  Convolutions have long been regarded as fundamental to applied mathematics,
physics and engineering. Their mathematical elegance allows for common tasks
such as numerical differentiation to be computed efficiently on large data
sets. Efficient computation of convolutions is critical to artificial
intelligence in real-time applications, like machine vision, where convolutions
must be continuously and efficiently computed on tens to hundreds of kilobytes
per second. In this paper, we explore how convolutions are used in fundamental
machine vision applications. We present an accelerated n-dimensional
convolution package in the high performance computing language, Julia, and
demonstrate its efficacy in solving the time to contact problem for machine
vision. Results are measured against synthetically generated videos and
quantitatively assessed according to their mean squared error from the ground
truth. We achieve over an order of magnitude decrease in compute time and
allocated memory for comparable machine vision applications. All code is
packaged and integrated into the official Julia Package Manager to be used in
various other scenarios.
