2012
DOI: 10.1007/s10851-012-0379-2
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Lattice-Based High-Dimensional Gaussian Filtering and the Permutohedral Lattice

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 naï… Show more

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Cited by 9 publications
(4 citation statements)
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“…The significance is equivalent to independence, the background colour of the image is usually distributed in any direction of the image, with high spatial variance, while the foreground colour instead of more concentrated, while the spatial variance is much lower. The resulting super-pixel images have better compactness and local features, which makes the pixels clustered in a particular area of the image have higher saliency values than the pixels distributed in the entire image [31]. Therefore, the colour space distribution of the super-pixel unit is defined as the spatial variance corresponding to the unit colour value.…”
Section: Colour Space Distributionmentioning
confidence: 99%
“…The significance is equivalent to independence, the background colour of the image is usually distributed in any direction of the image, with high spatial variance, while the foreground colour instead of more concentrated, while the spatial variance is much lower. The resulting super-pixel images have better compactness and local features, which makes the pixels clustered in a particular area of the image have higher saliency values than the pixels distributed in the entire image [31]. Therefore, the colour space distribution of the super-pixel unit is defined as the spatial variance corresponding to the unit colour value.…”
Section: Colour Space Distributionmentioning
confidence: 99%
“…Taking Equations ( 7) and ( 23) into account, it is apparent that both equations are similar, except that in the former, Gaussian weights are shifted. Baek et al [30] proved that to use shifted Gaussian kernels, it is sufficient to slice the lattice at shifted positions. Using the ImageStack library, the lattice points are ordinary position vectors without shifting and the values of ( ) are blurred in the lattice space by using position vectors in Gaussian weights.…”
Section: -4-implementation Details Of Shifted Gaussian Kernelsmentioning
confidence: 99%
“…Due to the mixture of Gaussian kernels form of the pairwise term, the updates can be computed in parallel by convolution with Gaussian kernels. This can be achieved efficiently by exploiting fast Gaussian filtering techniques, such as the permutohedral lattice-based method of [2].…”
Section: Crf Formulationmentioning
confidence: 99%