Fast O(1) Bilateral Filtering Using Trigonometric Range Kernels

It is well known that spatial averaging can be realized (in space or frequency domain) using algorithms whose complexity does not scale with the size or shape of the filter. These fast algorithms are generally referred to as constant-time or O(1) algorithms in the image-processing literature. Along...

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Bibliographic Details
Published in:IEEE transactions on image processing 2011-12, Vol.20 (12), p.3376-3382
Main Authors: Chaudhury, K. N., Sage, D., Unser, M.
Format: Article
Language:English
Subjects:
Algorithm design and analysis
Algorithms
Applied sciences
Approximation
Approximation algorithms
Approximation methods
Bilateral filter
constant-time algorithm
edge-preserving smoothing
Exact sciences and technology
Filtering
Gaussian
Image edge detection
Image processing
Information, signal and communications theory
Kernel
Kernels
Mathematical analysis
O complexity
Pixels
raised cosines
Signal processing
Spatial filters
Telecommunications and information theory
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Summary:It is well known that spatial averaging can be realized (in space or frequency domain) using algorithms whose complexity does not scale with the size or shape of the filter. These fast algorithms are generally referred to as constant-time or O(1) algorithms in the image-processing literature. Along with the spatial filter, the edge-preserving bilateral filter involves an additional range kernel. This is used to restrict the averaging to those neighborhood pixels whose intensity are similar or close to that of the pixel of interest. The range kernel operates by acting on the pixel intensities. This makes the averaging process nonlinear and computationally intensive, particularly when the spatial filter is large. In this paper, we show how the O(1) averaging algorithms can be leveraged for realizing the bilateral filter in constant time, by using trigonometric range kernels. This is done by generalizing the idea presented by Porikli, i.e., using polynomial kernels. The class of trigonometric kernels turns out to be sufficiently rich, allowing for the approximation of the standard Gaussian bilateral filter. The attractive feature of our approach is that, for a fixed number of terms, the quality of approximation achieved using trigonometric kernels is much superior to that obtained by Porikli using polynomials.
ISSN:1057-7149
1941-0042
DOI:10.1109/TIP.2011.2159234