An Improved Image Fusion Scheme Based on Markov Random Fields with Image Enhancement Scheme

International Journal of Computer Applications Technology and Research
Volume 3– Issue 1, 29 - 32, 2014

An Improved Image Fusion Scheme Based on Markov
Random Fields with Image Enhancement Scheme
Nalla Aravind Babu
Department of ECE
Vardhaman College of Engineering
Hyderabad, India

M. Veeraswamy
Department of ECE
Vardhaman College of engineering
Hyderabad, India

Abstract: Image fusion is an important field in many image processing and analysis tasks in which fusion image data are acquired
from multiple sources. In this paper, we investigate the Image fusion of remote sensing images which are highly corrupted by salt and
pepper noise. In our paper we propose an image fusion technique based Markov Random Field (MRF). MRF models are powerful
tools to analyze image characteristics accurately and have been successfully applied to a large number of image processing
applications like image segmentation, image restoration and enhancement, etc.,. To de-noise the corrupted image we propose a
Decision based algorithm (DBA). DBA is a recent powerful algorithm to remove high-density Salt and Pepper noise using sheer
sorting method is proposed. Previously many techniques have been proposed to image fusion. In this paper experimental results are
shown our proposed Image fusion algorithm gives better performance than previous techniques.
Keywords: Markov Random Field, image fusion, image segmentation, image restoration and enhancement, Decision based algorithm.

1. INTRODUCTION
The applications were image data should be gathered (or
collected) from many input images as source images, in such
applications image fusion plays an important role. The source
images contain about some information of the original scene
but individually they cannot represent full scene perfectly in
order to gather the original scene from the source images
image fusion is used. The input images for fusion can be
capture at different time and/or by an utilizing various
sensors, because of this source images individually cannot
represent full scene [1]. Thus we perform image fusion in
order to get an accurate view at the scene, that‟s why it is
more applicable in many image processing applications [2]. In
applications like satellite image sensing image fusion is utilize
to improve the resolution of the images [3], [4]. Here, we
propose fusion scheme for source images having same
resolution. The multispectral fusion scheme consists of a
range of bands so as to improve spectral resolution [4]. We
use several bands improving spectral resolution.
The available schemes of image fusion can be broadly
classified into three categories: feature level, decision level
and pixel level. In our paper we are using pixel level type of
image fusion; so many techniques have been proposed of
image fusion for various applications. In general there are two
steps involved in pixel level image fusion.
a)

We have to estimate whether given source image
will contribute to the final fused image or not. For
each and every pixel.

b)

By using all the source images the intensity of the
fused image can be formed.

The true previous techniques of fusion are by averaging pixel
intensities of input images or by taking maximum pixel
intensity out of total available source images pixel values.
Gaussian noise can be effectively removed in case of
averaging scheme and also it increases SNR value but fails to
maintain proper contrast.

Recently, a name approach has been introduced i.e. MD-based
scheme (multi scale-decomposition) and it shows better
results for various applications of image processing. It
consists of following three steps.
a)

The input images are decomposed into n levels by
using wavelet transform.

b)

At, each and every level of source images the fusion
approach is applied.

c)

Convert the image spatial domain by applying
inverse wavelet transform, in order to synthesize the
resultant image.

This MD-based approach attains good performance and
increases computational complexity became use of wavelet
transform, so depending on application requirement one can
select or skip the transformation step. The pixel level fusion
approach may introduce distortion ine2 the resultant fused
image, because of the drawback of pixel level fusion that the
decision on a specific input image or not, is difficult.
This noteworthy to consider spatial co-relation while we are
doing fusion and the users such model will increase the
performance, one of the way to use this spatial co-relation is
by the use of window based or region based method [5][6][8] .
Here in our paper we introduce MRF(Markov Random Field)
as it has been used in image processing applications such as
change detection[10], image de-noising [9][12], edge
detection [11] and image restoration [13][14].
MRF can also be used for pixel level image fusion. The first
algorithm focus on decision making as an MRF and the next
algorithm both on decision making and exact image as an
MRF and the contrast can be improved by finding the upper
and lower band intensity values for the resultant image. Our
scheme can be tested in the presence of salt and pepper noise
and impulse noise as well and it shows better performance.

2. PROBLEMM FORMULATION
The main aim of imager fusion is to predict the specified
scene, by considering that every source image has good view

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of small part of scene [1]. Consider there are source images
each can be represented as,
yi(r) = Hi x(r) + wi(r),

i=1,……,N

(1)

Where r represents spatial coordinates, yi(r) is the brightness
or intensity of ith image, x(r) is the intensity of original scene
or source scene at r which has to be predicted wi(r), we
presents noise and sensor selectivity coefficient is represented
by Hi(r). The above equation (1) represents a relationship
between actual scene and input image; in practice this model
has some drawbacks. The images captured from various
sensor gives different aspects of original scene in this case this
scheme is an approximation.
The fusion problem necessarily include the prediction of x and
Hi. Previous algorithms may also be represented by above
model. In case of averaging Hi=1 for any i and for
maximizing case Hi=1 if i= maxi{yi};Hi=0 otherwise. If Hi is
known the gray scale values of fused image will be calculated
by least square scheme [15] as,

case of second algorithm coefficient as well as fused image
will be modeled via MRF (MRF_HX) few notations.

