional Convolutional Networks for Geometric Pattern Recognition

Christopher Choy, Junha Lee, Rene Ranftl, Jaesik Park, Vladlen Koltun; Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2020, pp. 11227-11236

Abstract


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.

Related Material


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[bibtex]
@InProceedings{Choy_2020_CVPR,
author = {Choy, Christopher and Lee, Junha and Ranftl, Rene and Park, Jaesik and Koltun, Vladlen},
title = {High-Dimensional Convolutional Networks for Geometric Pattern Recognition},
booktitle = {Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)},
month = {June},
year = {2020}
}