KEYWORDS: Image filtering, Smoothing, Signal to noise ratio, Digital filtering, Denoising, Image restoration, Monte Carlo methods, Image fusion, Hassium, Electronic filtering
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.
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