Weighted Bilateral Filter — A new image filter for noise removing and detail information preserving

A new kind of adaptive image filter - Weighted Bilateral Filter (WBF) has been shown in this paper. The WBF can perform as a detail information-preserving smoothing and Gaussian noise removing filter like the Bilateral Filter (BF), meanwhile it can remove the impulse noise as Order-Statistic Filter (OSF) or nonlinear filter do. Derived from the Bilateral Filter, the coefficient of WBF is combined by geometric closeness and color value similarity among the pixels, and a weighted coefficient which is determined by whether the pixel is polluted by impulse noise. By analyzing Clifford Algebra, we can present the color difference between two color pixels in Clifford Algebra form, which can be applied in the color image processing of WBF, instead of operating on the three bands of a color image separately. WBF combines the advantage of BF and OSF, and it is local, no iterative, simple and adaptive.