Clustering-based Acceleration for High-dimensional Gaussian Filtering

Oishi, Sou; Fukushima, Norishige

doi:10.5220/0010548600650072

Cited by 2 publications

(2 citation statements)

References 22 publications

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“…where λ k (λ 1 ≥ λ 2 ≥, ..., ≥ λ m ∈ R) are the eigenvalues, and u k is the corresponding eigenvectors. Substituting (12) to (11) gives…”

Section: Clustering-based Constant-time Bilateral Filtermentioning

confidence: 99%

“…To solve this problem, a constant-time BF (O(1)BF) 10 has been proposed, which speeds up BF by decomposing it into multiple spatially invariant filters, and its speed does not depend on its kernel radius. However, while a grayscale convolution works as fast as O(K), the color implementation suffers from the curse of dimensionality, as in O(K 3 ), where K is the approximate order and K << r. Clustering-based approaches 11,12 solve this curse, and the order is O(K) or O(K 2 ). However, the accuracy of the filter approximation depends on the clustering results, and the randomness of the clustering makes the filter results unstable.…”

Section: Introductionmentioning

confidence: 99%

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Principal component analysis for accelerating color bilateral filtering

Ishikawa

Oishi

Fukushima

2023

International Workshop on Advanced Imaging Technology (IWAIT) 2023

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In this paper, we propose to speed up bilateral filtering by principal component analysis (PCA)-based dimensionality compression method with constant-time bilateral filtering. Constant-time bilateral filtering speeds up the filtering by representing it as a summation of the multiple Gaussian filters. However, a simple implementation is of the order of O(K 3 ) for color and suffers from the curse of dimensionality. A clustering-based approximation speedup solves this problem with an order of O(K) or O(K 2 ). PCA can provide a more informative signal relative to the transformation matrix. We have accelerated the process by converting the color information of the input image from 3-channel to 1-channel by PCA, considering the constant-time bilateral filter as joint bilateral filtering, and using the transformed image as a guide image. This dimensional reduction allowed us to filter images with sufficient accuracy at a higher speed.

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“…where λ k (λ 1 ≥ λ 2 ≥, ..., ≥ λ m ∈ R) are the eigenvalues, and u k is the corresponding eigenvectors. Substituting (12) to (11) gives…”

Section: Clustering-based Constant-time Bilateral Filtermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Principal component analysis for accelerating color bilateral filtering

Ishikawa

Oishi

Fukushima

2023

International Workshop on Advanced Imaging Technology (IWAIT) 2023

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Tiling and PCA Strategy for Clustering-Based High-Dimensional Gaussian Filtering

Oishi,

Fukushima

2023

SN COMPUT. SCI.

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Edge-preserving filtering is an essential tool for image processing applications and has various types of filtering. High-dimensional Gaussian filtering (HDGF) supports a wide range of edge-preserving filtering. This paper approximates HDGF by clustering with Nyström approximation, tiling, and principal component analysis (PCA) to accelerate HDGF. Also, we compare it with the conventional HDGF approximations and clarify its effective range. We accelerate HDGF by clustering-based constant-time algorithm, which has O(K) order for convolution, where K is the number of clusters. First, we perform PCA for dimensionality reduction and then cluster signals with k-means++. HDGF is decomposed to Gaussian filtering by approximate eigenvalue decomposition of Nyström approximation using the clusters. The Gaussian filtering is performed in a constant-time algorithm. The process is further accelerated by the tiling strategy cooperating with PCA. In our experimental results, we compared three approximated HDGFs: clustering-based HDGF, permutohedral lattice, and Gaussian KD-tree. Also, we evaluated six types of high dimensional signals: RGB, RGB-IR, RGB-D, flash/no-flash, hyperspectral image, and non-local means. The proposed clustering-based HDGF was effective for low/middle-dimensional cases: RGB, RGB-IR, RGB-D, flash/no-flash, and hyperspectral images. Also, tiling with PCA strategy is effective for the conventional permutohedral lattice and Gaussian KD-tree. In the approximation of HDGF, the clustering-based HDGF is the better solution for low/middle-dimensional signals. For the higher-dimensional case of non-local means filtering, the conventional HDGF of the permutohedral lattice with the proposed PCA tiling is effective. Our code and dataset are available at https://norishigefukushima.github.io/TilingPCA4CHDGF/.

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Clustering-based Acceleration for High-dimensional Gaussian Filtering

Cited by 2 publications

References 22 publications

Principal component analysis for accelerating color bilateral filtering

Principal component analysis for accelerating color bilateral filtering

Tiling and PCA Strategy for Clustering-Based High-Dimensional Gaussian Filtering

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