A

The Bilateral Filter

The bilateral filter [349,368] is a non-linear filter that maintains strong edges while smoothing internal values. It is related to thetropic diffusion [52,297,307]. The filter for an image I is defined as

(A.1)

B F [ I ] ( x , f s , g r ) = = 1 K [ I ] ( x , f s , g r ) y Ω ( x ) I ( y ) f s ( | | x - y | | ) g r ( | | I ( y ) - I ( x ) | | ) , K [ I ] ( x , f s , g r ) = y Ω ( x ) f s ( | | x - y | | ) g r ( | | I ( y ) - I ( x ) | | ) ,

where f s is the smoothing function for the distance term, g r is the smoothing function for the intensity term, Ω(x)is the pixel neighborhood around pixel x that ...

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