Image smoothing with Savitzky-Golay filters

Srinivasan Rajagopalan, Richard Robb

Research output: Chapter in Book/Report/Conference proceedingConference contribution

12 Citations (Scopus)

Abstract

Noise in medical images is common. It occurs during the image formation, recording, transmission, and subsequent image processing. Image smoothing attempts to locally preprocess these images primarily to suppress image noise by making use of the redundancy in the image data. One-dimensional Savitzky-Golay filtering provides smoothing without loss of resolution by assuming that the distant points have significant redundancy. This redundancy is exploited to reduce the noise level. Using this assumed redundancy, the underlying function is locally fitted by a polynomial whose coefficients are data independent and hence can be calculated in advance. Geometric representations of data as patches and surfaces have been used in volumetric modeling and reconstruction. Similar representations could also be used in image smoothing. This paper shows the two and three-dimensional extensions of one-dimensional Savitzky-Golay filters. The idea is to fit a two/three-dimensional polynomial to a two/three-dimensional sub region of the image. As in the one-dimensional case, the coefficients of the polynomial are computed a priori with a linear filter. The filter coefficients preserve higher moments. The coefficients always have a central positive lobe with smaller outlying corrections of both positive and negative magnitudes. To show the efficacy of this smoothing, it is used in-line with volume rendering while computing the sampling points and the gradient.

Original languageEnglish (US)
Title of host publicationProceedings of SPIE - The International Society for Optical Engineering
EditorsR.L. Galloway Jr.
Pages773-781
Number of pages9
Volume5029
DOIs
StatePublished - 2003
Externally publishedYes
EventMedical Imaging 2003: Visualization, Image-Guided Procedures and Display - San Diego, CA, United States
Duration: Feb 16 2003Feb 18 2003

Other

OtherMedical Imaging 2003: Visualization, Image-Guided Procedures and Display
CountryUnited States
CitySan Diego, CA
Period2/16/032/18/03

Fingerprint

smoothing
Redundancy
filters
Polynomials
redundancy
Image processing
Volume rendering
polynomials
coefficients
Sampling
linear filters
lobes
image processing
recording
sampling
moments
gradients

Keywords

  • Anisotropic diffusion
  • Edge preservation
  • Image preprocessing
  • Linear filters
  • Raycasting
  • Savitzky-Golay filters
  • Smoothing
  • Splatting
  • Volume rendering

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Condensed Matter Physics

Cite this

Rajagopalan, S., & Robb, R. (2003). Image smoothing with Savitzky-Golay filters. In R. L. Galloway Jr. (Ed.), Proceedings of SPIE - The International Society for Optical Engineering (Vol. 5029, pp. 773-781) https://doi.org/10.1117/12.479596

Image smoothing with Savitzky-Golay filters. / Rajagopalan, Srinivasan; Robb, Richard.

Proceedings of SPIE - The International Society for Optical Engineering. ed. / R.L. Galloway Jr. Vol. 5029 2003. p. 773-781.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Rajagopalan, S & Robb, R 2003, Image smoothing with Savitzky-Golay filters. in RL Galloway Jr. (ed.), Proceedings of SPIE - The International Society for Optical Engineering. vol. 5029, pp. 773-781, Medical Imaging 2003: Visualization, Image-Guided Procedures and Display, San Diego, CA, United States, 2/16/03. https://doi.org/10.1117/12.479596
Rajagopalan S, Robb R. Image smoothing with Savitzky-Golay filters. In Galloway Jr. RL, editor, Proceedings of SPIE - The International Society for Optical Engineering. Vol. 5029. 2003. p. 773-781 https://doi.org/10.1117/12.479596
Rajagopalan, Srinivasan ; Robb, Richard. / Image smoothing with Savitzky-Golay filters. Proceedings of SPIE - The International Society for Optical Engineering. editor / R.L. Galloway Jr. Vol. 5029 2003. pp. 773-781
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