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International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN
0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEME
399
PERFORMANCE AND ANALYSIS OF IMPROVED UNSHARP
MASKING ALGORITHM FOR IMAGE ENHANCEMENT
1
Dnyaneshwar V.Haralkar, 2
Dr. Sudhir S. Kanade
1
(Department of ECE, TPCT’s C.O.E.Osmanabad, India)
2 (
Head of Department of ECE, TPCT’s C.O.E.Osmanabad Maharashtra, India)
ABSTRACT
In this paper we propose an improved unsharp masking algorithm. Contrast
enhancement and image sharpness is required in many applications. Unsharp masking is a
classical tool for sharpening an image. Unsharp masking algorithm is used for the exploratory
data model as a unified framework. Proposed algorithms have three issues: 1) Contrast is
increased and image is sharp by means of individual treatment of the residual and the model
component. 2) Halo effect is reduced by means of wavelet based denoising methods 3) Out-
of-range problem is solved by means of log-ratio and tangent operation. Experimental result
shows that the our proposed algorithm provides the better result as compared with the
previous one the contrast of the image is enhanced and sharpness of the image is increased. In
the proposed method the user can adjust the two parameters by controlling the contrast and
sharpness to produce the better result.
Keywords: Generalized linear system, image enhancement, Unsharp masking, and wavelet
denoising
1. INTRODUCTION
Enhancing the contrast and sharpness of the images has many practical applications.
Continuous research has been carried out to develop new algorithms. In this section detail
review of the previous works are carried out .These related work include unsharp masking
and its variants, retinex, histogram equalization and dehazing algorithm and generalized
linear systems.
INTERNATIONAL JOURNAL OF ELECTRONICS AND
COMMUNICATION ENGINEERING & TECHNOLOGY (IJECET)
ISSN 0976 – 6464(Print)
ISSN 0976 – 6472(Online)
Volume 4, Issue 2, March – April, 2013, pp. 399-411
© IAEME: www.iaeme.com/ijecet.asp
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International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN
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1.1. Related works
1.1.1 Sharpness and Contrast Enhancement
The classical unsharp masking algorithm expressed in detail as the equation: ߭ ൌ ‫ݕ‬ ൅
ߛሺ‫ݔ‬ െ ‫ݕ‬ሻwhere ‫ݔ‬ is the input image,‫ݕ‬ is the result of a linear low-pass filter, and the gain
ߛሺߛ ൐ 0ሻ is real scaling factor. The signal ݀ ൌ ‫ݔ‬ െ ‫ݕ‬ is amplified ሺߛ ൐ 1ሻ to increases the
sharpness. The signal ݀ contains 1) detail of the image, 2) noise, and 3) over-shoots and
under-shoots in area of sharp edges due to the smoothing edges. Enhancement of the noise is
clearly unacceptable; the enhancement of the under-shoot and over-shoot creates the
unpleasant halo effect. This need the filter not sensitive to noise and does not have smooth
sharp edges. These issues have been studied in much research. For example, the edge-
preserving filter [2]-[4] and the cubic filter [1] have been used to replace the linear low-pass
filter. The former is less sensitive to noise. The latter does not smooth sharp edges. Adaptive
gain control has also been studied [5].
To decreases the halo affect, edge preserving filter such as: weighted least-squares
based filters [13] adaptive Gaussian filter [12] and bilateral filter [11], [14] are used. Novel
algorithm for contrast enhancement in dehazing application has been published [15],
[16].Unsharp masking and retinex type of algorithm is that result usually out of range of the
image [12], [17]-[19]. A histogram-based a number of the internal scaling process and
rescaling process are used in the retinex algorithm presented in [19]
1.1.2 Generalized linear system and the Log-Ratio Approach
Marr [20] has pointed out that to develop an effective computer vision technique is
consider: 1) Why the particular operation is used, 2) How the signal can be represented, 3)
what implementation can be used. Myers presented a particular operation [21] usual addition
and multiplication if via abstract analysis, more easily implemented and more generalized or
abstract version of mathematical operation can be created for digital signal processing.
Abstract analysis provides a way to create system with desirable properties. The generalized
system is shown in Figure.1 is developed. The generalized addition and scalar multiplication
denoted by ْandٔ.
Are defined as follows:
‫ݔ‬ ْ ‫ݕ‬ ൌ ߶ିଵሾ߶ሺ‫ݔ‬ሻ ൅ ߶ሺ‫ݕ‬ሻሿሺ1ሻ
ߙ ٔ ‫ݔ‬ ൌ ߶ିଵሾߙ߶ሺ‫ݔ‬ሻሿ ሺ2ሻ
Fig.1: Block diagram of a generalized linear system
Where߶ሺ‫ݔ‬ሻ is usually a nonlinear function,x and y are the signal samples ߙusually a
real scalar, and is a non linear function. In [17] log ratio is proposed systematically tackle out
of range problem in the image restoration. The generalized linear system point provides the
log ratio point of view, where the operation are defined by using (1) and (2). Property of the
log ratio is that of gray scale image set ‫߳ܫ‬ሺ0, 1ሻ is closed under the new operation.
Φ(x) Linear
system
߶ିଵ
ሺ‫ݔ‬ሻ
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN
0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEME
401
1.2 Issue Addressed, Motivation and Contributions
In this section issues related to the contrast and sharpness enhancement is given in
detail. 1) Contrast and sharpness enhancement are two similar tasks. 2) The main goal of the
Unsharp is to increase the sharpness of the image and remove the halo effect. 3) While
improving the contrast of the image the minute details are improved and the noise well.
Contrast and sharpness enhancement have a rescaling process. It is performed carefully to
provide the best result. The exploratory data model in 1)-3) and issue 4) using the log-ratio
operation and a new generalized linear system is presented in this paper. This proposed work
is partly motivated by the classic work in unsharp masking [1], an excellent approach of the
halo effect [12], [19]. In [17] log-ratio operation was defined. Motivated by the LIP model
[24] , we study the properties of the linear system.
2. EXPLORATORY DATA ANALYSIS MODEL FOR IMAGE ENHANCEMENT
2.1Image model and generalized unsharp masking
In exploratory data analysis is to decompose a signal into two parts. In one part is of
particular model and other part is of residual model. In tukey’s own words the data model is:
“data=fit PLUS residuals”. ([28] Pp.208). The output of the filtering process can be denoted
by the‫ݕ‬ ൌ ݂ሺ‫ݔ‬ሻ. It can be regarded as the part of the image that can be fit in the model. Thus
we can show an image using generalized operation as follow
‫ݔ‬ ൌ ‫ݕ‬ ْ ݀ ሺ3ሻ
Where ݀is called as the detail signal (the residual). The detail signal is defined as
݀ ൌ ‫ݔ‬Ө‫,ݕ‬ Ө is the generalized operation. It provides the unified framework to study Unsharp
masking algorithms. A general form of the unsharp masking is given as
߭ ൌ ݄ሺ‫ݕ‬ሻ ْ ݃ሺ݀ሻ ሺ4ሻ
Where υ is the output of the algorithm and both ݄ሺ‫ݕ‬ሻand ݀ሺ‫ݕ‬ሻcould be linear or non
linear functions. Model explicitly states that the image sharpness is the model residual. It
forces the algorithm developer to carefully select an appropriate model and avoid model such
as linear filters. This model permits the incorporation of the contrast enhancement by means
of suitable processing function ݄ሺ‫ݕ‬ሻas adaptive equalization function.. The generalized
algorithm can enhance the overall contrast and sharpness of the image.
2.2 Outline of the Proposed Algorithm
Fig.2 shows the proposed algorithm based upon the previous model and generalized
the classical Unsharp masking algorithm by addressing issues started in Section I-B. The IMF
is selected due to its properties such as root signal and simplicity. Advantage of edge
preserving filter is nonlocal means filter and wavelet-based denoising filter can also be used.
Rescaling process is used by the new operation defined according to the log-ratio and new
generalized linear system.
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN
0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEME
402
Fig.2 Block diagram of the proposed un-sharp generalized masking algorithm
3. LOG-RATIO, GENERALIZED LINEAR SYSTEMS & BREGMAN DIVERGENCE
This Section deals with new operation using generalized linear system approach. To
provide a simple presentation we use (1) and (2). These operations are defined from the
vector space point of view which is similar to the development of the LIP model [26]. We
provide the connection between the log-ratio, generalized systems and the Bregman
divergence. As a result we show novel interpretation of two existing generalized linear
systems, but also develop a new system.
