Higher order bilateral filters and their properties

Bilateral filtering1, 2 has proven to be a powerful tool for adaptive denoising purposes. Unlike conventional filters, the bilateral filter defines the closeness of two pixels not only based on geometric distance but also based on radiometric (graylevel) distance. In this paper, to further improve the performance and find new applications, we make contact with a classic non-parametric image reconstruction technique called kernel regression,3 which is based on local Taylor expansions of the regression function. We extend and generalize the kernel regression method and show that bilateral filtering is a special case of this new class of adaptive image reconstruction techniques, considering a specific choice for weighting kernels and zeroth order Taylor approximation. We show improvements over the classic bilateral filtering can be achieved by using higher order local approximations of the signal.

[1]  Wen-Chung Kao,et al.  Mltistage bilateral noise filtering and edge detection for color image enhancement , 2005, IEEE Trans. Consumer Electron..

[2]  Peyman Milanfar,et al.  Kernel Regression for Image Processing and Reconstruction , 2007, IEEE Transactions on Image Processing.

[3]  L. Rudin,et al.  Nonlinear total variation based noise removal algorithms , 1992 .

[4]  Danny Barash,et al.  A Fundamental Relationship between Bilateral Filtering, Adaptive Smoothing, and the Nonlinear Diffusion Equation , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[5]  S. Farsiu,et al.  Regularized Kernel Regression for Image Deblurring , 2006, 2006 Fortieth Asilomar Conference on Signals, Systems and Computers.

[6]  S. Kay.  Fundamentals of statistical signal processing: estimation theory , 1993 .

[7]  Roberto Manduchi,et al.  Bilateral filtering for gray and color images , 1998, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271).

[8]  Michael Elad,et al.  On the origin of the bilateral filter and ways to improve it , 2002, IEEE Trans. Image Process..

[9]  Dorin Comaniciu,et al.  A common framework for nonlinear diffusion, adaptive smoothing, bilateral filtering and mean shift , 2004, Image Vis. Comput..

[10]  Michael Elad,et al.  Fast and Robust Multi-Frame Super-Resolution , 2004, IEEE Transactions on Image Processing.

[11]  Nirmal K. Bose,et al.  Superresolution and noise filtering using moving least squares , 2006, IEEE Transactions on Image Processing.

[12]  Zhihui Wei,et al.  Fast and Robust Filtering-Based Image Magnification , 2006, ICIAR.

[13]  Dorin Comaniciu,et al.  Mean Shift: A Robust Approach Toward Feature Space Analysis , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[14]  E. Nadaraya.  On Estimating Regression , 1964 .

[15]  G. Pflug.  Kernel Smoothing. Monographs on Statistics and Applied Probability - M. P. Wand; M. C. Jones. , 1996 .

[16]  Lucas J. van Vliet,et al.  Separable bilateral filtering for fast video preprocessing , 2005, 2005 IEEE International Conference on Multimedia and Expo.

[17]  M. Stone.  Cross‐Validatory Choice and Assessment of Statistical Predictions , 1976 .

[18]  Larry D. Hostetler,et al.  The estimation of the gradient of a density function, with applications in pattern recognition , 1975, IEEE Trans. Inf. Theory.

[19]  Samuel Morillas,et al.  Fuzzy Bilateral Filtering for Color Images , 2006, ICIAR.

[20]  Michael Elad,et al.  Fast and robust multiframe super resolution , 2004, IEEE Transactions on Image Processing.