81,136 research outputs found
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 depend on 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 [Tomasi1998] 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 non-linear and computationally intensive,
especially 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 in [Porikli2008] of using polynomial range 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 in [Porikli2008] using polynomials.Comment: Accepted in IEEE Transactions on Image Processing. Also see addendum:
https://sites.google.com/site/kunalspage/home/Addendum.pd
Fast and Accurate Bilateral Filtering using Gauss-Polynomial Decomposition
The bilateral filter is a versatile non-linear filter that has found diverse
applications in image processing, computer vision, computer graphics, and
computational photography. A widely-used form of the filter is the Gaussian
bilateral filter in which both the spatial and range kernels are Gaussian. A
direct implementation of this filter requires operations per
pixel, where is the standard deviation of the spatial Gaussian. In
this paper, we propose an accurate approximation algorithm that can cut down
the computational complexity to per pixel for any arbitrary
(constant-time implementation). This is based on the observation that the range
kernel operates via the translations of a fixed Gaussian over the range space,
and that these translated Gaussians can be accurately approximated using the
so-called Gauss-polynomials. The overall algorithm emerging from this
approximation involves a series of spatial Gaussian filtering, which can be
implemented in constant-time using separability and recursion. We present some
preliminary results to demonstrate that the proposed algorithm compares
favorably with some of the existing fast algorithms in terms of speed and
accuracy.Comment: To appear in the IEEE International Conference on Image Processing
(ICIP 2015
Improvements on "Fast space-variant elliptical filtering using box splines"
It is well-known that box filters can be efficiently computed using
pre-integrations and local finite-differences
[Crow1984,Heckbert1986,Viola2001]. By generalizing this idea and by combining
it with a non-standard variant of the Central Limit Theorem, a constant-time or
O(1) algorithm was proposed in [Chaudhury2010] that allowed one to perform
space-variant filtering using Gaussian-like kernels. The algorithm was based on
the observation that both isotropic and anisotropic Gaussians could be
approximated using certain bivariate splines called box splines. The attractive
feature of the algorithm was that it allowed one to continuously control the
shape and size (covariance) of the filter, and that it had a fixed
computational cost per pixel, irrespective of the size of the filter. The
algorithm, however, offered a limited control on the covariance and accuracy of
the Gaussian approximation. In this work, we propose some improvements by
appropriately modifying the algorithm in [Chaudhury2010].Comment: 7 figure
Image Denoising using Optimally Weighted Bilateral Filters: A Sure and Fast Approach
The bilateral filter is known to be quite effective in denoising images
corrupted with small dosages of additive Gaussian noise. The denoising
performance of the filter, however, is known to degrade quickly with the
increase in noise level. Several adaptations of the filter have been proposed
in the literature to address this shortcoming, but often at a substantial
computational overhead. In this paper, we report a simple pre-processing step
that can substantially improve the denoising performance of the bilateral
filter, at almost no additional cost. The modified filter is designed to be
robust at large noise levels, and often tends to perform poorly below a certain
noise threshold. To get the best of the original and the modified filter, we
propose to combine them in a weighted fashion, where the weights are chosen to
minimize (a surrogate of) the oracle mean-squared-error (MSE). The
optimally-weighted filter is thus guaranteed to perform better than either of
the component filters in terms of the MSE, at all noise levels. We also provide
a fast algorithm for the weighted filtering. Visual and quantitative denoising
results on standard test images are reported which demonstrate that the
improvement over the original filter is significant both visually and in terms
of PSNR. Moreover, the denoising performance of the optimally-weighted
bilateral filter is competitive with the computation-intensive non-local means
filter.Comment: To appear in the IEEE International Conference on Image Processing
(ICIP 2015). Link to the Matlab code added in the revisio
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