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Fast High‐Dimensional Filtering Using the Permutohedral Lattice
Author(s) -
Adams Andrew,
Baek Jongmin,
Davis Myers Abraham
Publication year - 2010
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/j.1467-8659.2009.01645.x
Subject(s) - lattice (music) , gaussian , curse of dimensionality , algorithm , high dimensional , lattice phase equaliser , computer science , filter (signal processing) , linear filter , mathematics , theoretical computer science , adaptive filter , artificial intelligence , computer vision , physics , quantum mechanics , acoustics
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.