### Abstract

Original language | English |
---|---|

Pages (from-to) | 202-206 |

Journal | IEEE Signal Processing Letters |

Volume | 22 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2015 |

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*IEEE Signal Processing Letters*, vol. 22, no. 2, pp. 202-206. https://doi.org/10.1109/LSP.2014.2353694

**Quantitative error analysis of bilateral filtering.** / An, Senjian; Boussaïd, Farid; Bennamoun, Mohammed; Sohel, Ferdous.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Quantitative error analysis of bilateral filtering

AU - An, Senjian

AU - Boussaïd, Farid

AU - Bennamoun, Mohammed

AU - Sohel, Ferdous

PY - 2015

Y1 - 2015

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.

U2 - 10.1109/LSP.2014.2353694

DO - 10.1109/LSP.2014.2353694

M3 - Article

VL - 22

SP - 202

EP - 206

JO - IEEE Signal Processing Letters

JF - IEEE Signal Processing Letters

SN - 1070-9908

IS - 2

ER -