Image Processing Reference

In-Depth Information

Fig. 3.1
Illustration of bilateral filtering for edge preservation operation.
a
A step edge and its

noisy surroundings,
b
Output, and not output of the bilateral filter, and
c
Output, and not output of

an averaging-based low pass filter

A real time bilateral filter with complexity

has been designed by decompos-

ing into a number of constant time spatial filters in [198]. Porikli has presented three

methods for the computation of constant time bilateral filtering, i.e., with complexity

O(

O(

1

)

. These different implementations are based on polynomial filter expressions,

linear filters, and a Taylor series approximation of bilateral filters, respectively [142].

Very recently Chaudhury et al. have proposed

1

)

O(

1

)

complexity bilateral filter using

trigonometric range kernels [32].

In recent years, several improvements over the original bilateral filter in [175]

have also been suggested. Pham et al. have proposed a separable implementation of

bilateral filter which has been shown to be equivalent to the traditional filtering in

terms of execution time [134]. An adaptive bilateral filter which tunes the parameters

for every pixel based on its perceptual significance has been discussed in [190]. A

trilateral filter which tracks the high gradient region in images by tilting the bilaterally

smoothed image gradient vector has been proposed in [41]. Fattal et al. have applied

a multi-scale strategy for improvement in the performance of bilateral filter [58]. The

equivalence between bilateral filter, and anisotropic diffusion and adaptive smoothing

has already been discussed in [11]. Barash and Comaniciu also proved that bilateral

filter is an extension of the anisotropic diffusion process where the weights have been

chosen with a certain geometrical considerations. Mean shift [43] algorithm can be

employed in the joint spatial-range domains for discontinuity preserving smoothing.

However, when the local mode search space is restricted to the range domain, it is

equivalent to the bilateral filtering [12]. Elad has proved that the theoretical basis for

bilateral filter lies in the Bayesian framework [55]. A recently developed non-local

means filter [19] is a more generalized scheme where the small regions around the

pixels are taken into consideration as opposed to the single pixel values in the case

of bilateral filter during averaging.