29-01-2013, 02:53 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 scalar diffusion-shock filter coupling
model, where noisy and blurred images are denoised and
sharpened. The proposed model is based on using single vectors
of the gradient magnitude and the second derivatives as a
technique to relate different color components of the image. This
model can be viewed as a generalization of Bettahar-Stambouli
filter to multi-valued images. The proposed algorithm is more
efficient than the mentioned filter and some previous works on
color image denoising and deblurring without creating false
colors.
INTRODUCTION
APTURING 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. So, 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. Since, several deconvolution and denoising
techniques have been proposed in the literature: Statistics
based filters [3,4,5], wavelets [6,7], Partial Differential
Equations (PDE) based algorithms [8,9] and variational
methods [10,11]. Particularly, 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. Hence, partial differential
equations based on diffusion methods [8,12,13,14,15] and
shock filter [16,17,18] have recently dominated image
processing research.
BACKGROUND
Originated from a well known physical heat transfer process,
the PDE- based approaches consist in evolving in time the
filtered image u(t) under a PDE. When coupling diffusion and
shock filter the PDE is a combination of three terms:
The last term in (1), which is weighted by Csk, represents the contribution of
the shock filter in the enhancement of the image. The function
F(s) should satisfy the conditions F(0)=0 and F(s).s 0. The
choice of F(s) = sign(s) gives the classical shock filter [15].
Hence, by considering adaptive weights C, C and Csk as
functions of the local contrast, we can favor smoothing
process under diffusion terms in homogeneous parts of the
image or enhancement operation under shock filter at edge
locations.
COLOR IMAGES
Only a very few works tackle the shock diffusion coupling
using an approach specifically dedicated to color images [30].
A. Tschumperlé-Deriche model
To avoid the effect of the apparition of false colors, the
processing applied to the image must be driven in a common
and coherent manner for all image components. This type of
approach is denoted as “vector processing”, in opposition to
the marginal processing which is a multi-scalar processing.
Thus, in order to describe vector-valued image variations and
structures, Di Zenzo [26] and Lee [27] have proposed to use
the local variation of a vector gradient norm |u| that detects
edges and corners when its value becomes high.
EXPERIMENTAL RESULTS
We evaluate performances of our model by comparing it to
marginal channel by channel methods of Alvarez-Mazorra,
Kornprobst, Gilboa, Fu, Bettahar-Stambouli and the vector
regularization of Tschumperlé-Deriche only. These are
developed especially to enhance degraded images in presence
of blur and additive noise simultaneously. We are not dealing
with the evaluation of other types of methods, as our focus is
on diffusion-shock filter coupling.
Direct observation
For this comparison, we choose the parameters that give
better results for each filter, except for the number of
iterations which must be the same for objective comparison.
The number of iterations is chosen in 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 criterions while getting more
details in the visual aspect of the restored images. So, we can
converge to the solution with small numbers of iterations in
reference to the number that we use in this paper, excepted to
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
Region segmentation
The second comparison is performed after region
segmentation. The segmentation which is used is a classical
region growing technique: blob-coloring using a 4
neighborhood [35]. This technique is a quick and simple one
which is known to give over-segmentation, providing a lot of
small regions in noisy situation. In our case, this drawback
will be used to extract a measure of performance.
Nevertheless, to limit over-segmentation, the region growing
is realized iteratively, the aggregation threshold being
incremented at each iteration. Fig. 16 shows the results of the
segmentation on Face image. All the different segmentations
have been realized using the same parameter values (initial
threshold = 3, threshold increment = 2, iteration number = 30).
CONCLUSION
We have proposed a novel filter of coupling shock filter to
curvature diffusion for color image enhancement in RGB
space, which is based on using single vectors for all
components of the image. This filter produces a selective
smoothing reducing 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
presence of blur and noise simultaneously. In that it denoises
homogeneous parts of the multi-valued image, while it keeps
edges enhanced. However, due to the fact of using single
vectors with the specific reaction, our filter doesn’t create
false colors that can appear when each component of the
image is enhanced separately.