International Journal of Engineering Trends and Technology- Volume4Issue3- 2013
A Novel Approach For The Enrichment Of Digital
Images Using Morphological Operators
V. Karthikeyan*1,V.J.Vijayalakshmi*2, P.Jeyakumar*3
*1Assistant Professor, Department of Electronics and Communication Engineering,
SVS College of Engineering, Coimbatore, India,
*2Assistant Professor, Department of Electrical and Electronics Engineering,
Sri Krishna College of Engineering and Technology, Coimbatore, India,
*3Student, Department of Electronics and Communication Engineering
Karpagam University, Coimbatore, India,
Abstract- In the proposed task A novel approach for the
enrichment of digital images using morphological operators is
presented. The main theme of our work in this paper is to
implement the enhancement of the digital images by using the
global morphological technique to detect the background features
of the images which is characterized by poor lighting. The contrast
image enhancement carried out by the application of two operators
based on the Weber’s law. The first operator employs information
from blocked analysis, while the second transformation utilizes the
opening by reconstruction, which is employed to define the multi
background.. Finally, the performance of the proposed operators is
illustrated through the processing of images with different
backgrounds, the majority of them with poor lighting condition.
Keywords—Image
background,
morphological
contrast,
Morphological filters by reconstruction, multi background,
Weber’s law.
I.
INTRODUCTION
The contrast enhancement problem in digital images can be
approached from various Methodologies, among which is
mathematical morphology (MM). Initial studies on contrast
Enhancement in this area were carried out and introduced the
contrast mappings notion. Such operators consist in accordance
to some proximity criterion, in selecting for each point of the
analyzed image, a new grey level between two patterns
(primitives). Other works based on the contrast mapping
concept have been developed elsewhere .With regard to MM,
several studies based on contrast multi scale criterion have been
carried out. In our work, a scheme is defined to enhance local
contrast based on morphological top-hat transformations and
implements a processing system in real time for its application
in the enhancement of angio cardio graphic images. Even
though morphological contrast has been largely studied, there
are no methodologies, from the point of view MM, capable of
simultaneously normalizing and enhancing the contrast in
images with poor lighting. On the other side, one of the most
common techniques in image processing to enhance dark
regions is the use of nonlinear functions, such as logarithm or
power functions otherwise, a method that works in the
frequency domain is the homo morphic filter . In addition, there
are techniques based on data statistical analysis, such as global
and local histogram equalization. During the histogram
equalization process, grey level intensities are reordered within
the image to obtain a uniform distributed histogram. However,
the main disadvantage of histogram equalization is that the
global properties of the image can not be properly applied in a
local context, frequently producing a poor performance in detail
preservation. In a method to enhance contrast is proposed; the
methodology consists in solving an optimization problem that
maximizes the average local contrast of an image.
II.
OPTIMIZATION FORMULATION
The optimization formulation includes a perceptual constraint
derived directly from human threshold contrast sensitivity
function. The proposed operators to some images with poor
lighting with good results. On the other hand, in, a methodology
to enhance contrast based on color statistics from a training set
of images which look visually appealing is presented. Here, the
basic idea is to select a set of raining images which look good
perceptually, next a Gaussian mixture model for the color
distribution in the face region is built, and for any given input
image, a color tone mapping is performed so that the color
statistics in the face region matches the training examples. In
this way, even though the reported algorithms to compensate
changes in lighting are varied, some are more adequate than
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International Journal of Engineering Trends and Technology- Volume4Issue3- 2013
others. Two methodologies to compute the image background
are proposed. Also, some operators to enhance and normalize
the contrast in grey level images with poor lighting are
introduced. Contrast operators are based on the logarithm
function in a similar way to Weber’s law .The use of the
logarithm function avoids abrupt changes in lighting. Also, two
approximations to compute the background in the processed
images are proposed. The first proposal consists in an analysis
by blocks, whereas in the second proposal, the opening by
reconstruction is used given its following properties: a) it passes
through regional minima, and b) it merges components of the
image without considerably modifying other Structures. The
proposals given in this paper are illustrated with several cases.
The project is organized as follows. Chapter 3 presents a brief
background on Weber’s law and some morphological
transformations. Chapter 4 gives description about Weber’s Law
and chapter 5 gives an approximation to the background by
means of block analysis in conjunction with transformations that
enhance images with poor lighting The multi background is
introduced by means of the opening by reconstruction.
III.
MORPHOLOGICAL TRANSFORMATIONS
In mathematical morphology, increasing and idempotent
transformations
are
frequently
used.
