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Constant Time Median and Bilateral Filtering

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Abstract

This paper formulates both the median filter and bilateral filter as a cost volume aggregation problem whose computational complexity is independent of the filter kernel size. Unlike most of the previous works, the proposed framework results in a general bilateral filter that can have arbitrary spatial\(^{1}\) and arbitrary range filter kernels. This bilateral filter takes about 3.5 s to exactly filter a one megapixel 8-bit grayscale image on a 3.2 GHz Intel Core i7 CPU. In practice, the intensity/range and spatial domain can be downsampled to improve the efficiency. This compression can maintain very high accuracy (e.g., 40 dB) but over \(100\times \) faster.

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Notes

  1. an IIR O (1) solution needs to be available for the kernel.

  2. Integral image is an image representation. The integral image at a pixel location contains the sum of the pixels above and to the left of the pixel.

  3. \(\sigma _R\) is the standard deviation of the Gaussian range filter kernel defined in Eq. (6). In this paper, the image intensity is normalized so that it ranges from 0 to 1.

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Acknowledgments

This work was supported in part by a GRF Grant from the Research Grants Council of Hong Kong (Project No. CityU 122212) and a grant from HP lab.

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Authors and Affiliations

  1. City University of Hong Kong, Kowloon Tong, Hong Kong, China

    Qingxiong Yang

  2. University of Illinois at Urbana-Champaign, Champaign, IL, USA

    Narendra Ahuja

  3. Hewlett-Packard Laboratories, Palo Alto, CA, USA

    Kar-Han Tan

Authors
  1. Qingxiong Yang
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  2. Narendra Ahuja
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  3. Kar-Han Tan
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Corresponding author

Correspondence to Qingxiong Yang.

Additional information

Communicated by C. Schnörr.

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Yang, Q., Ahuja, N. & Tan, KH. Constant Time Median and Bilateral Filtering. Int J Comput Vis 112, 307–318 (2015). https://doi.org/10.1007/s11263-014-0764-y

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