Name
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 na茂ve 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. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1007/s10851-012-0379-2 | Journal of Mathematical Imaging and Vision |
Keywords | Field | DocType |
Bilateral filtering,High-dimensional filtering,Non-local means,Lattices,Gaussian filtering,Permutohedral lattice | Gaussian filter,Mathematical optimization,Non-local means,Geometry processing,Filter (signal processing),Gaussian,Smoothing,Mean-shift,Bilateral filter,Mathematics | Journal |
Volume | Issue | ISSN |
46 | 2 | 0924-9907 |
Citations | PageRank | References |
3 | 0.39 | 27 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jongmin Baek | 1 | 283 | 14.08 |
| Andrew Adams | 2 | 936 | 53.55 |
| Jennifer Dolson | 3 | 271 | 14.03 |