Sparse Convolutional Networks using the Permutohedral Lattice

This paper introduces an efficient, non-linear image adaptive filtering as a generalization of the standard spatial convolution of convolutional neural networks (CNNs). We build on the bilateral filtering operation, a commonly used edgeaware image processing technique. Our implementation of bilateral filters uses specialized data structures, and in this paper we demonstrate how these lead to generalizations and make the filters amendable to learning. This development enriches the convolutional operation found in CNNs, which becomes image adaptive, can process sparse input data, and produce continuous output. Our result also generalizes a class of densely connected graphical models with tractable mean field inference. It has previously been shown that mean field approximations in the subclass of models with Gaussian edge potentials reduce to a bilateral filtering operation. Here, we generalize this to the non-Gaussian case and allow highly parameterized potential functions. A diverse set of experiments validates the empirical performance and highlights the different aspects of the proposed operation.