3.1 Definitions and properties of log-Ratio operations
3.1.1Nonlinear function
In nonlinear function pixel of the gray scale of an image ‫ݔ‬ ‫א‬ ሺ0, 1ሻis considered. For
an – bit image, first we add a very small positive constant to the pixel gray value then scale it
by 2ିே
such that it is in the range(0, 1). The non linear function can be defined as
фሺ‫ݔ‬ሻ ൌ ݈‫݃݋‬
1 െ ‫ݔ‬
‫ݔ‬
ሺ5ሻ
To simplify the notation, we define the ratio of the negative image to the original image as
follows:
ܺ ൌ ߰ሺ‫ݔ‬ሻ ൌ
1 െ ‫ݔ‬
‫ݔ‬
ሺ6ሻ
d=xӨ y
Wavelet
Based
denoising
Adaptive
gain control
Contrast
enhancement
Ө
ْ
ٔ
Y
yٔ ݀
ߛ
X Z
߭ ൌ ‫ݖ‬ ْ ሺߛ ٔ ݀ሻ
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN
0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEME
403
3.1.2 Addition and scalar Multiplication
Using (1), the addition of two gray scales ‫ݔ‬ଵand ‫ݔ‬ଶ is defined as
‫ݔ‬ଵ ْ ‫ݔ‬ଶ ൌ
1
1 ൅ ߰ሺ‫ݔ‬ଵሻ߰ሺ‫ݔ‬ଶሻ
ൌ
1
1 ൅ ܺଵܺଶ
ሺ7ሻ
Whereܺଵ ൌ ߰ሺ‫ݔ‬ଵሻand ܺଶ ൌ ߰ሺ‫ݔ‬ଶሻ. The multiplication of gray scale ‫ݔ‬ by a real scalar
ߙሺെ∞ ൏ ߙ ൏ ∞ is defined by using (2) as follows:
ߙ ٔ ‫ݔ‬ ൌ
1
1 ൅ ܺఈ
ሺ8ሻ
This operation is called as scalar multiplication which is a derived from a vector space point
of view [29]. We can define a non-zero gray scale, denoted as follows:
݁ ْ ‫ݔ‬ ൌ ‫ݔ‬ ሺ9ሻ
It is easy to show that݁ ൌ 1/2. We can regard the interval (0, (1/2)) and ((1/2),1) as the new
definitions of negative and positive numbers. Absolute value is denoted as |‫|ݔ‬଴ can be
defined in the similar way as the absolute value of the real number as follows.
|‫|ݔ‬଴ ൌ ൞
‫,ݔ‬
1
2
൑ ‫ݔ‬ ൏ 1
1 െ ‫,ݔ‬ 0 ൏ ‫ݔ‬ ൏
1
2
ሺ10ሻ
3.1.3 Negative Image and Subtraction Operation
A natural extension is to describe the negative of the gray scale value. Although this
can be defined by (8) and (9). The negative value of the gray scale‫,ݔ‬ denoted by ‫ݔ‬′
, is
obtained by solving
‫ݔ‬ ْ ‫ݔ‬′
ൌ
1
2
ሺ11ሻ
The result is ‫ݔ‬′
ൌ 1 െ ‫ݔ‬ which is varying with the classical definition of the negative
image. This definition is also varying with the scalar multiplication in that ሺെ1ሻ ٔ x ൌ 1 െ
xthe notation of the classical notation is negative which is given as:Ө‫ݔ‬ ൌ ሺെ1ሻ ٔ ‫ݔ‬ .
We can also define the subtraction operation using the addition operation in (8) as follows:
‫ݔ‬ଵӨ xଶ ൌ xଵ ْ ሺӨ xଶሻ
ൌ
1
߰ሺ‫ݔ‬ଵሻ߰ሺӨxଶሻ ൅ 1
ൌ
1
ܺଵܺଶ
ିଵ
൅ 1
ሺ12ሻ
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN
0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEME
404
Fig.3 Effects of the log ratio addition ‫ݕ‬ ൌ ‫ݔ‬ ْ ߙ(top row) and scalar multiplication operation
‫ݕ‬ ൌ ߙ ٔ ‫(ݔ‬bottom row)
Where߰ሺӨ‫ݔ‬ଶሻ ൌ 1/߰ሺ‫ݔ‬ଶሻ ൌ ܺଶ
ିଵ
using the definition of gray scale, we also have a
clear understanding of the scalar multiplication forߙ ൏ 0.
‫ݕ‬ ൌ ߙ ٔ ‫ݔ‬
ൌ ሺെ1ሻ ٔ ሺ|ߙ| ٔ ‫ݔ‬ሻ
ൌ 1 െ |ߙ| ٔ ‫ݔ‬ ሺ13ሻ
Here we used ߙ ൌ ሺെ1ሻ ൈ |ߙ| and the distribution law for two real scalars ߙ and ߚ
ሺߙ ൈ ߚሻ ٔ ‫ݔ‬ ൌ ߙ ٔ ሺߚ ٔ ‫ݔ‬ሻ ሺ14ሻ
3.2. Log-Ratio, the Generalized Linear system and the Bregman Divergence
We study the connection between the log-ratio and the Bregman divergence. This
connection not only provides geometrical interpretation and new insight of the log-ratio, but
also suggests a new way to develop generalized linear systems.
3.2.1 Log-Ratio and The Bregman Divergence
The classical weighted average can be regarded as the solution of the following
optimization problem:
‫ݑ‬ௐ஺ ൌ ܽ‫݃ݎ‬ min
௨
෍ ߙ௡ሺ‫ݔ‬௡
ே
௡ୀଵ
െ ‫ݑ‬ሻଶ
ሺ15ሻ
What is the corresponding optimization problem that leads to the generalized weighted
average stated in (19) ?
To study this problem, we need to recall some result in the Bregman divergence [30], [31].
The Bregman divergence of two vectors x and y, denoted by‫ܦ‬ிሺ‫ݔ‬ ‫פ‬ ‫ݕ‬ሻ, is defined as follows:
‫ܦ‬ிሺ‫,ݔ‬ ‫ݕ‬ሻ ൌ ‫ܨ‬ሺ‫ݔ‬ሻ െ ‫ܨ‬ሺ‫ݕ‬ሻ െ ሺ‫ݔ‬ െ ‫ݕ‬ሻ்
‫ܨ׏‬ሺ‫ݕ‬ሻ ሺ16ሻ
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN
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Where ‫:ܨ‬ ܺ ՜ ܴconvex and differentiable function is defined over an open convex domain ܺ
and ‫ܨ׏‬ሺ‫ݕ‬ሻ is the gradient of F evaluated at the point y. Centroid of a set of vector denoted
ሼ‫ݔ‬௡ሽ௡ୀଵ: ܰ in terms of minimizing the sum of the Bregman divergence is studied in a recent
paper [31]. The weighted left-sided Centroid is given by
ܿ௅ ൌ arg min
௖‫א‬௫
෍ ߙ௡
ே
௡ୀଵ
‫ܦ‬ிሺܿԡ‫ݔ‬௡ሻ
ൌ ‫ܨ׏‬ିଵ
൭෍ ߙ௡‫ܨ׏‬ሺ‫ݔ‬௡
ே
௡ୀଵ
ሻ൱ ሺ17ሻ
Comparing (19) and (22), we can see that when ‫ݔ‬௡a scalar is, the generalized
weighted average of the log-ratio is a special case of the weighted left-sided Centroid
with߶ሺ‫ݔ‬ሻ ൌ ‫ܨ׏‬ሺ‫ݔ‬ሻ. It easy to show that
‫ܨ‬ሺ‫ݔ‬ሻ ൌ න фሺ‫ݔ‬ሻ݀‫ݔ‬
ൌ െ‫݃݋݈ݔ‬ሺ‫ݔ‬ሻ െ ሺ1 െ ‫ݔ‬ሻ logሺ1 െ ‫ݔ‬ሻ ሺ18ሻ
Where the constant of the indefinite integral is omitted. ‫ܨ‬ሺ‫ݔ‬ሻis called the bit entropy
and the corresponding Bregman divergence is defined as
‫ܨ‬ሺ‫ݔ‬ሻ ൌ න фሺ‫ݔ‬ሻ݀‫ݔ‬
ൌ െ‫݃݋݈ݔ‬ሺ‫ݔ‬ሻ െ ሺ1 െ ‫ݔ‬ሻ logሺ1 െ ‫ݔ‬ሻ ሺ19ሻ
Where the constant of the indefinite integral is omitted ‫ܨ‬ሺ‫ݔ‬ሻ is called the bit entropy and the
corresponding Bregman divergence is defined as
‫ܦ‬ிሺ‫ݔ‬ԡ‫ݕ‬ሻ ൌ െ‫݃݋݈ݔ‬
‫ݔ‬
‫ݕ‬
െ ሺ1 െ ‫ݔ‬ሻ݈‫݃݋‬
1 െ ‫ݔ‬
1 െ ‫ݕ‬
ሺ20ሻ
Where is called the logistic loss
Therefore, the log-ratio has an intrinsic connection with the Bregman divergence through the
generalized weighted average. This connection reveals a geometrical property of the log-ratio
which uses a particular Bregman divergence to measure the generalized distance between two
points. It is compared with the weighted average which uses the Euclidean distance. Loss
function of log-ratio uses the logistic loss function; the classical weighted average uses the
square loss function.
3.2.2 Generalizedlinear system and the Bregman Divergence
The connection between the Bregman divergence with other well establish generalized
linear system such as the MHS with ߶ሺ‫ݔ‬ሻ ൌ log ሺ‫ݔ‬ሻ where ‫߳ݔ‬ሺ0, ∞ሻ and the LIP model [26]
with ߶ሺ‫ݔ‬ሻ ൌ െlog ሺ1 െ ‫ݔ‬ሻwhere‫߳ݔ‬ሺെ∞, 1ሻ. The corresponding Bregman divergences are the
Kullback-Leibler (KL) divergence for the MHS [31]
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN
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‫ܦ‬ிሺ‫,ݔ‬ ‫ݕ‬ሻ ൌ ‫݃݋݈ݔ‬
‫ݔ‬
‫ݕ‬
െ ሺ‫ݔ‬ െ ‫ݕ‬ሻ ሺ21ሻ
And the LIP
‫ܦ‬ிሺ‫,ݔ‬ ‫ݕ‬ሻ ൌ ሺ1 െ ‫ݔ‬ሻ݈‫݃݋‬
1 െ ‫ݔ‬
1 െ ‫ݕ‬
െ ሾሺ1 െ ‫ݔ‬ሻ െ ሺ1 െ ‫ݕ‬ሻሿ ሺ22ሻ
LIP model demonstrate the information-theoretic interpretation. The relationship between the
KL divergence and the LIP model reveals a novel into its geometrical property.
