Bilateral Filter Algorithm

The bilateral filter is a nonlinear algorithm for smoothing a digital image while preserving its sharp edges, in contrast to an ordinary Gaussian blur, which softens edges along with everything else. It replaces each pixel with a weighted average of its neighbors, as a Gaussian blur does, but multiplies the usual distance based weight by a second weight that falls off with how different two pixels' brightness or color values are, so that a nearby pixel on the opposite side of a sharp edge, whose value differs greatly from the pixel being processed, contributes very little to the result even though it is spatially close. Carlo Tomasi and Roberto Manduchi introduced the bilateral filter under that name in 1998, building on the general idea of edge preserving smoothing that had appeared earlier in related forms such as Beltrami flow, and it became a widely used technique for noise reduction, tone mapping and other image processing tasks where blurring across a genuine edge is undesirable.