Quantitative error analysis of bilateral filtering

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

© 2014 IEEE. One of the fastest acceleration techniques for bilateral image filtering is the real time $O(1)$ quantization method proposed by Yang 2009, which first computes some Principal Bilateral Filtered Image Components (PBFICs) and then applies linear interpolation to estimate the filtered output images. There is a trade-off between accuracy and efficiency in selecting the number of PBFICs: the more PBFICs are used, the higher the accuracy, and the higher the computational cost. A question arises: how many PBFICs are required to achieve a certain level of accuracy? In this letter, we address this question by investigating the properties of bilateral filtering and deriving the linear interpolation error bounds when only a subset of PBFICs is used. The provided theoretical analysis indicates that the necessary number of PBFICs for user-provided precision depends on the range kernel and, for typical Gaussian range kernels, a small percentage (typically less than 4%) of the PBFICs are enough for good approximations.
Original languageEnglish
Pages (from-to)202-206
JournalIEEE Signal Processing Letters
Volume22
Issue number2
DOIs
Publication statusPublished - 2015

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Quantitative Analysis
Error Analysis
Error analysis
Interpolation
Filtering
Set theory
Linear Interpolation
Costs
kernel
Image Filtering
Interpolation Error
Range of data
Error Bounds
Percentage
Computational Cost
Quantization
Theoretical Analysis
Trade-offs
Subset
Necessary

Cite this

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title = "Quantitative error analysis of bilateral filtering",
abstract = "{\circledC} 2014 IEEE. One of the fastest acceleration techniques for bilateral image filtering is the real time $O(1)$ quantization method proposed by Yang 2009, which first computes some Principal Bilateral Filtered Image Components (PBFICs) and then applies linear interpolation to estimate the filtered output images. There is a trade-off between accuracy and efficiency in selecting the number of PBFICs: the more PBFICs are used, the higher the accuracy, and the higher the computational cost. A question arises: how many PBFICs are required to achieve a certain level of accuracy? In this letter, we address this question by investigating the properties of bilateral filtering and deriving the linear interpolation error bounds when only a subset of PBFICs is used. The provided theoretical analysis indicates that the necessary number of PBFICs for user-provided precision depends on the range kernel and, for typical Gaussian range kernels, a small percentage (typically less than 4{\%}) of the PBFICs are enough for good approximations.",
author = "Senjian An and Farid Boussa{\"i}d and Mohammed Bennamoun and Ferdous Sohel",
year = "2015",
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language = "English",
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Quantitative error analysis of bilateral filtering. / An, Senjian; Boussaïd, Farid; Bennamoun, Mohammed; Sohel, Ferdous.

In: IEEE Signal Processing Letters, Vol. 22, No. 2, 2015, p. 202-206.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Quantitative error analysis of bilateral filtering

AU - An, Senjian

AU - Boussaïd, Farid

AU - Bennamoun, Mohammed

AU - Sohel, Ferdous

PY - 2015

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N2 - © 2014 IEEE. One of the fastest acceleration techniques for bilateral image filtering is the real time $O(1)$ quantization method proposed by Yang 2009, which first computes some Principal Bilateral Filtered Image Components (PBFICs) and then applies linear interpolation to estimate the filtered output images. There is a trade-off between accuracy and efficiency in selecting the number of PBFICs: the more PBFICs are used, the higher the accuracy, and the higher the computational cost. A question arises: how many PBFICs are required to achieve a certain level of accuracy? In this letter, we address this question by investigating the properties of bilateral filtering and deriving the linear interpolation error bounds when only a subset of PBFICs is used. The provided theoretical analysis indicates that the necessary number of PBFICs for user-provided precision depends on the range kernel and, for typical Gaussian range kernels, a small percentage (typically less than 4%) of the PBFICs are enough for good approximations.

AB - © 2014 IEEE. One of the fastest acceleration techniques for bilateral image filtering is the real time $O(1)$ quantization method proposed by Yang 2009, which first computes some Principal Bilateral Filtered Image Components (PBFICs) and then applies linear interpolation to estimate the filtered output images. There is a trade-off between accuracy and efficiency in selecting the number of PBFICs: the more PBFICs are used, the higher the accuracy, and the higher the computational cost. A question arises: how many PBFICs are required to achieve a certain level of accuracy? In this letter, we address this question by investigating the properties of bilateral filtering and deriving the linear interpolation error bounds when only a subset of PBFICs is used. The provided theoretical analysis indicates that the necessary number of PBFICs for user-provided precision depends on the range kernel and, for typical Gaussian range kernels, a small percentage (typically less than 4%) of the PBFICs are enough for good approximations.

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