3.2.3A New Generalized Linear System
In Bregman divergence corresponding generalized weighted average can be defined
as ߶ሺ‫ݔ‬ሻ ൌ ‫ܨ׏‬ሺ‫ݔ‬ሻ. For example the log-ratio, MHS and lip can be developed from the
Bregman divergences. Bregman divergence measures the distance of two signal samples. The
measure is related to the geometrical properties of two signal space. Generalized linear
system for solving the out-of-0range problem can be developed by the following Bregman
divergence (called “Hollinger-like” divergence in Table I on [31])
‫݂ܦ‬ሺ‫,ݔ‬ ‫ݕ‬ሻ ൌ
1 െ ‫ݕݔ‬
ඥ1 െ ‫ݕ‬ଶ
െ ඥ1 െ ‫ݔ‬ଶ ሺ23ሻ
Which is generated by the convex function ‫ܨ‬ሺ‫ݔ‬ሻ ൌ െ√1 െ ‫ݔ‬ଶ whose domain is (-1, 1). The
nonlinear function ߶ሺ‫ݔ‬ሻ for the corresponding generalized linear system is as follows:
фሺ‫ݔ‬ሻ ൌ
݀ሺ‫ܨ‬ሺ‫ݔ‬ሻ
݀‫ݔ‬
ൌ
‫ݔ‬
√1 െ ‫ݔ‬ଶ
ሺ24ሻ
In this paper the generalized linear system is called the tangent system and the new
addition and scalar multiplication operation are called tangent operations. In image
processing application, first linearly map pixel value from the interval [0,2ே
ሿ to a new
interval (-1, 1). Then the image is processed by using the tangent operation. The result is then
mapped back to the interval ሾ0,2ே
) through inversing mapping. We can verify the signal with
the signal set ‫߳ܫ‬ሺെ1, 1ሻ is closed under the tangent operations. The tangent system can be
used as an alternative to the log-ratio to solve the out-of-range problem. The application and
the properties of the tangent operation can be studied in a similar way as those presented
Section III-A. The negative image and the subtraction operation, and study the order relation
for the tangent operations. As shown in Figure.5 the result of adding a constant to an N-bit
image (N=8) using the tangent addition. In simulation, we use a simple function ‫ݍ‬ሺ‫ݔ‬ሻ ൌ
ଶሺ௫ାଵሻ
ଶಿାଵ
െ 1 to map the image from [0,2ே
ሻ to (-1, 1). We can see that the effect is similar to the
log-ratio addition.
4. PROPOSED ALGORITHM
4.1Dealing with color images
First the color image is converted from the RGB color space to the HIS or the LAB
color space. The chrominance components such as the H and S components are not
processed. After the luminance component is processed the inverse conversion is performed.
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN
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Enhanced color image in RGB is obtained. Rationale processing is carried out in luminance
component to avoid a potential problem of altering the white balance of the image when the
RGBcomponents are processed individually two iteration ‫ܪ‬ሺ‫ݕ‬௞, ‫ݕ‬௞ାଵሻ ൌሻ1/ܰሻԡ‫ݕ‬௞ െ ‫ݕ‬௞ାଵԡ
మ
మ
where N is the number of pixels in the image Result using two setting of the wavelet based
denoising and using the "cameraman" image are shown.
4.2Enhancement of the detail Signal
The root Signal and the Detail Signal : Let us denote the median filtering operation as
a function ‫ݕ‬ ൌ ݂ሺ‫ݔ‬ሻ which maps the input ‫ݔ‬ to the output y. An IMF operation can be
denoted as: ‫ݕ‬௞ାଵ ൌ ݂ሺ‫ݕ‬௞ሻ where ݇ ൌ 0, 1, 2, … is the iterantion index and ‫ݕ‬଴ ൌ ‫.ݔ‬The signal
‫ݕ‬௡ is usually called the root signal of the filtering process if ‫ݕ‬௡ାଵ ൌ ‫ݕ‬௡. It is convenient to
define a root signal ‫ݕ‬௡ as follows:
݊ ൌ min ݇ , ‫ܪ݋ݐݐ݆ܾܿ݁ݑݏ‬ሺ‫ݕ‬௞, ‫ݕ‬௞ାଵ ൏ ߜሻ ሺ25ሻ
Where ‫ܪ‬ሺ‫ݕ‬௞, ‫ݕ‬௞ାଵሻ is a sultable measur of the difference between the two images. ߜ is a user
defined threshold. For natural image, mean square difference, defined as ‫ܪ‬ሺ‫ݕ‬௞, ‫ݕ‬௞ାଵሻ ൌ ቀ
ଵ
ே
ቁ ‫פ‬
‫פ‬ ‫ݕ‬௞ െ ‫ݕ‬௞ାଵሻ ൌ ሺ1/ܰሻ ‫פפ‬ ሺ‫ݕ‬௞ െ ‫ݕ‬௞ାଵ ‫פפ‬
ଶ
ଶ
(N is the number of the pixels), is a monotonic
decreasing function of K. An example is shown is figure belowit is clear that the defination of
the thershold is depends upon the threshold. It is possible to set a large value of the ߜsuch that
‫ݕ‬ଵ is the root signal. After five iteration ሺ݇ ൒ 5ሻ the difference ‫ܪ‬ሺ‫ݕ‬௞,‫ݕ‬௞ାଵሻ changes occurs
slightly. We can regard ‫ݕ‬ସ‫ݕݎ݋‬ହthe root signal.
Of course, the numaber of thr iterations, tha size and the shape pf the filter mask have
certain impact on the root signal. The original signal in shown in Figure. 7. Which is the 100th
row of the “cameraman” image. The root signal ‫ݕ‬is produced by an IMF filter with a ሺ3 ൈ 3ሻ
mask and the three iteration. The signal ‫ݏ‬ is produced by a linear low-pass filter with a
uniform mask of ሺ5 ൈ 5ሻ. The gain of the both algorithm is three. On comparing the
enhanced signal we can see clearly that while the result for the classical unsharp masking
algorithm suffers from the out of range problem and halo effect (under-shoot and over-shoot),
the result of the proposed algorithm is free of such problem.
4.3 Adaptive Gain Control
In Fig.3 to enhance the detail the gain must be greater than one. Using a universal
gain for the whole image does not lead to good results, because to enhance the small deatil a
relatively large gain is needed. A large gain can lead to the saturation of the detailed signal
whose values are larger than the threshold. Saturation is undesirable because different
amplitude of the detail signal are mapped to the same amplitude of either 1 or 0. This leads to
loss of information. The gain must be adaptively controlled.
We describe the gain control algorithm for using with the log-ratio operation. To control the
gain, linear mapping of the detail signal d to a new signal c.
ܿ ൌ 2݀ െ 1 ሺ26ሻ
Such that the dynamic range of c is (-1,1). A simple idea is to set the gain as a function of the
signal c and to gradually decrease the gain frim its maximum value ߛெ஺௑ when ܿ ‫פ‬൏ ܶ to ots
minimum value ߛெூே when ‫פ‬ ܿ ՜ 1. We propose the following adaptive gain function
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN
0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEME
408
ߛሺܿሻ ൌ ߙ ൅ ߚ expሺെ|ܿఎሻ ሺ27ሻ
where ߟ is a parameter that controlsthe rate of decreasing. The parameter ߙ and ߚ are
obtained by solving the equation:
ߛሺ0ሻ ൌ ߛெ஺௑ and ߛሺ1ሻ ൌ ߛெூே. For a fixed ߟ, we can easily determine the parameter as
follows:
ߚ ൌ ሺߛெ஺௑ െ ߛெூேሻ/ሺ1 െ ݁ିଵ
ሻ ሺ28ሻ
and
ߙ ൌ ߛெ஺௑ െ ߚ ሺ29ሻ
Both ߛெ஺௑ and ߛெூேcould be chosen based upon each individual image processing task. It is
reasonable to set ߛெூே ൌ 1. This setting follows the intuition that when the amplitude of the
detailed signal is large enough, it does not need any further amplification. For example we
can see that
lim
|ௗ|బ
ߛ ٔ ݀ ൌ lim
ௗబ՜ଵ
1
1 ൅ ቀ
ଵିௗ
ௗ
ቁ ߛ
ൌ 1 ሺ30ሻ
Scalar multiplication has little effect.
We now study the effect of ߟ and ߛெ஺௫ by setting ߛெூே ൌ 1.
4.4Contrast Enhancement of the Root Signal
For contrast enhancement, we use adaptive histogram equalisation implement by
Matlab function in the Image processing Toolbox. The function called “adapthisteq”, has a
parameter contorlling the contrast. This parameter is determined by user through experiment
to obtain the most visually pleasing result. In simulation, we use default values for other
parameters if the function
5. WAVELET DENOISING
The wavelet transform has been a powerful and widely used tool in image denoising
because of its energy compaction and multi resolution properties. Denoising an image
corrupted with additive white Gaussian noise was initially proposed by thresholding the
wavelet coefficients. Subsequently, various decomposition strategies and thresholding
schemes have been proposed. However, most of these use classical orthogonal wavelets
which are independent of the image and noise characteristics and focus on finding the best
threshold. Unlike the Fourier transform with its complex exponential basis, the wavelet
transforms do not have a unique basis. Noting this point several attempts at designing
matched wavelets have been made with the goal of match varying from match to a signal and
energy compaction to maximizing the signal energy in the scaling sub-space.
