Voronoi Convolutional Neural Networks
This work addresses the challenge of applying CNNs to irregularly sampled data, which is incremental as it adapts existing CNN concepts to a new setting.
The authors tackled the problem of extending convolutional neural networks to non-grid sampled functions by treating samples as cell averages, enabling equivalent CNN layers, and they developed an exact inference algorithm using convex geometry.
In this technical report, we investigate extending convolutional neural networks to the setting where functions are not sampled in a grid pattern. We show that by treating the samples as the average of a function within a cell, we can find a natural equivalent of most layers used in CNN. We also present an algorithm for running inference for these models exactly using standard convex geometry algorithms.