Fast High‐Dimensional Filtering Using the Permutohedral Lattice

Adams, Andrew; Baek, Jiwon; Davis, Myers Abraham

doi:10.1111/j.1467-8659.2009.01645.x

Cited by 367 publications

(459 citation statements)

References 38 publications

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“…The authors noted, however, that KD-tree construction and querying is difficult to parallelize efficiently. Adams et al [2] relied on a different lattice, called the permutohedral lattice, to sample the high-dimensional space, and obtained considerable speed-up over the previous work that used a Cartesian grid for higher-dimensional cases.…”

Section: Accelerating High-dimensional Gaussian Filteringmentioning

confidence: 99%

“…Equation (5.3) amounts to setting Q = 1 and θ = ln √ 2 (d+1) 2 in Algorithm 2. If a different standard deviation is desired, the input signal may be scaled appropriately instead, as discussed in Sect.…”

Section: Proposition 57mentioning

confidence: 99%

“…One intuitive approach is to use a lattice to sample the space, as a lattice has a predictable, repetitive structure that facilitates indexing. This approach was taken by Chen et al [9] and Adams et al [2]. These represent the state of the art in fast high-dimensional Gaussian filtering.…”

Section: Introductionmentioning

confidence: 99%

“…Overview This article is an extension of the work of Adams, Baek, and Davis [2], which introduced the permutohedral lattice algorithm for Gaussian filtering and showcased its applications. In contrast to the previous work, this article focuses on the mathematical theory underlying the technique, rather than its applications.…”

Section: Introductionmentioning

confidence: 99%

“…The aim of this paper is to rigorously analyze the use of a lattice as the underlying data structure for high dimensional Gaussian filtering, using the two existing examples by Chen et al [9] and Adams et al [2] as case studies and drawing from the existing body of mathematics literature.…”

Section: Introductionmentioning

confidence: 99%

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Lattice-Based High-Dimensional Gaussian Filtering and the Permutohedral Lattice

2012

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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.

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Section: Accelerating High-dimensional Gaussian Filteringmentioning

confidence: 99%

Section: Proposition 57mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Lattice-Based High-Dimensional Gaussian Filtering and the Permutohedral Lattice

2012

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High Dynamic Range Imaging

Mantiuk

Seidel

2015

Wiley Encyclopedia of Electrical and Electronics Engineering

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High dynamic range (HDR) images and video contain pixels, which can represent much greater range of colors and brightness levels than that offered by existing, standard dynamic range images. Such “better pixels” greatly improve the overall quality of visual content, making it appear much more realistic and appealing to the audience. HDR is one of the key technologies of the future imaging pipeline, which will change the way the digital visual content is represented and manipulated. This article offers a broad review of the HDR methods and technologies with an introduction to fundamental concepts behind the perception of HDR imagery. It serves as both an introduction to the subject and a review of the current state of the art in HDR imaging. It covers the topics related to capture of HDR content with cameras and its generation with computer graphics methods; encoding and compression of HDR images and video; tone mapping for displaying HDR content on standard dynamic range displays; inverse tone mapping for upscaling legacy content for presentation on HDR displays; the display technologies offering HDR range; and finally image and video quality metrics suitable for HDR content.

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2022

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Optimization and machine learning are both extremely active research topics. In this thesis, we explore problems at the intersection of the two fields. In particular, we will develop two main ideas.First, optimization can be used to improve machine learning. We illustrate this idea by considering computer vision tasks that are modelled with dense conditional random fields. Existing solvers for these models are either slow or inaccurate. We show that, by introducing a specialized solver based on proximal minimization and fast filtering, these models can be solved both quickly and accurately. Similarly, we introduce a specialized linear programming solver for block bounded problems, a common class of problems encountered in machine learning. This solver is efficient, easy to tune and simple to integrate inside larger machine learning algorithms.Second, machine learning can be used to improve optimization, in particular for NP-hard problems. For problems solved by using hand-tuned heuristics, machine learning can be used to discover and improve these heuristics. We show that, for the problem of super-optimization, a better heuristic to explore the space of programs can be learnt using reinforcement learning. For problems where no such heuristics exist, machine learning can be used to get an approximate solution of the original problem. We use this idea to tackle the problem of program synthesis by reformulating it as the problem of learning a program that performs the required task. We introduce a new differentiable formulation of the execution and show that the fastest programs can be recovered for simple tasks.

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Fast High‐Dimensional Filtering Using the Permutohedral Lattice

Cited by 367 publications

References 38 publications

Lattice-Based High-Dimensional Gaussian Filtering and the Permutohedral Lattice

Lattice-Based High-Dimensional Gaussian Filtering and the Permutohedral Lattice

High Dynamic Range Imaging

Optimization and Machine Learning

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