The most important way of distinguishing information from noise in the wavelet domain
consists of thresholding the wavelet coefficients. Mainly hard and soft thresholding
techniques are performed. Thresholding is the simplest method of image denoising .In this
from a gray scale image, thresholding can be used to create binary image. Thresholding is
used to segment an image by setting all pixels whose intensity values are above a threshold to
a foreground value and all the remaining pixels to a background value. Thresholding is
mainly divided into two categories.
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN
0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, I
Hard threshold is a "keep or kill" procedure and is more intuitively appealing. The transfer
function of the hard thresholding is shown in the figure. Hard thresholding may seem to be
natural. Sometimes pure noise coefficien
Soft threshold shrinks coefficients above the threshold in absolute value. The false structures
in hard thresholding can be overcome by soft thresholding. Now a days, wavelet based
denoising methods have received a greater at
6. EXPERIMENTAL ANALYSIS
Here we considered wavelet based Denoising using hard and soft thresholding
approaches as stated in [22].We have tested our experimented five different images samples
compared against different parameters
(a) Original Image
(c)Proposed method with HT thresholding
(d)Proposed method with ST Thresholding
(e) Performance analysis contrast parameter Vs average contrast fo
Fig.4: the output results of the proposed methods
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN
6472(Online) Volume 4, Issue 2, March – April (2013), © IAEME
409
is a "keep or kill" procedure and is more intuitively appealing. The transfer
function of the hard thresholding is shown in the figure. Hard thresholding may seem to be
natural. Sometimes pure noise coefficients may pass the hard threshold
shrinks coefficients above the threshold in absolute value. The false structures
in hard thresholding can be overcome by soft thresholding. Now a days, wavelet based
denoising methods have received a greater attention
EXPERIMENTAL ANALYSIS
Here we considered wavelet based Denoising using hard and soft thresholding
approaches as stated in [22].We have tested our experimented five different images samples
compared against different parameters
Original Image (b) detailed coefficients
c)Proposed method with HT thresholding
(d)Proposed method with ST Thresholding
(e) Performance analysis contrast parameter Vs average contrast for different images
the output results of the proposed methods
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN
April (2013), © IAEME
is a "keep or kill" procedure and is more intuitively appealing. The transfer
function of the hard thresholding is shown in the figure. Hard thresholding may seem to be
shrinks coefficients above the threshold in absolute value. The false structures
in hard thresholding can be overcome by soft thresholding. Now a days, wavelet based
Here we considered wavelet based Denoising using hard and soft thresholding
approaches as stated in [22].We have tested our experimented five different images samples
r different images
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN
0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEME
410
7. CONCLUSION
In this paper an improved approach for classical unsharp masking algorithm is
proposed by introducing wavelet based thresholding. From the above obtained results we can
clued that the proposed method out performs for different images under different block size
and average contrast parameter. This method can significantly increase the sharpness and
contrast ratios appropriately.
REFERENCES
[1] G. Ramponi, “A cubic unsharp masking technique for contrast enhancement, “Signal
Process., pp. 211–222, 1998.
[2] S. J. Ko and Y. H. Lee, “Center weighted median filters and their applications to image
enhancement,” IEEE Trans. Circuits Syst., vol. 38, no. 9, pp. 984–993, Sep. 1991.
[3] M. Fischer, J. L. Paredes, and G. R. Arce, “Weighted median image sharpeners for the
world wide web,” IEEE Trans. Image Process., vol. 11, no. 7, pp. 717–727, Jul. 2002.
[4] R. Lukac, B. Smolka, and K. N. Plataniotis, “Sharpening vector median filters,” Signal
Process., vol. 87, pp. 2085–2099, 2007.
[5] A. Polesel, G. Ramponi, and V. Mathews, “Image enhancement via adaptive unsharp
masking,” IEEE Trans. Image Process., vol. 9, no. 3, pp. 505–510, Mar. 2000.
[6] E. Peli, “Contrast in complex images,” J. Opt. Soc. Amer., vol. 7, no. 10, pp. 2032–2040,
1990.
[7] S. Pizer, E. Amburn, J. Austin, R. Cromartie, A. Geselowitz, T. Greer, B. Romeny, J.
Zimmerman, and K. Zuiderveld, “Adaptive histogram equalization and its variations,”
Comput. Vis. Graph. Image Process. vol. 39, no. 3, pp. 355–368, Sep. 1987.
[8] J. Stark, “Adaptive image contrast enhancement using generalizations of histogram
equalization,” IEEE Trans. Image Process., vol. 9, no. 5, pp. 889–896, May 2000.
[9] E. Land and J. McCann, “Lightness and retinex theory,” J. Opt. Soc. Amer., vol. 61, no. 1,
pp. 1–11, 1971.
[10] B. Funt, F. Ciurea, and J. McCann, “Retinex in MATLAB™,” J. Electron. Image., pp.
48–57, Jan. 2004.
[11] M. Elad, “Retinex by two bilateral filters,” in Proc. Scale Space, 2005, pp. 217–229.
[12] J. Zhang and S. Kamata, “Adaptive local contrast enhancement for the visualization of
high dynamic range images,” in Proc. Int. Conf. PatternRecognit., 2008, pp. 1–4.
[13] Z. Farbman, R. Fattal, D. Lischinski, and R. Szeliski, “Edge-preserving decompositions
for multi-scale tone and detail manipulation,” ACMTrans. Graph., vol. 27, no. 3, pp. 1–10,
Aug. 2008.
[14] F. Durand and J. Dorsey, “Fast bilateral filtering for the display of highdynamic- range
images,” in Proc. 29th Annu. Conf. Comput. Graph.Interactive Tech., 2002, pp. 257–266.
[15] R. Fattal, “Single image dehazing,” ACM Trans. Graph., vol. 27, no. 3, pp. 1–9, 2008.
[16] K. M. He, J. Sun, and X. O. Tang, “Single image haze removal using dark channel
prior,” in Proc. IEEE Conf. Comput. Vis. PatternRecognit., Jun. 2009, pp. 1956–1963.
[17] H. Shvaytser and S. Peleg, “Inversion of picture operators,” Pattern Recognit. Lett., vol.
5, no. 1, pp. 49–61, 1987.
[18] G. Deng, L. W. Cahill, and G. R. Tobin, “The study of logarithmic image processing
model and its application to image enhancement,” IEEE Trans. Image Process., vol. 4, no. 4,
pp. 506–512, Apr. 1995.
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN
0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEME
411
[19] L. Meylan and S. Süsstrunk, “High dynamic range image rendering using a retinex-
based adaptive filter,” IEEE Trans. Image Process., vol. 15, no. 9, pp. 2820–2830, Sep. 2006.
[20] D. Marr, Vision: A Computational Investigation into the Human Representation and
Processing of Visual Information. San Francisco, CA:Freeman, 1982.
[21] D. G. Myers, Digital Signal Processing Efficient Convolution and Fourier Transform
Technique. Upper Saddle River, NJ: Prentice-Hall, 1990.
[22] Nevine Jacob and Aline Martin, Image Denoising In The Wavelet Domain Using Wiener
Filtering,December 17, 2004.
[23] I.Suneetha and Dr.T.Venkateswarlu, “Spatial Domain Image Enhancement using
Parameterized Hybrid Model”, International Journal of Electronics and Communication
Engineering &Technology (IJECET), Volume 3, Issue 2, 2012, pp. 209 - 216, ISSN Print:
0976- 6464, ISSN Online: 0976 –6472.
[24] R. Pushpavalli and G.Sivaradje, “A New Tristate Switching Median Filtering Technique
for Image Enhancement”, International Journal of Advanced Research in Engineering &
Technology (IJARET), Volume 3, Issue 1, 2012, pp. 55 - 65, ISSN Print: 0976-6480, ISSN
Online: 0976-6499
APPENDIX
TABLE I
Key components of some generalized linear system motivated by the bregman divergence.
