Fast and Provably Accurate Bilateral Filtering

ABSTRACT:

The bilateral filter is a non-linear filter that uses a range filter along with a spatial filter to perform edge-preserving smoothing of images. A direct computation of the bilateral filter requires O(S) operations per pixel, where S is the size of the support of the spatial filter. In this paper, we present a fast and provably accurate algorithm for approximating the bilateral filter when the range kernel is Gaussian. In particular, for box and Gaussian spatial filters, the proposed algorithm can cut down the complexity to O(1) per pixel for any arbitrary S. The algorithm has a simple implementation involving N + 1 spatial filterings, where N is the approximation order. We give a detailed analysis of the filtering accuracy that can be achieved by the proposed approximation in relation to the target bilateral filter. This allows us to estimate the order N required to obtain a given accuracy. We also present comprehensive numerical results to demonstrate that the proposed algorithm is competitive with the state-of-the art methods in terms of speed and accuracy.

PROJECT OUTPUT VIDEO:

EXISTING SYSTEM:

we build on this work but we interpret the bilateral filter in terms of signal processing in a higher-dimensional space. This allows us to derive an improved acceleration scheme that yields equivalent running times but dramatically improves numerical accuracy. This paper introduces the following contributions: – An interpretation of the bilateral filter in a signal processing framework. Using a higher dimensional space, we formulate the bilateral filter as a convolution followed by simple nonlinearities. – Using this higher dimensional space, we demonstrate that the convolution computation can be downsampled without significantly impacting the result accuracy. This approximation technique enables a speed-up of several orders of magnitude while controlling the error induced.

DISADVANTAGES OF EXISTING SYSTEM:

It is sufficient to sample with a rate at least twice shorter than the smallest wavelength band-limited function which is well approximated by its low frequencies

PROPOSED SYSTEM:

proposed algorithm is generally faster and more accurate than Yang’s algorithm, which is currently considered to be the state-of-theart. In particular, we perform an error analysis whereby we compare the output obtained using the proposed algorithm with that of the exact bilateral filter. Due to the particular nature of the proposed approximation, our analysis is much more simple than that carried out for Yang’s algorithm in. Nevertheless, compared to Yang’s algorithm, we are able to establish a smaller bound on the number of spatial filterings required to achieve a given filtering accuracy. The latter is defined in terms of the error between the outputs of the bilateral filter and the fast algorithm To best of our knowledge, with the exception of , this is the only fast algorithm that comes with a provable guarantee on the quality of approximation. At this point, we note that the term “accurate” is used in the paper not just to signify that the output of the fast algorithm is visibly close to that of the target bilateral filter. It also has a precise technical meaning, namely, that we can control the approximation order to make the error between the outputs of the bilateral filter and the fast algorithm arbitrarily small.

ADVANTAGES OF PROPOSED SYSTEM:

For a fixed approximation order (to be defined shortly), the proposed approximation requires half the number of spatial filterings required by the approximations

It only involves polynomials (and just a single Gaussian), and hence can be efficiently implemented on hardware

SYSTEM REQUIREMENTS:

HARDWARE REQUIREMENTS:

• System            : Pentium Dual Core.

• Hard Disk       : 120 GB.

• Monitor          : 15’’ LED

• Input Devices : Keyboard, Mouse

• Ram                : 1GB.

SOFTWARE REQUIREMENTS:

• Operating system : Windows 7.

• Coding Language : MATLAB

• Tool                      : MATLAB R2013A

REFERENCE:

Kunal N. Chaudhury, Senior Member, IEEE, and Swapnil D. Dabhade, “Fast and Provably Accurate Bilateral Filtering”, IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 25, NO. 6, JUNE 2016.