30 May 2003 Image smoothing with Savtizky-Golai filters
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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 imagse primarily to suppress image noise by making use of the redundancy in the image data. 1D 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 functin is locally fitted by a polynomial whose coefficients are data independent and hence can be calculated in advance. Geometric representations of data as a patches and surfaces have been used in volumetric modeling and reconstruction. Similar representations could also be used in image smoothing. This paper shows the 2D and 3D extensions of 1D Savitzky-Golay filters. The idea is to fit a 2D/3D polynomial to a 2D/3D sub region of the image. As in the 1D 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.
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Srinivasan Rajagopalan, Srinivasan Rajagopalan, Richard A. Robb, Richard A. Robb, } "Image smoothing with Savtizky-Golai filters", Proc. SPIE 5029, Medical Imaging 2003: Visualization, Image-Guided Procedures, and Display, (30 May 2003); doi: 10.1117/12.479596; https://doi.org/10.1117/12.479596

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