The domain of the lip model isሺെ∞, ‫ܯ‬ሻ. In this table, it is normalized by M
TO SIMPLIFY NOTATION
Domain D୊ሺx, yሻ Ԅሺxሻ x ْ y α ٔ x, ሺα ‫א‬ Rሻ
Log-
ratio
(0, 1) െ‫݃݋݈ݔ‬
‫ݔ‬
‫ݕ‬
െ ሺ1
െ ‫ݔ‬ሻ݈‫݃݋‬
1 െ ‫ݔ‬
1 െ ‫ݕ‬
݈‫݃݋‬
1 െ ‫ݔ‬
‫ݔ‬
1
1 ൅
ଵି௫
௫
ଵି௬
௬
1
1 ൅ ቀ
ଵି௫
௫
ቁ
ఈ
LIP (-∞, 1ሻ ሺ1
െ ‫ݔ‬ሻ݈‫݃݋‬
1 െ ‫ݔ‬
1 െ ‫ݕ‬
െ ሾሺ1 െ ‫ݔ‬ሻ
െ ሺ1 െ ‫ݕ‬ሻሿ
െlog ሺ1
െ ‫ݔ‬ሻ
‫ݔ‬ ൅ ‫ݕ‬ െ ‫ݕݔ‬ 1 െ ሺ1 െ ‫ݔ‬ሻଶ
MHS (0,∞ሻ ‫݃݋݈ݔ‬
‫ݔ‬
‫ݕ‬
െ ሺ‫ݔ‬
െ ‫ݕ‬ሻ
െlog ሺ‫ݔ‬ሻ ‫ݕݔ‬ ‫ݔ‬ఈ
Tangent (-1, 1) 1 െ ‫ݕݔ‬
ඥ1 െ ‫ݕ‬ଶ
െ ඥ1 െ ‫ݔ‬ଶ
‫ݔ‬
√1 െ ‫ݔ‬ଶ
߶ሺ‫ݔ‬ሻ ൅ ߶ሺ‫ݕ‬ሻ
ඥ1 ൅ ሺ߶ሺ‫ݔ‬ሻ ൅ ߶ሺ‫ݕ‬ሻሻଶ
ߙ߶ሺ‫ݔ‬ሻ
ඥ1 ൅ ሺߙ߶ሺ‫ݔ‬ሻሻଶ

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Performance and analysis of improved unsharp masking algorithm for image

  • 1. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEME 399 PERFORMANCE AND ANALYSIS OF IMPROVED UNSHARP MASKING ALGORITHM FOR IMAGE ENHANCEMENT 1 Dnyaneshwar V.Haralkar, 2 Dr. Sudhir S. Kanade 1 (Department of ECE, TPCT’s C.O.E.Osmanabad, India) 2 ( Head of Department of ECE, TPCT’s C.O.E.Osmanabad Maharashtra, India) ABSTRACT In this paper we propose an improved unsharp masking algorithm. Contrast enhancement and image sharpness is required in many applications. Unsharp masking is a classical tool for sharpening an image. Unsharp masking algorithm is used for the exploratory data model as a unified framework. Proposed algorithms have three issues: 1) Contrast is increased and image is sharp by means of individual treatment of the residual and the model component. 2) Halo effect is reduced by means of wavelet based denoising methods 3) Out- of-range problem is solved by means of log-ratio and tangent operation. Experimental result shows that the our proposed algorithm provides the better result as compared with the previous one the contrast of the image is enhanced and sharpness of the image is increased. In the proposed method the user can adjust the two parameters by controlling the contrast and sharpness to produce the better result. Keywords: Generalized linear system, image enhancement, Unsharp masking, and wavelet denoising 1. INTRODUCTION Enhancing the contrast and sharpness of the images has many practical applications. Continuous research has been carried out to develop new algorithms. In this section detail review of the previous works are carried out .These related work include unsharp masking and its variants, retinex, histogram equalization and dehazing algorithm and generalized linear systems. INTERNATIONAL JOURNAL OF ELECTRONICS AND COMMUNICATION ENGINEERING & TECHNOLOGY (IJECET) ISSN 0976 – 6464(Print) ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April, 2013, pp. 399-411 © IAEME: www.iaeme.com/ijecet.asp Journal Impact Factor (2013): 5.8896 (Calculated by GISI) www.jifactor.com IJECET © I A E M E
  • 2. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEME 400 1.1. Related works 1.1.1 Sharpness and Contrast Enhancement The classical unsharp masking algorithm expressed in detail as the equation: ߭ ൌ ‫ݕ‬ ൅ ߛሺ‫ݔ‬ െ ‫ݕ‬ሻwhere ‫ݔ‬ is the input image,‫ݕ‬ is the result of a linear low-pass filter, and the gain ߛሺߛ ൐ 0ሻ is real scaling factor. The signal ݀ ൌ ‫ݔ‬ െ ‫ݕ‬ is amplified ሺߛ ൐ 1ሻ to increases the sharpness. The signal ݀ contains 1) detail of the image, 2) noise, and 3) over-shoots and under-shoots in area of sharp edges due to the smoothing edges. Enhancement of the noise is clearly unacceptable; the enhancement of the under-shoot and over-shoot creates the unpleasant halo effect. This need the filter not sensitive to noise and does not have smooth sharp edges. These issues have been studied in much research. For example, the edge- preserving filter [2]-[4] and the cubic filter [1] have been used to replace the linear low-pass filter. The former is less sensitive to noise. The latter does not smooth sharp edges. Adaptive gain control has also been studied [5]. To decreases the halo affect, edge preserving filter such as: weighted least-squares based filters [13] adaptive Gaussian filter [12] and bilateral filter [11], [14] are used. Novel algorithm for contrast enhancement in dehazing application has been published [15], [16].Unsharp masking and retinex type of algorithm is that result usually out of range of the image [12], [17]-[19]. A histogram-based a number of the internal scaling process and rescaling process are used in the retinex algorithm presented in [19] 1.1.2 Generalized linear system and the Log-Ratio Approach Marr [20] has pointed out that to develop an effective computer vision technique is consider: 1) Why the particular operation is used, 2) How the signal can be represented, 3) what implementation can be used. Myers presented a particular operation [21] usual addition and multiplication if via abstract analysis, more easily implemented and more generalized or abstract version of mathematical operation can be created for digital signal processing. Abstract analysis provides a way to create system with desirable properties. The generalized system is shown in Figure.1 is developed. The generalized addition and scalar multiplication denoted by ْandٔ. Are defined as follows: ‫ݔ‬ ْ ‫ݕ‬ ൌ ߶ିଵሾ߶ሺ‫ݔ‬ሻ ൅ ߶ሺ‫ݕ‬ሻሿሺ1ሻ ߙ ٔ ‫ݔ‬ ൌ ߶ିଵሾߙ߶ሺ‫ݔ‬ሻሿ ሺ2ሻ Fig.1: Block diagram of a generalized linear system Where߶ሺ‫ݔ‬ሻ is usually a nonlinear function,x and y are the signal samples ߙusually a real scalar, and is a non linear function. In [17] log ratio is proposed systematically tackle out of range problem in the image restoration. The generalized linear system point provides the log ratio point of view, where the operation are defined by using (1) and (2). Property of the log ratio is that of gray scale image set ‫߳ܫ‬ሺ0, 1ሻ is closed under the new operation. Φ(x) Linear system ߶ିଵ ሺ‫ݔ‬ሻ
  • 3. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEME 401 1.2 Issue Addressed, Motivation and Contributions In this section issues related to the contrast and sharpness enhancement is given in detail. 1) Contrast and sharpness enhancement are two similar tasks. 2) The main goal of the Unsharp is to increase the sharpness of the image and remove the halo effect. 3) While improving the contrast of the image the minute details are improved and the noise well. Contrast and sharpness enhancement have a rescaling process. It is performed carefully to provide the best result. The exploratory data model in 1)-3) and issue 4) using the log-ratio operation and a new generalized linear system is presented in this paper. This proposed work is partly motivated by the classic work in unsharp masking [1], an excellent approach of the halo effect [12], [19]. In [17] log-ratio operation was defined. Motivated by the LIP model [24] , we study the properties of the linear system. 2. EXPLORATORY DATA ANALYSIS MODEL FOR IMAGE ENHANCEMENT 2.1Image model and generalized unsharp masking In exploratory data analysis is to decompose a signal into two parts. In one part is of particular model and other part is of residual model. In tukey’s own words the data model is: “data=fit PLUS residuals”. ([28] Pp.208). The output of the filtering process can be denoted by the‫ݕ‬ ൌ ݂ሺ‫ݔ‬ሻ. It can be regarded as the part of the image that can be fit in the model. Thus we can show an image using generalized operation as follow ‫ݔ‬ ൌ ‫ݕ‬ ْ ݀ ሺ3ሻ Where ݀is called as the detail signal (the residual). The detail signal is defined as ݀ ൌ ‫ݔ‬Ө‫,ݕ‬ Ө is the generalized operation. It provides the unified framework to study Unsharp masking algorithms. A general form of the unsharp masking is given as ߭ ൌ ݄ሺ‫ݕ‬ሻ ْ ݃ሺ݀ሻ ሺ4ሻ Where υ is the output of the algorithm and both ݄ሺ‫ݕ‬ሻand ݀ሺ‫ݕ‬ሻcould be linear or non linear functions. Model explicitly states that the image sharpness is the model residual. It forces the algorithm developer to carefully select an appropriate model and avoid model such as linear filters. This model permits the incorporation of the contrast enhancement by means of suitable processing function ݄ሺ‫ݕ‬ሻas adaptive equalization function.. The generalized algorithm can enhance the overall contrast and sharpness of the image. 2.2 Outline of the Proposed Algorithm Fig.2 shows the proposed algorithm based upon the previous model and generalized the classical Unsharp masking algorithm by addressing issues started in Section I-B. The IMF is selected due to its properties such as root signal and simplicity. Advantage of edge preserving filter is nonlocal means filter and wavelet-based denoising filter can also be used. Rescaling process is used by the new operation defined according to the log-ratio and new generalized linear system.
