27,423 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
Constant-time filtering using shiftable kernels
It was recently demonstrated in [5] that the non-linear bilateral filter [14]
can be efficiently implemented using a constant-time or O(1) algorithm. At the
heart of this algorithm was the idea of approximating the Gaussian range kernel
of the bilateral filter using trigonometric functions. In this letter, we
explain how the idea in [5] can be extended to few other linear and non-linear
filters [14, 17, 2]. While some of these filters have received a lot of
attention in recent years, they are known to be computationally intensive. To
extend the idea in [5], we identify a central property of trigonometric
functions, called shiftability, that allows us to exploit the redundancy
inherent in the filtering operations. In particular, using shiftable kernels,
we show how certain complex filtering can be reduced to simply that of
computing the moving sum of a stack of images. Each image in the stack is
obtained through an elementary pointwise transform of the input image. This has
a two-fold advantage. First, we can use fast recursive algorithms for computing
the moving sum [15, 6], and, secondly, we can use parallel computation to
further speed up the computation. We also show how shiftable kernels can also
be used to approximate the (non-shiftable) Gaussian kernel that is ubiquitously
used in image filtering.Comment: Accepted in IEEE Signal Processing Letter
- …