### 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 language | English (US) |
---|---|

Title of host publication | Proceedings of SPIE - The International Society for Optical Engineering |

Editors | R.L. Galloway Jr. |

Pages | 773-781 |

Number of pages | 9 |

Volume | 5029 |

DOIs | |

State | Published - 2003 |

Externally published | Yes |

Event | Medical Imaging 2003: Visualization, Image-Guided Procedures and Display - San Diego, CA, United States Duration: Feb 16 2003 → Feb 18 2003 |

### Other

Other | Medical Imaging 2003: Visualization, Image-Guided Procedures and Display |
---|---|

Country | United States |

City | San Diego, CA |

Period | 2/16/03 → 2/18/03 |

### Fingerprint

### 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

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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

}

TY - GEN

T1 - Image smoothing with Savitzky-Golay filters

AU - Rajagopalan, Srinivasan

AU - Robb, Richard

PY - 2003

Y1 - 2003

N2 - 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.

AB - 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.

KW - Anisotropic diffusion

KW - Edge preservation

KW - Image preprocessing

KW - Linear filters

KW - Raycasting

KW - Savitzky-Golay filters

KW - Smoothing

KW - Splatting

KW - Volume rendering

UR - http://www.scopus.com/inward/record.url?scp=0042123975&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0042123975&partnerID=8YFLogxK

U2 - 10.1117/12.479596

DO - 10.1117/12.479596

M3 - Conference contribution

AN - SCOPUS:0042123975

VL - 5029

SP - 773

EP - 781

BT - Proceedings of SPIE - The International Society for Optical Engineering

A2 - Galloway Jr., R.L.

ER -