Fast High‐Dimensional Filtering Using the Permutohedral Lattice

Abstract Many useful algorithms for processing images and geometry fall under the general framework of high‐dimensional Gaussian filtering. This family of algorithms includes bilateral filtering and non‐local means. We propose a new way to perform such filters using the permutohedral lattice, which tessellates high‐dimensional space with uniform simplices. Our algorithm is the first implementation of a high‐dimensional Gaussian filter that is both linear in input size and polynomial in dimensionality. Furthermore it is parameter‐free, apart from the filter size, and achieves a consistently high accuracy relative to ground truth (> 45 dB). We use this to demonstrate a number of interactive‐rate applications of filters in as high as eight dimensions.