A Fast Approximation of the Bilateral Filter Using a Signal Processing Approach

  • Sylvain Paris
  • Frédo Durand
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3954)


The bilateral filter is a nonlinear filter that smoothes a signal while preserving strong edges. It has demonstrated great effectiveness for a variety of problems in computer vision and computer graphics, and a fast version has been proposed. Unfortunately, little is known about the accuracy of such acceleration. In this paper, we propose a new signal-processing analysis of the bilateral filter, which complements the recent studies that analyzed it as a PDE or as a robust statistics estimator. Importantly, this signal-processing perspective allows us to develop a novel bilateral filtering acceleration using a downsampling in space and intensity. This affords a principled expression of the accuracy in terms of bandwidth and sampling. The key to our analysis is to express the filter in a higher-dimensional space where the signal intensity is added to the original domain dimensions. The bilateral filter can then be expressed as simple linear convolutions in this augmented space followed by two simple nonlinearities. This allows us to derive simple criteria for downsampling the key operations and to achieve important acceleration of the bilateral filter. We show that, for the same running time, our method is significantly more accurate than previous acceleration techniques.


Bilateral Filter Fast Approximation Homogeneous Intensity Nonlinear Operation Adaptive Smoothing 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Sylvain Paris
    • 1
  • Frédo Durand
    • 1
  1. 1.Massachusetts Institute of Technology, Computer Science and Artificial Intelligence LaboratoryUSA

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