Morphological
transformation complying with these properties are known as
morphological filters .The basic morphological filters are the
morphological opening and closing using a given structural
element. In this project, a square structuring element is
employed, which represents the structuring element of size 3 ×3
pixels, which contains its origin. While is the transposed stand is
a homothetic parameter. Formally, the morphological opening
and closing are expressed and where the morphological erosion
and the morphological dilation are respectively inf operator and
is the sup operator. On the other hand, throughout the paper, we
will use either size 1 or size for the structuring element. Size 1
means a square of 3 ×3 pixels, while size means a square of
pixels. For example, if the structuring element is size 3, then the
square will be 7× 7 pixels, to render an analysis of
49neighbouringregions.
IV. OPENING AND CLOSING BY RECONSTRUCTION
The reconstruction transformation is a useful concept introduced
by MM. These transformations allow the elimination of
undesirable regions without considerably affecting the
remaining structures of the image. This characteristic arises
from the way in which these transformations are built by means
of geodesic transformations. The geodesic dilation ɠ1f(g)(x) and
geodesic erosion Σ1f(g)║(x) of size one are given by
ɠ1f(g)(x)=f(x)^ ɠ(g)(x) with g(x)≤f(x) and
Σ1f(g)(x)=f(x)˅Σ(g)(x)withg(x)≥f(x)
(1)
respectively. When the function g(x) is equal to the erosion
(dilation, respectively) of the original function, we obtain the
opening ϔ µB (f)(x)
(closing φµB (f)(x) respectively) by reconstruction.
ϔ µB(f)(x)=limn→∞ δfn(‫ع‬µB(f))(x)&φµB(f)(x)=limn→∞ ‫ع‬nf(δ µB(f))(x)
Fig. 1 (a)original image (b)original image and the marker (c)opening by
reconstruction using erosion as marker,. (d), performance of the opening and
closing by reconstruction.
Simillar to Weber’s law we have considered by taking the
luminance L as the grey level intensity of a function (image) and
the expression (5) is written as
C=Klog f+b
f>0
(2)
On the other hand, in a methodology to compute the background
parameter was proposed. The methodology consists in
calculating the average between the smallest and largest regional
minima, as illustrated in Fig. 4.1.
Fig 2. Background detection from largest and smallest minima of image.
V.IMAGE BACKGROUND APPROXIMATION BY BLOCKS
The image background approximation is enhanced and the
image is divided into blocks of size. Each block is a sub image
of the original image. The minimum and maximum intensity
values in each sub image are denoted as
m i= ˄Ɯi(x)
(3)
Mi=˅ Ɯ i(x)
(4)
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International Journal of Engineering Trends and Technology- Volume4Issue3- 2013
For each analyzed block, maximum and minimum values are
used to determine the background criteria in the following way:
Ti=mi+Mi∕2
(5)
erosion defined by the order-statistical filters. A better local
analysis is achieved when erosion dilation is applied instead of
opening and Closing to detect the background criterion. This
situation occurs, because the structuring element allows the
analysis of sets of neighboring pixels at each point in the image.
If size increases, more pixels will be taken into account to
compute such parameter. The improved images were obtained
with using equation. Notice that several characteristics not
visible at first sight appear in the enhanced images.
Fig .3 Background criteria obtained by block analysis
The value of Ʈ irepresents a division line between clear (f >Ʈi)
and dark(f ≤Ʈi) intensity levels. Once is calculated, this value is
used to select the background parameter associated with the Fig .4 (a) Original Image ( b) Enhanced image after applying opening and
analyzed block. As follows, an expression to enhance the closing
contrast is stated as
VI. IMAGE BACKGROUND DETERMINATION USING
ΓTi(f) = kilog(f+1)+ Mi , f ≤ Ti kilog(f+1)+mi ,
(6)
THE EROSION DILATION BY RECONSTRUCTION
otherwise
The Background parameter Ʈi depends on the value. If (f ≤Ʈi) It is desirable to obtain a function that resembles the image
(dark region), the background parameter takes the value of the background without changing the original image into blocks,
maximum intensity Mi within the analyzed block, and the and without using the morphological erosion and dilation, since
minimum intensity mi value otherwise. Also, the unit was added these morphological transformations generate new contours
when the structuring element is increased. This process is shown
to the logarithm function in (10) to avoid indetermination.