  • 4. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEME 402 Fig.2 Block diagram of the proposed un-sharp generalized masking algorithm 3. LOG-RATIO, GENERALIZED LINEAR SYSTEMS & BREGMAN DIVERGENCE This Section deals with new operation using generalized linear system approach. To provide a simple presentation we use (1) and (2). These operations are defined from the vector space point of view which is similar to the development of the LIP model [26]. We provide the connection between the log-ratio, generalized systems and the Bregman divergence. As a result we show novel interpretation of two existing generalized linear systems, but also develop a new system. 3.1 Definitions and properties of log-Ratio operations 3.1.1Nonlinear function In nonlinear function pixel of the gray scale of an image ‫ݔ‬ ‫א‬ ሺ0, 1ሻis considered. For an – bit image, first we add a very small positive constant to the pixel gray value then scale it by 2ିே such that it is in the range(0, 1). The non linear function can be defined as фሺ‫ݔ‬ሻ ൌ ݈‫݃݋‬ 1 െ ‫ݔ‬ ‫ݔ‬ ሺ5ሻ To simplify the notation, we define the ratio of the negative image to the original image as follows: ܺ ൌ ߰ሺ‫ݔ‬ሻ ൌ 1 െ ‫ݔ‬ ‫ݔ‬ ሺ6ሻ d=xӨ y Wavelet Based denoising Adaptive gain control Contrast enhancement Ө ْ ٔ Y yٔ ݀ ߛ X Z ߭ ൌ ‫ݖ‬ ْ ሺߛ ٔ ݀ሻ
  • 5. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEME 403 3.1.2 Addition and scalar Multiplication Using (1), the addition of two gray scales ‫ݔ‬ଵand ‫ݔ‬ଶ is defined as ‫ݔ‬ଵ ْ ‫ݔ‬ଶ ൌ 1 1 ൅ ߰ሺ‫ݔ‬ଵሻ߰ሺ‫ݔ‬ଶሻ ൌ 1 1 ൅ ܺଵܺଶ ሺ7ሻ Whereܺଵ ൌ ߰ሺ‫ݔ‬ଵሻand ܺଶ ൌ ߰ሺ‫ݔ‬ଶሻ. The multiplication of gray scale ‫ݔ‬ by a real scalar ߙሺെ∞ ൏ ߙ ൏ ∞ is defined by using (2) as follows: ߙ ٔ ‫ݔ‬ ൌ 1 1 ൅ ܺఈ ሺ8ሻ This operation is called as scalar multiplication which is a derived from a vector space point of view [29]. We can define a non-zero gray scale, denoted as follows: ݁ ْ ‫ݔ‬ ൌ ‫ݔ‬ ሺ9ሻ It is easy to show that݁ ൌ 1/2. We can regard the interval (0, (1/2)) and ((1/2),1) as the new definitions of negative and positive numbers. Absolute value is denoted as |‫|ݔ‬଴ can be defined in the similar way as the absolute value of the real number as follows. |‫|ݔ‬଴ ൌ ൞ ‫,ݔ‬ 1 2 ൑ ‫ݔ‬ ൏ 1 1 െ ‫,ݔ‬ 0 ൏ ‫ݔ‬ ൏ 1 2 ሺ10ሻ 3.1.3 Negative Image and Subtraction Operation A natural extension is to describe the negative of the gray scale value. Although this can be defined by (8) and (9). The negative value of the gray scale‫,ݔ‬ denoted by ‫ݔ‬′ , is obtained by solving ‫ݔ‬ ْ ‫ݔ‬′ ൌ 1 2 ሺ11ሻ The result is ‫ݔ‬′ ൌ 1 െ ‫ݔ‬ which is varying with the classical definition of the negative image. This definition is also varying with the scalar multiplication in that ሺെ1ሻ ٔ x ൌ 1 െ xthe notation of the classical notation is negative which is given as:Ө‫ݔ‬ ൌ ሺെ1ሻ ٔ ‫ݔ‬ . We can also define the subtraction operation using the addition operation in (8) as follows: ‫ݔ‬ଵӨ xଶ ൌ xଵ ْ ሺӨ xଶሻ ൌ 1 ߰ሺ‫ݔ‬ଵሻ߰ሺӨxଶሻ ൅ 1 ൌ 1 ܺଵܺଶ ିଵ ൅ 1 ሺ12ሻ
  • 6. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEME 404 Fig.3 Effects of the log ratio addition ‫ݕ‬ ൌ ‫ݔ‬ ْ ߙ(top row) and scalar multiplication operation ‫ݕ‬ ൌ ߙ ٔ ‫(ݔ‬bottom row) Where߰ሺӨ‫ݔ‬ଶሻ ൌ 1/߰ሺ‫ݔ‬ଶሻ ൌ ܺଶ ିଵ using the definition of gray scale, we also have a clear understanding of the scalar multiplication forߙ ൏ 0. ‫ݕ‬ ൌ ߙ ٔ ‫ݔ‬ ൌ ሺെ1ሻ ٔ ሺ|ߙ| ٔ ‫ݔ‬ሻ ൌ 1 െ |ߙ| ٔ ‫ݔ‬ ሺ13ሻ Here we used ߙ ൌ ሺെ1ሻ ൈ |ߙ| and the distribution law for two real scalars ߙ and ߚ ሺߙ ൈ ߚሻ ٔ ‫ݔ‬ ൌ ߙ ٔ ሺߚ ٔ ‫ݔ‬ሻ ሺ14ሻ 3.2. Log-Ratio, the Generalized Linear system and the Bregman Divergence We study the connection between the log-ratio and the Bregman divergence. This connection not only provides geometrical interpretation and new insight of the log-ratio, but also suggests a new way to develop generalized linear systems. 3.2.1 Log-Ratio and The Bregman Divergence The classical weighted average can be regarded as the solution of the following optimization problem: ‫ݑ‬ௐ஺ ൌ ܽ‫݃ݎ‬ min ௨ ෍ ߙ௡ሺ‫ݔ‬௡ ே ௡ୀଵ െ ‫ݑ‬ሻଶ ሺ15ሻ What is the corresponding optimization problem that leads to the generalized weighted average stated in (19) ? To study this problem, we need to recall some result in the Bregman divergence [30], [31]. The Bregman divergence of two vectors x and y, denoted by‫ܦ‬ிሺ‫ݔ‬ ‫פ‬ ‫ݕ‬ሻ, is defined as follows: ‫ܦ‬ிሺ‫,ݔ‬ ‫ݕ‬ሻ ൌ ‫ܨ‬ሺ‫ݔ‬ሻ െ ‫ܨ‬ሺ‫ݕ‬ሻ െ ሺ‫ݔ‬ െ ‫ݕ‬ሻ் ‫ܨ׏‬ሺ‫ݕ‬ሻ ሺ16ሻ
  • 7. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEME 405 Where ‫:ܨ‬ ܺ ՜ ܴconvex and differentiable function is defined over an open convex domain ܺ and ‫ܨ׏‬ሺ‫ݕ‬ሻ is the gradient of F evaluated at the point y. Centroid of a set of vector denoted ሼ‫ݔ‬௡ሽ௡ୀଵ: ܰ in terms of minimizing the sum of the Bregman divergence is studied in a recent paper [31]. The weighted left-sided Centroid is given by ܿ௅ ൌ arg min ௖‫א‬௫ ෍ ߙ௡ ே ௡ୀଵ ‫ܦ‬ிሺܿԡ‫ݔ‬௡ሻ ൌ ‫ܨ׏‬ିଵ ൭෍ ߙ௡‫ܨ׏‬ሺ‫ݔ‬௡ ே ௡ୀଵ ሻ൱ ሺ17ሻ Comparing (19) and (22), we can see that when ‫ݔ‬௡a scalar is, the generalized weighted average of the log-ratio is a special case of the weighted left-sided Centroid with߶ሺ‫ݔ‬ሻ ൌ ‫ܨ׏‬ሺ‫ݔ‬ሻ. It easy to show that ‫ܨ‬ሺ‫ݔ‬ሻ ൌ න фሺ‫ݔ‬ሻ݀‫ݔ‬ ൌ െ‫݃݋݈ݔ‬ሺ‫ݔ‬ሻ െ ሺ1 െ ‫ݔ‬ሻ logሺ1 െ ‫ݔ‬ሻ ሺ18ሻ Where the constant of the indefinite integral is omitted. ‫ܨ‬ሺ‫ݔ‬ሻis called the bit entropy and the corresponding Bregman divergence is defined as ‫ܨ‬ሺ‫ݔ‬ሻ ൌ න фሺ‫ݔ‬ሻ݀‫ݔ‬ ൌ െ‫݃݋݈ݔ‬ሺ‫ݔ‬ሻ െ ሺ1 െ ‫ݔ‬ሻ logሺ1 െ ‫ݔ‬ሻ ሺ19ሻ Where the constant of the indefinite integral is omitted ‫ܨ‬ሺ‫ݔ‬ሻ is called the bit entropy and the corresponding Bregman divergence is defined as ‫ܦ‬ிሺ‫ݔ‬ԡ‫ݕ‬ሻ ൌ െ‫݃݋݈ݔ‬ ‫ݔ‬ ‫ݕ‬ െ ሺ1 െ ‫ݔ‬ሻ݈‫݃݋‬ 1 െ ‫ݔ‬ 1 െ ‫ݕ‬ ሺ20ሻ Where is called the logistic loss Therefore, the log-ratio has an intrinsic connection with the Bregman divergence through the generalized weighted average. This connection reveals a geometrical property of the log-ratio which uses a particular Bregman divergence to measure the generalized distance between two points. It is compared with the weighted average which uses the Euclidean distance. Loss function of log-ratio uses the logistic loss function; the classical weighted average uses the square loss function. 3.2.2 Generalizedlinear system and the Bregman Divergence The connection between the Bregman divergence with other well establish generalized linear system such as the MHS with ߶ሺ‫ݔ‬ሻ ൌ log ሺ‫ݔ‬ሻ where ‫߳ݔ‬ሺ0, ∞ሻ and the LIP model [26] with ߶ሺ‫ݔ‬ሻ ൌ െlog ሺ1 െ ‫ݔ‬ሻwhere‫߳ݔ‬ሺെ∞, 1ሻ. The corresponding Bregman divergences are the Kullback-Leibler (KL) divergence for the MHS [31]
  • 8. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEME 406 ‫ܦ‬ிሺ‫,ݔ‬ ‫ݕ‬ሻ ൌ ‫݃݋݈ݔ‬ ‫ݔ‬ ‫ݕ‬ െ ሺ‫ݔ‬ െ ‫ݕ‬ሻ ሺ21ሻ And the LIP ‫ܦ‬ிሺ‫,ݔ‬ ‫ݕ‬ሻ ൌ ሺ1 െ ‫ݔ‬ሻ݈‫݃݋‬ 1 െ ‫ݔ‬ 1 െ ‫ݕ‬ െ ሾሺ1 െ ‫ݔ‬ሻ െ ሺ1 െ ‫ݕ‬ሻሿ ሺ22ሻ LIP model demonstrate the information-theoretic interpretation. The relationship between the KL divergence and the LIP model reveals a novel into its geometrical property. 3.2.3A New Generalized Linear System In Bregman divergence corresponding generalized weighted average can be defined as ߶ሺ‫ݔ‬ሻ ൌ ‫ܨ׏‬ሺ‫ݔ‬ሻ. For example the log-ratio, MHS and lip can be developed from the Bregman divergences. Bregman divergence measures the distance of two signal samples. The measure is related to the geometrical properties of two signal space. Generalized linear system for solving the out-of-0range problem can be developed by the following Bregman divergence (called “Hollinger-like” divergence in Table I on [31]) ‫݂ܦ‬ሺ‫,ݔ‬ ‫ݕ‬ሻ ൌ 1 െ ‫ݕݔ‬ ඥ1 െ ‫ݕ‬ଶ െ ඥ1 െ ‫ݔ‬ଶ ሺ23ሻ Which is generated by the convex function ‫ܨ‬ሺ‫ݔ‬ሻ ൌ െ√1 െ ‫ݔ‬ଶ whose domain is (-1, 1). The nonlinear function ߶ሺ‫ݔ‬ሻ for the corresponding generalized linear system is as follows: фሺ‫ݔ‬ሻ ൌ ݀ሺ‫ܨ‬ሺ‫ݔ‬ሻ ݀‫ݔ‬ ൌ ‫ݔ‬ √1 െ ‫ݔ‬ଶ ሺ24ሻ In this paper the generalized linear system is called the tangent system and the new addition and scalar multiplication operation are called tangent operations. In image processing application, first linearly map pixel value from the interval [0,2ே ሿ to a new interval (-1, 1). Then the image is processed by using the tangent operation. The result is then mapped back to the interval ሾ0,2ே ) through inversing mapping. We can verify the signal with the signal set ‫߳ܫ‬ሺെ1, 1ሻ is closed under the tangent operations. The tangent system can be used as an alternative to the log-ratio to solve the out-of-range problem. The application and the properties of the tangent operation can be studied in a similar way as those presented Section III-A. The negative image and the subtraction operation, and study the order relation for the tangent operations. As shown in Figure.5 the result of adding a constant to an N-bit image (N=8) using the tangent addition. In simulation, we use a simple function ‫ݍ‬ሺ‫ݔ‬ሻ ൌ ଶሺ௫ାଵሻ ଶಿାଵ െ 1 to map the image from [0,2ே ሻ to (-1, 1). We can see that the effect is similar to the log-ratio addition. 4. PROPOSED ALGORITHM 4.1Dealing with color images First the color image is converted from the RGB color space to the HIS or the LAB color space. The chrominance components such as the H and S components are not processed. After the luminance component is processed the inverse conversion is performed.
