Fast High-Dimensional Filtering Using the Permutohedral Lattice

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.