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.