01-12-2012, 01:38 PM
PDE-Based Enhancement of Color Images in RGB Space
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Abstract
A novel method for color image enhancement is proposed
as an extension of the scalar-diffusion–shock-filter coupling
model, where noisy and blurred images are denoised and sharpened.
The proposed model is based on using the single vectors of
the gradient magnitude and the second derivatives as a manner
to relate different color components of the image. This model can
be viewed as a generalization of the Bettahar–Stambouli filter to
multivalued images. The proposed algorithm is more efficient than
the mentioned filter and some previous works at color images denoising
and deblurring without creating false colors.
INTRODUCTION
CAPTURING an image with sensors is an important step in
many areas. The captured image is used in several applications,
which all have their own requests on the quality of the
captured image. Acquired images are often degraded with blur,
noise, or blur and noise simultaneously. The processing to be applied
to these images depends on the way of extracting wanted
information. Therefore, the frequent problem in low-level computer
vision arises from the goal to eliminate noise and uninteresting
details from an image, without blurring semantically important
structures such as edges [1], [2]. Two operations would
be done: denoising and sharpening. Several deconvolution and
denoising techniques have been proposed in the literature since:
statistics-based filters [3]–[5], wavelets [6], [7], partial-differential-
equation-based (PDE) algorithms [8], [9], and variational
methods [10], [11]. In particular, a large number of PDE-based
methods have been proposed to tackle the problem of image denoising
with a good preservation of edges and also to explicitly
account for intrinsic geometry. In this paper, we are interested
in PDE-based methods.
Direct Observation
For this comparison, we choose the parameters that give
better results for each filter, except for the number of iterations
that must be the same for objective comparison. The number
of iterations is chosen in the function of the visual quality of
the result. For each test image, we opt for the same number
of iterations, and for the step time , we prefer a small value
in order to converge to the solution with more precision about
the values of the objective criteria while getting more details
in the visual aspect of the restored images. Therefore, we can
converge to the solution with small numbers of iterations in
reference to the number that we use in this paper, excepted to
the Tschumperlé–Deriche filter that employs an adaptive step
time . All models are applied to blurry and noised images. In
the production of artificially blurry images, we use the Gaussian
convolution of original test images . Noised images
are produced by adding random Gaussian noise to blurred
images .
CONCLUSION
We have proposed a novel filter of coupling a shock filter to
curvature diffusion for color image enhancement in the RGB
space, which is based on using single vectors for all components
of the image. This filter produces selective smoothing
that reduces efficiently noise and sharpens edges. Our analysis
shows that the proposed method is more efficient than Alvarez–
Mazorra, Kornprobst, Gilboa, Fu, Bettahar–Stambouli,
and Tschumperlé–Deriche models at color image restoration
in the presence of blur and noise simultaneously. In that, it
denoises homogeneous parts of the multivalued image while it
keeps edges enhanced. However, due to the fact of using single
vectors with the specific reaction, our filter does not create false
colors that can appear when each component of the image is
enhanced separately.