X: total original scene;

Hi: ith source image coefficients;

Yi: ith source image intensity;

H: source images coefficients, where H(r,i)=H i;

Y: source images intensities, where Y(r,i)=Yi

A. Image fusion: H coefficients will be modeled
using MRF.
This approach is motivated by the fact that an input
images coefficient has spatial correlation. We proceed
with H coefficients via MRF. Assume a sites in an
image be represented by „S‟ and
{0,1,….,L-1}. The
phase space with [14] the marginal pdf H can be
expressed as below (5) with normalization constant ZH
is given below.
PH(H)
(5)

(2)
Where H is a vector having values [H1,H2,…..,HN]T and Y is
a vector [y1,y2,…..,yN]T. in general H will be available without
any information about H to predict the values of H. the LS
algorithm says that H will take the values which generates
highest energy i.e.

(6)
The value can be express in (6) and the optimal value of
H can be represented in (7). The steps involved in these
algorithms are as follows,
1)

2)

(3)

3)

N

Hi {0,1}, H has 2 possible values, now the values x
will be estimated by LS technique as

(4)
The above scheme is sensitive to noise as H as well as
intensity of resultant image x estimated pixel. The accuracy of
estimation of H coefficients has much impact on resultant
image accuracy. A simple way is to consider that the pixel
values lie in a small window will be constant now choose
coefficients which generates highest energy in that window
[7]. The main aim of LS technique is to reduce the
2
error
, a famous scheme for enhancing the predicted
error of LS is by incorporation of prior knowledge of H or x
[16]. We presented to use an MRF model in order to predict
the coefficients of H. it is predicted to enhance the accuracy of
H coefficients and resultant image quality.

4)

First, find the initial estimate of H and x and decide
initial parameters and a looping variable has to be
initiated in looping variable.
For every iteration a new estimate of H will be
obtained by Gibbs pdf and with Gibbs potential
E(H).
Make obtaining the resultant fused image by using
(4).
Reduce the value of looping variable and repeat
above (2) and (3) steps till convergence.

B. Image fusion: H coefficients and x image will be
modeled.
The resultant fused image also consists of properties
of spatial coefficients. Therefore we assume that the
resultant fused image will also followed Markov
Random Field along with Gibbs potential Vc(X).
Therefore X marginal pdf in [9].

(7)
Here ZX is normalization constant and can be written as
(6) by this consideration the optimal X given as,

3. PROPOSED ALGORITHM
The problem in image fusion is to predict the
original scene. The estimation of H is performed first before
we go for x, which will decide whether the previous work we
predict the value of H by using maximizing, LS, Averaging
and Windowing scheme. Here in this session we represent the
two schemes based on MRF which will consider the spatial
coordinates as well. Therefore, the intensity value in the
resultant image will be decided by intensity of source images
and also by neighboring pixels as well. The first scheme
(MRF_H) with MRF models the coefficients only, but in the

(8)
Therefore the

estimation will reduces to,

(9)
Where,

(10)

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Volume *– No.*, ___________ 2012
As compare to scheme proposed previously i.e. MRF_H
in that by using LS algorithm we updated the fused image X.
in this technique we use (10) to update the resultant image the
algorithm is as follows.
1) As a first step de-noise the input images.
2) Start with an initial estimate of H and X. Estimate
the initial parameters and set the initial variable.
3) For every iteration new H vale will be obtain on the
basis of its Gibbs pdf(5) with E(H) using Gibbs
sampling method [9].
4) Make update the fused image by using (10).
5) Reduce the looping variable and repeating the (2
and 3) steps till convergence.
6) Finding the upper and lower band intensity values
from the resultant values.

4. EXPERIMENTAL RESULTS
As an example we have taken three multispectral images to
demonstrate our algorithm and in evaluate the fusion scheme.
The fig.1 shows noisy source images, we improving quality of
source images by using median filter and the enhanced images
or as shown in fig.2 the different bands multispectral source
images. Each image is split or decompose into four sub
images by using desecrate wavelet transform method in case
of windowing scheme and fusion scheme approach is
employed to contribute or fuse the images and finally we have
to take the inverse wavelet transform for resultant image. In
fig.3 shows the fusion based results with our proposed
algorithm and we present the performance resultant
maximizing approach, LS approach, averaging approach,
windowing based and
our proposed approach. The
maximizing approach is too bright resultant image. The LS
approach is having drawback of showing more noise in
resultant image and the resultant image produce by window
based shows mosaic pattern.

(a)

(b)
Fig.2: Enhanced source images

(a)

(b)

(c)

(c)

(d)
(e)
(f)
Fig.3: Fusion results based on (a) maximizing algorithm
(b) averaging algorithm (c) LS algorithm (d) Window
algorithm (e) MRF_H algorithm (f) Proposed algorithm.

5. ACKNOWLEDGMENTS
Here in this paper we have analyze the problem of image
fusion on the basis of statistical model. We consider the
importance of correlation and assume that it can also be
modeled via MRF_H has been introduced. We presented
different image fusion approaches such as LS, maximizing,
averaging, windowing based and our proposed method.
Which utilizes Gibbs pdf, Gibbs distribution and the results of
which can be further more resultant fused image. Hear we
assume a simple relation between true scene and input source
image i.e. a source image may contribute or may not
contribute fused image and we assume that the coefficients
can take any real value in the data model. These may increase
the accuracy of the image fusion.

6. REFERENCES
(a)

(b)

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(c)
Fig. 1: Noisy source images

[4] C. Thomas, T. Ranchin, L. Wald, and J. Chanussot,
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An Improved Image Fusion Scheme Based on Markov Random Fields with Image Enhancement Scheme

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