  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.