Since in the projected work grey level images are used, and the in Fig. 5. When morphological erosion or dilation are used with
large sizes of to reveal the background, inappropriate values
constant ki in (5.4) is: obtained as follows
may be obtained. there is other class of transformations that
Ki=255-mi*/log(256)mi*=mi, f>Ʈi
allows the filtering of the image without generating new
Mi, f≤ Ʈi
(7 )
The above process is similar to a contrast mapping which components.
modifies the intensity values depending on certain criterion.
The criterion to modify the contrast in (4) is given by Ʈi. The
values are used as background parameters to improve the
contrast depending on the background which is different for
clear and dark regions. An example to illustrate the performance
of (4) considering a 1-D signal is presented in Fig. Notice that,
in this figure, the intensity levels are stretched in an important
way by the behavior of the logarithm function and the
background parameter Mi or mi. In this way, the transformation
ΓƮi (f) fulfils the next properties.The set composed by high
Fig .5 (a) Original Image (b) Erosion size µ=20
contrast areas, and the set composed by low contrast areas. The
composition of contrast mappings using opening closing will These process are called transformations by reconstruction. In
result in lighter images for each iteration, reaching a limit our case, the opening by reconstruction is our choice because it
imposed by the value of the highest level of intensity of the contact the regional minima and merges regional maxima. This
image.If image is subdivided into smaller blocks each time, the characteristic allows the modification of the altitude of regional
background function tends to be similar to the original function. maxima when the size of the structuring element increases. This
On the other hand, given that, maximum and minimum values effect can be used to detect the background criteria in (5),
are analyzed for each block, an extension using morphological
operators is presented as follows. Notice that the window
corresponds to the structuring element . For the sake of
Ʈ(x)=ϒµ(f)(x)
(8)
simplicity values correspond to the morphological dilation and
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International Journal of Engineering Trends and Technology- Volume4Issue3- 2013
(a)
(a)
(b)
Opening & Closing is maintained and only the way to detect the
background is modified. An example of this modification is
shown in Fig. 7.2. Input images are located in Fig. 6(a) where as
enhanced images are presented in Fig. 6(b). The image
background criteria were calculated with a structuring element
size 10. On the other hand, it is possible to use the opening by
reconstruction to generate the image background similarly to
that presented, and not only, as a criterion to detect the
background as was presented. An uneven background,which is
detected from an image with important variations in lighting.
Observe that the background touches only regional minima,
while the other regions contain local information of the original
function. From these extreme points and the local information
provided by the original function and the important information
about the image can be acquired. When considering the opening
by reconstruction to detect the background, one further
operation is necessary to detect the local information given by
the original The morphological transformation in opening &
Closing is maintained and only the way to detect the background
is modified. An example of this modification is shown in Fig. 6.
Input images are located in Fig. 6(a), whereas enhanced images
are presented in Fig. 6(b). The image background criteria were
calculated with a structuring element size µ=10 for all output
images.
TABLE.1
(b)
Fig.7 Histogram for Dialation (a) Original images. (b)Enhanced
images.
Fig .6 Erosion by reconstruction as background criteria (a) Original images.
(b)Enhanced images.
The following expression derived is proposed to enhance the
contrast in images with poor lighting
‫ع‬ϒµ(f)=k(x)log(f+1)+‫ع‬1[ϒµ(f)]
(11)
(7.3)
(10)
Fig.8 Image background approximation by Erosion Dilation
VII.EMPIRICAL RESULTS
The Erosion dilation and opening closing Results was listed
below.
PERFORMANCE ANALYSIS FOR VARIOUS IMAGES
PSNR & MEAN VALUES
Erosion Dialation
Opening Closing
PSNR
Mean
PSNR
MEAN
Tumor
Tower
14.9124
2.7778
37.8881
57.3989
18.3777
7.4313
110.3905
87.3987
Man
6.3124
49.5454
9.5674
70.6574
Original
image
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International Journal of Engineering Trends and Technology- Volume4Issue3- 2013
Original image
Enhanced image
Fig .9 Histogram equalization
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Fig.10 Background approximation
VIII. CONCLUSION
This paper presents a study to detect the image background and
to enhance the contrast in grey level images with poor lighting.
First, a methodology was introduced to compute an
approximation to the background using blocks analysis. This
proposal was subsequently extended using mathematical
morphology operators. However, a difficulty was detected when
the morphological erosion and dilation were employed;
therefore, a new proposal to detect the image background was
propounded, that is based on the use of morphological
connected transformations. These contrast transformations are
characterized by the normalization of grey level intensities;
avoiding abrupt changes in illumination The performance of the
proposals provided in this work were illustrated by means of
several examples throughout the paper.
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