Bilateral Filter

http://www.super.tka4.org/materials/lib/Articles-Books/Filters/Bilateral/tomasi98bilateral.pdf

An image filter that attmepts to keep edges sharp by weighting th contribution if each pixel in the filter footprint by the similarity with the to-be-filtered pixel.

bilateral_filter_7797f74f6285f79058cb7e93699ea73c4450df5d.svg

Where bilateral_filter_4a43487e0ff1662fb332331518c035138f7820ff.svg is the total mount of weight used for this pixel:

bilateral_filter_edf08dfd83331bf3d20efbb257517d90b6c92a5e.svg

bilateral_filter_2927108ea3fa861d34d33940c4392b647fd6ba2c.svg is the image at position bilateral_filter_4c331405047e31fa129009cf7a41fc1688f2f613.svg bilateral_filter_1bc994f6b652c56b1c26f8fb99863111f793af0e.svg is the pdf for pixel similarity (can be gaussian) bilateral_filter_d6951322b37a1f24ca2de9564c79a1615765ee76.svg is the pdf for pixel distance (can be gaussian)

Paper #

@inproceedings{tomasi1998bilateral,
  title={Bilateral filtering for gray and color images},
  author={Tomasi, Carlo and Manduchi, Roberto},
  booktitle={Sixth international conference on computer vision (IEEE Cat. No. 98CH36271)},
  pages={839--846},
  year={1998},
  organization={IEEE}
}

Drawbacks #

Staircasing effect #

taken from:

@article{buades2006staircasing,
  title={The staircasing effect in neighborhood filters and its solution},
  author={Buades, Antoni and Coll, Bartomeu and Morel, J-M},
  journal={IEEE transactions on Image Processing},
  volume={15},
  number={6},
  pages={1499--1505},
  year={2006},
  publisher={IEEE}
}

Gradient reversal #

taken from paper of Guided Image Filtering .

Happens because:

We realize that the halo artifacts, that occur in detail enhancement, come from the weak discrimination between pixel pairs in the local window. In general, the simple intensity difference of the standard model is insufficient to determine which pixels should be smoothed and which detail- and edge-pixels should be preserved.

source:

@inproceedings{pham2012local,
  title={A local variance-based bilateral filtering for artifact-free detail-and edge-preserving smoothing},
  author={Pham, Cuong Cao and Ha, Synh Viet Uyen and Jeon, Jae Wook},
  booktitle={Advances in Image and Video Technology: 5th Pacific Rim Symposium, PSIVT 2011, Gwangju, South Korea, November 20-23, 2011, Proceedings, Part II 5},
  pages={60--70},
  year={2012},
  organization={Springer}
}