Lattice-Based High-Dimensional Gaussian Filtering and the Permutohedral Lattice
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10851_2012_Article_379.pdf
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Author(s)
Baek, Jongmin
Adams, Andrew
Dolson, Jennifer
Date Issued
September 2012
Journal
Journal of Mathematical Imaging and Vision
Publisher
Springer US
Citation
Baek, Jongmin, Andrew Adams, and Jennifer Dolson. “Lattice-Based High-Dimensional Gaussian Filtering and the Permutohedral Lattice.” Journal of Mathematical Imaging and Vision 46.2 (2013): 211–237.
Version
Author's final manuscript
Abstract
High-dimensional Gaussian filtering is a popular technique in image processing, geometry processing and computer graphics for smoothing data while preserving important features. For instance, the bilateral filter, cross bilateral filter and non-local means filter fall under the broad umbrella of high-dimensional Gaussian filters. Recent algorithmic advances therein have demonstrated that by relying on a sampled representation of the underlying space, one can obtain speed-ups of orders of magnitude over the naïve approach. The simplest such sampled representation is a lattice, and it has been used successfully in the bilateral grid and the permutohedral lattice algorithms. In this paper, we analyze these lattice-based algorithms, developing a general theory of lattice-based high-dimensional Gaussian filtering. We consider the set of criteria for an optimal lattice for filtering, as it offers a good tradeoff of quality for computational efficiency, and evaluate the existing lattices under the criteria. In particular, we give a rigorous exposition of the properties of the permutohedral lattice and argue that it is the optimal lattice for Gaussian filtering. Lastly, we explore further uses of the permutohedral-lattice-based Gaussian filtering framework, showing that it can be easily adapted to perform mean shift filtering and yield improvement over the traditional approach based on a Cartesian grid.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
http://dx.doi.org/10.1007/s10851-012-0379-2