  • 9. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEME 407 Enhanced color image in RGB is obtained. Rationale processing is carried out in luminance component to avoid a potential problem of altering the white balance of the image when the RGBcomponents are processed individually two iteration ‫ܪ‬ሺ‫ݕ‬௞, ‫ݕ‬௞ାଵሻ ൌሻ1/ܰሻԡ‫ݕ‬௞ െ ‫ݕ‬௞ାଵԡ మ మ where N is the number of pixels in the image Result using two setting of the wavelet based denoising and using the "cameraman" image are shown. 4.2Enhancement of the detail Signal The root Signal and the Detail Signal : Let us denote the median filtering operation as a function ‫ݕ‬ ൌ ݂ሺ‫ݔ‬ሻ which maps the input ‫ݔ‬ to the output y. An IMF operation can be denoted as: ‫ݕ‬௞ାଵ ൌ ݂ሺ‫ݕ‬௞ሻ where ݇ ൌ 0, 1, 2, … is the iterantion index and ‫ݕ‬଴ ൌ ‫.ݔ‬The signal ‫ݕ‬௡ is usually called the root signal of the filtering process if ‫ݕ‬௡ାଵ ൌ ‫ݕ‬௡. It is convenient to define a root signal ‫ݕ‬௡ as follows: ݊ ൌ min ݇ , ‫ܪ݋ݐݐ݆ܾܿ݁ݑݏ‬ሺ‫ݕ‬௞, ‫ݕ‬௞ାଵ ൏ ߜሻ ሺ25ሻ Where ‫ܪ‬ሺ‫ݕ‬௞, ‫ݕ‬௞ାଵሻ is a sultable measur of the difference between the two images. ߜ is a user defined threshold. For natural image, mean square difference, defined as ‫ܪ‬ሺ‫ݕ‬௞, ‫ݕ‬௞ାଵሻ ൌ ቀ ଵ ே ቁ ‫פ‬ ‫פ‬ ‫ݕ‬௞ െ ‫ݕ‬௞ାଵሻ ൌ ሺ1/ܰሻ ‫פפ‬ ሺ‫ݕ‬௞ െ ‫ݕ‬௞ାଵ ‫פפ‬ ଶ ଶ (N is the number of the pixels), is a monotonic decreasing function of K. An example is shown is figure belowit is clear that the defination of the thershold is depends upon the threshold. It is possible to set a large value of the ߜsuch that ‫ݕ‬ଵ is the root signal. After five iteration ሺ݇ ൒ 5ሻ the difference ‫ܪ‬ሺ‫ݕ‬௞,‫ݕ‬௞ାଵሻ changes occurs slightly. We can regard ‫ݕ‬ସ‫ݕݎ݋‬ହthe root signal. Of course, the numaber of thr iterations, tha size and the shape pf the filter mask have certain impact on the root signal. The original signal in shown in Figure. 7. Which is the 100th row of the “cameraman” image. The root signal ‫ݕ‬is produced by an IMF filter with a ሺ3 ൈ 3ሻ mask and the three iteration. The signal ‫ݏ‬ is produced by a linear low-pass filter with a uniform mask of ሺ5 ൈ 5ሻ. The gain of the both algorithm is three. On comparing the enhanced signal we can see clearly that while the result for the classical unsharp masking algorithm suffers from the out of range problem and halo effect (under-shoot and over-shoot), the result of the proposed algorithm is free of such problem. 4.3 Adaptive Gain Control In Fig.3 to enhance the detail the gain must be greater than one. Using a universal gain for the whole image does not lead to good results, because to enhance the small deatil a relatively large gain is needed. A large gain can lead to the saturation of the detailed signal whose values are larger than the threshold. Saturation is undesirable because different amplitude of the detail signal are mapped to the same amplitude of either 1 or 0. This leads to loss of information. The gain must be adaptively controlled. We describe the gain control algorithm for using with the log-ratio operation. To control the gain, linear mapping of the detail signal d to a new signal c. ܿ ൌ 2݀ െ 1 ሺ26ሻ Such that the dynamic range of c is (-1,1). A simple idea is to set the gain as a function of the signal c and to gradually decrease the gain frim its maximum value ߛெ஺௑ when ܿ ‫פ‬൏ ܶ to ots minimum value ߛெூே when ‫פ‬ ܿ ՜ 1. We propose the following adaptive gain function
  • 10. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEME 408 ߛሺܿሻ ൌ ߙ ൅ ߚ expሺെ|ܿఎሻ ሺ27ሻ where ߟ is a parameter that controlsthe rate of decreasing. The parameter ߙ and ߚ are obtained by solving the equation: ߛሺ0ሻ ൌ ߛெ஺௑ and ߛሺ1ሻ ൌ ߛெூே. For a fixed ߟ, we can easily determine the parameter as follows: ߚ ൌ ሺߛெ஺௑ െ ߛெூேሻ/ሺ1 െ ݁ିଵ ሻ ሺ28ሻ and ߙ ൌ ߛெ஺௑ െ ߚ ሺ29ሻ Both ߛெ஺௑ and ߛெூேcould be chosen based upon each individual image processing task. It is reasonable to set ߛெூே ൌ 1. This setting follows the intuition that when the amplitude of the detailed signal is large enough, it does not need any further amplification. For example we can see that lim |ௗ|బ ߛ ٔ ݀ ൌ lim ௗబ՜ଵ 1 1 ൅ ቀ ଵିௗ ௗ ቁ ߛ ൌ 1 ሺ30ሻ Scalar multiplication has little effect. We now study the effect of ߟ and ߛெ஺௫ by setting ߛெூே ൌ 1. 4.4Contrast Enhancement of the Root Signal For contrast enhancement, we use adaptive histogram equalisation implement by Matlab function in the Image processing Toolbox. The function called “adapthisteq”, has a parameter contorlling the contrast. This parameter is determined by user through experiment to obtain the most visually pleasing result. In simulation, we use default values for other parameters if the function 5. WAVELET DENOISING The wavelet transform has been a powerful and widely used tool in image denoising because of its energy compaction and multi resolution properties. Denoising an image corrupted with additive white Gaussian noise was initially proposed by thresholding the wavelet coefficients. Subsequently, various decomposition strategies and thresholding schemes have been proposed. However, most of these use classical orthogonal wavelets which are independent of the image and noise characteristics and focus on finding the best threshold. Unlike the Fourier transform with its complex exponential basis, the wavelet transforms do not have a unique basis. Noting this point several attempts at designing matched wavelets have been made with the goal of match varying from match to a signal and energy compaction to maximizing the signal energy in the scaling sub-space. The most important way of distinguishing information from noise in the wavelet domain consists of thresholding the wavelet coefficients. Mainly hard and soft thresholding techniques are performed. Thresholding is the simplest method of image denoising .In this from a gray scale image, thresholding can be used to create binary image. Thresholding is used to segment an image by setting all pixels whose intensity values are above a threshold to a foreground value and all the remaining pixels to a background value. Thresholding is mainly divided into two categories.
