Accelerate bilateral filter using Hermite polynomials

The bilateral filter (BF) as an edge-preserving lowpass filter is a valuable tool in various image processing tasks, including noise reduction and dynamic range compression. However, its computational cost is too high to apply in the real-time processing tasks as the range kernel, which acts on the pixel intensities, making the averaging process nonlinear and computationally intensive, particularly when the spatial filter is large. Using the well-known Hermite polynomials, a BF accelerating method is proposed, which reduces the computational complexity from O(r²n) to O(n), where r denotes the filter size of a BF and n is the total number of pixels in an image.