A fast bilateral filtering algorithm based on rising cosine function

  • Jie Guo
  • Changhai Chen
  • Shoubing Xiang
  • Yang Ou
  • Bailin LiEmail author
Original Article


In order to speed up the bilateral filtering algorithm, a fast bilateral filtering algorithm based on raised cosine with compressibility factor (BRCF) is proposed. The BRCF uses a raised cosine function with a compression coefficient to replace Gaussian function as the range kernel function, and uses a limited number of linear convolution calculations to achieve bilateral filtering. Then, the improved BRCF (IBRCF) with a compression factor is proposed to accelerate the convergence rate of the raised cosine function. Compared to the published raised cosine algorithm, Taylor polynomial algorithm, and Gaussian polynomial algorithm, the computer simulation results show that the proposed IBRCF has a faster convergence rate with almost the same peak signal-to-noise ratio. After filtered seven images by various algorithms, the running time of the new IBRCF algorithm was confirmed to be less than 1/5 of Gaussian polynomial algorithm, while Gaussian polynomial algorithm was faster than the published raised cosine algorithm and Taylor polynomial algorithm. The mathematical proofs and algorithm flowcharts of the IBRCF algorithm are described in this paper in detail.


Bilateral filtering Rising cosine Compression coefficient Amplitude suppression 



Algorithm based on raised cosine with compressibility factor


The improved BRCF


The bilateral filter


Taylor polynomial


The basic raised cosine


Gaussian polynomial


The relative rate of change in PSNR


Authors’ contributions

We propose a fast bilateral filtering algorithm based on raised cosine with compressibility factor (BRCF) and propose an improved BRCF with a compression factor to accelerate the convergence rate of the raised cosine function. Meanwhile, we present a rigorous performance analysis for these algorithms. All authors read and approved the final manuscript.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mechanical EngineeringSouthwest Jiaotong UniversityChengduChina
  2. 2.Sichuan Engineering Technical CollegeDeyangChina

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