  • 11. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, I Hard threshold is a "keep or kill" procedure and is more intuitively appealing. The transfer function of the hard thresholding is shown in the figure. Hard thresholding may seem to be natural. Sometimes pure noise coefficien Soft threshold shrinks coefficients above the threshold in absolute value. The false structures in hard thresholding can be overcome by soft thresholding. Now a days, wavelet based denoising methods have received a greater at 6. EXPERIMENTAL ANALYSIS Here we considered wavelet based Denoising using hard and soft thresholding approaches as stated in [22].We have tested our experimented five different images samples compared against different parameters (a) Original Image (c)Proposed method with HT thresholding (d)Proposed method with ST Thresholding (e) Performance analysis contrast parameter Vs average contrast fo Fig.4: the output results of the proposed methods International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEME 409 is a "keep or kill" procedure and is more intuitively appealing. The transfer function of the hard thresholding is shown in the figure. Hard thresholding may seem to be natural. Sometimes pure noise coefficients may pass the hard threshold shrinks coefficients above the threshold in absolute value. The false structures in hard thresholding can be overcome by soft thresholding. Now a days, wavelet based denoising methods have received a greater attention EXPERIMENTAL ANALYSIS Here we considered wavelet based Denoising using hard and soft thresholding approaches as stated in [22].We have tested our experimented five different images samples compared against different parameters Original Image (b) detailed coefficients c)Proposed method with HT thresholding (d)Proposed method with ST Thresholding (e) Performance analysis contrast parameter Vs average contrast for different images the output results of the proposed methods International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN April (2013), © IAEME is a "keep or kill" procedure and is more intuitively appealing. The transfer function of the hard thresholding is shown in the figure. Hard thresholding may seem to be shrinks coefficients above the threshold in absolute value. The false structures in hard thresholding can be overcome by soft thresholding. Now a days, wavelet based Here we considered wavelet based Denoising using hard and soft thresholding approaches as stated in [22].We have tested our experimented five different images samples r different images
  • 12. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEME 410 7. CONCLUSION In this paper an improved approach for classical unsharp masking algorithm is proposed by introducing wavelet based thresholding. From the above obtained results we can clued that the proposed method out performs for different images under different block size and average contrast parameter. This method can significantly increase the sharpness and contrast ratios appropriately. REFERENCES [1] G. Ramponi, “A cubic unsharp masking technique for contrast enhancement, “Signal Process., pp. 211–222, 1998. [2] S. J. Ko and Y. H. Lee, “Center weighted median filters and their applications to image enhancement,” IEEE Trans. Circuits Syst., vol. 38, no. 9, pp. 984–993, Sep. 1991. [3] M. Fischer, J. L. Paredes, and G. R. Arce, “Weighted median image sharpeners for the world wide web,” IEEE Trans. Image Process., vol. 11, no. 7, pp. 717–727, Jul. 2002. [4] R. Lukac, B. Smolka, and K. N. Plataniotis, “Sharpening vector median filters,” Signal Process., vol. 87, pp. 2085–2099, 2007. [5] A. Polesel, G. Ramponi, and V. Mathews, “Image enhancement via adaptive unsharp masking,” IEEE Trans. Image Process., vol. 9, no. 3, pp. 505–510, Mar. 2000. [6] E. Peli, “Contrast in complex images,” J. Opt. Soc. Amer., vol. 7, no. 10, pp. 2032–2040, 1990. [7] S. Pizer, E. Amburn, J. Austin, R. Cromartie, A. Geselowitz, T. Greer, B. Romeny, J. Zimmerman, and K. Zuiderveld, “Adaptive histogram equalization and its variations,” Comput. Vis. Graph. Image Process. vol. 39, no. 3, pp. 355–368, Sep. 1987. [8] J. Stark, “Adaptive image contrast enhancement using generalizations of histogram equalization,” IEEE Trans. Image Process., vol. 9, no. 5, pp. 889–896, May 2000. [9] E. Land and J. McCann, “Lightness and retinex theory,” J. Opt. Soc. Amer., vol. 61, no. 1, pp. 1–11, 1971. [10] B. Funt, F. Ciurea, and J. McCann, “Retinex in MATLAB™,” J. Electron. Image., pp. 48–57, Jan. 2004. [11] M. Elad, “Retinex by two bilateral filters,” in Proc. Scale Space, 2005, pp. 217–229. [12] J. Zhang and S. Kamata, “Adaptive local contrast enhancement for the visualization of high dynamic range images,” in Proc. Int. Conf. PatternRecognit., 2008, pp. 1–4. [13] Z. Farbman, R. Fattal, D. Lischinski, and R. Szeliski, “Edge-preserving decompositions for multi-scale tone and detail manipulation,” ACMTrans. Graph., vol. 27, no. 3, pp. 1–10, Aug. 2008. [14] F. Durand and J. Dorsey, “Fast bilateral filtering for the display of highdynamic- range images,” in Proc. 29th Annu. Conf. Comput. Graph.Interactive Tech., 2002, pp. 257–266. [15] R. Fattal, “Single image dehazing,” ACM Trans. Graph., vol. 27, no. 3, pp. 1–9, 2008. [16] K. M. He, J. Sun, and X. O. Tang, “Single image haze removal using dark channel prior,” in Proc. IEEE Conf. Comput. Vis. PatternRecognit., Jun. 2009, pp. 1956–1963. [17] H. Shvaytser and S. Peleg, “Inversion of picture operators,” Pattern Recognit. Lett., vol. 5, no. 1, pp. 49–61, 1987. [18] G. Deng, L. W. Cahill, and G. R. Tobin, “The study of logarithmic image processing model and its application to image enhancement,” IEEE Trans. Image Process., vol. 4, no. 4, pp. 506–512, Apr. 1995.
  • 13. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEME 411 [19] L. Meylan and S. Süsstrunk, “High dynamic range image rendering using a retinex- based adaptive filter,” IEEE Trans. Image Process., vol. 15, no. 9, pp. 2820–2830, Sep. 2006. [20] D. Marr, Vision: A Computational Investigation into the Human Representation and Processing of Visual Information. San Francisco, CA:Freeman, 1982. [21] D. G. Myers, Digital Signal Processing Efficient Convolution and Fourier Transform Technique. Upper Saddle River, NJ: Prentice-Hall, 1990. [22] Nevine Jacob and Aline Martin, Image Denoising In The Wavelet Domain Using Wiener Filtering,December 17, 2004. [23] I.Suneetha and Dr.T.Venkateswarlu, “Spatial Domain Image Enhancement using Parameterized Hybrid Model”, International Journal of Electronics and Communication Engineering &Technology (IJECET), Volume 3, Issue 2, 2012, pp. 209 - 216, ISSN Print: 0976- 6464, ISSN Online: 0976 –6472. [24] R. Pushpavalli and G.Sivaradje, “A New Tristate Switching Median Filtering Technique for Image Enhancement”, International Journal of Advanced Research in Engineering & Technology (IJARET), Volume 3, Issue 1, 2012, pp. 55 - 65, ISSN Print: 0976-6480, ISSN Online: 0976-6499 APPENDIX TABLE I Key components of some generalized linear system motivated by the bregman divergence. The domain of the lip model isሺെ∞, ‫ܯ‬ሻ. In this table, it is normalized by M TO SIMPLIFY NOTATION Domain D୊ሺx, yሻ Ԅሺxሻ x ْ y α ٔ x, ሺα ‫א‬ Rሻ Log- ratio (0, 1) െ‫݃݋݈ݔ‬ ‫ݔ‬ ‫ݕ‬ െ ሺ1 െ ‫ݔ‬ሻ݈‫݃݋‬ 1 െ ‫ݔ‬ 1 െ ‫ݕ‬ ݈‫݃݋‬ 1 െ ‫ݔ‬ ‫ݔ‬ 1 1 ൅ ଵି௫ ௫ ଵି௬ ௬ 1 1 ൅ ቀ ଵି௫ ௫ ቁ ఈ LIP (-∞, 1ሻ ሺ1 െ ‫ݔ‬ሻ݈‫݃݋‬ 1 െ ‫ݔ‬ 1 െ ‫ݕ‬ െ ሾሺ1 െ ‫ݔ‬ሻ െ ሺ1 െ ‫ݕ‬ሻሿ െlog ሺ1 െ ‫ݔ‬ሻ ‫ݔ‬ ൅ ‫ݕ‬ െ ‫ݕݔ‬ 1 െ ሺ1 െ ‫ݔ‬ሻଶ MHS (0,∞ሻ ‫݃݋݈ݔ‬ ‫ݔ‬ ‫ݕ‬ െ ሺ‫ݔ‬ െ ‫ݕ‬ሻ െlog ሺ‫ݔ‬ሻ ‫ݕݔ‬ ‫ݔ‬ఈ Tangent (-1, 1) 1 െ ‫ݕݔ‬ ඥ1 െ ‫ݕ‬ଶ െ ඥ1 െ ‫ݔ‬ଶ ‫ݔ‬ √1 െ ‫ݔ‬ଶ ߶ሺ‫ݔ‬ሻ ൅ ߶ሺ‫ݕ‬ሻ ඥ1 ൅ ሺ߶ሺ‫ݔ‬ሻ ൅ ߶ሺ‫ݕ‬ሻሻଶ ߙ߶ሺ‫ݔ‬ሻ ඥ1 ൅ ሺߙ߶ሺ‫ݔ‬ሻሻଶ