# INTRODUCTION

igital images are often corrupted during acquisition, transmission or due to faulty memory locations in hardware [1]. The impulse noise can be caused by a camera due to the faulty nature of the sensor or during transmission of coded images in a noisy communication channel [2]. Consequently, some pixel intensities are altered while others remain noise free. The noise density (severity of the noise) varies depending on various factors namely reflective surfaces, atmospheric variations, noisy communication channels and so on. In most image processing applications the images captured by different sensors are combined into a single image, which retains the important features of the images from the individual sensors, this process is known as image fusion [3] [4]. In this paper, the images captured by multiple (five) sensors are differently noised depending on the proximity to the object, environmental disturbances and sensor features. These noise images are filtered using five different vector median filtering algorithms such as Vector Median Filter, Rank Conditioned Vector Median Filter, Rank Conditioning and Threshold Vector Median Filter, Center Weighted Vector Median Filter and Absolute Deviation Vector Median Filter. The filtered images are fused into a single image using the quality assessment of spatial domain from the de-noised images, thus producing a high quality image. The performance evaluation of the image fusion is evaluated using PSNR between the original and fused image. This paper is organized as follows: Section II present the impulse noise in images, Section III present different filtering algorithms, Section IV present the image fusion algorithm, Section VI present experimental results and finally Section VII reports conclusion.


# II.


# IMPULSE NOISE IN IMAGES

Impulse noise [5] corruption is very common in digital images. Impulse noise is always independent and uncorrelated to the image pixels and is randomly distributed over the image. Hence unlike Gaussian noise, for an impulse noise corrupted image all the image pixels are not noisy, a number of image pixels will be noisy and the rest of pixels will be noise free. There are different types of impulse noise namely salt and pepper type of noise and random valued impulse noise.

In salt and pepper type of noise the noisy pixels takes either salt value (gray level -225) or pepper value (grey level -0) and it appears as black and white spots on the images. If p is the total noise density then salt noise and pepper noise will have a noise density of p/2. This can be mathematically represented by (1) (1)

Where y represents the noisy image pixel, p is the total noise density of impulse noise and xij is the uncorrupted image pixel.

In case of random valued impulse noise, noise can take any gray level value from zero to 225. In this case also noise is randomly distributed over the entire image and probability of occurrence of any gray level value as noise will be same. We can mathematically represent random valued impulse noise as in (2).

(
)2
Where n ij is the gray level value of the noisy pixel.


# III.


# FLTERING ALGORITHMS

In the Vector median filter (VMF) [6] for the ordering of the vectors in a particular kernel or mask a x ij with probability 1-p n ij with probability p y ij =

x ij with probability 1-p ij suitable distance measure is chosen. The vector pixels in the window are ordered on the basis of the sum of the distances between each vector pixel and the other vector pixels in the window. The sum of the distances is arranged in the ascending order and then the same ordering is associated with the vector pixels. The vector pixel with the smallest sum of distances is the vector median pixel. The vector median filter is represented as
(3)
If ? i is the sum of the distances of the i th vector pixel with all the other vectors in the kernel, then (4) where (1? i ? N) and X i and X j are the vectors, N=9. Î?"(X i , X j ) is the distance measure given by the L 1 norm or the city block distance which is more suited to non correlated noise. The ordering may be illustrated as (5) and this implies the same ordering to the corresponding vector pixels i.e. (6) where the subscripts are the ranks. Since the vector pixel with the smallest sum of distances is the vector med ian pixel, it will correspond to rank 1 of the ordered pixels, i.e., (7) The Rank Conditioned Vector Median Filter [7]   improves the performance of the vector median filter. The vector median of the kernel replaces the central pixel when the rank of the central pixel is greater than a predefined rank of a healthy vector pixel inside the window. The rank of the healthy vector pixel is obtained by simulating RCVMF codeon a noiseless image. Then, the mean value of the obtained ranks of the central vector pixel is calculated. This value is rounded off to a whole number, and it is considered to be rank of the healthy vector pixel of a kernel.The rank conditioned vector median filter can be expressed as: (8) Where r c is a rank of the central vector pixel and c=5.and r k is the predefined healthy vector pixel rank inside the window.

The Rank-Conditioned and Threshold Vector Median Filter [8] aims to further enhance the RCVMF by incorporating an additional test -a distance threshold for the detection of impulses. In RCVMF, a central vector having greater than the predefined rank implies a corrupt vector. However, it may not be true always, because the vectors may be close as per the distance measure. Hence another criterion ?"¨, is taken into account. It is the distance between the central vector pixel and the vector pixel corresponding to the predefined rank. To find out the value of this predetermined distance threshold ?"¨, the code simulating RCTVMF is executed on a noiseless image. Then the mean of the obtained ?"¨ values is calculated and used for the simulations at various noise percentages. The distance is calculated as follows : (9) Where Xc is the central vector and X (k) (1 < k < 9) is a rank ordered and healthy vector pixel inside the window. On the basis of the above information, the filter has the following form :

In Center Weighted Median Filter [8] the kernel vector pixels are assigned some non negative values called weights. The central vector pixel is assigned a non negative weight while the weight of the neighboring pixels is kept unity. The weights denote the number of copies is obtained. The output Y (say), of a weighted median filter of span N (where N generally denotes the kernel size, N=9) associated with N integer weights, (10) is given by , Where the vectormedian [.] denotes the vector median operation.

In Absolute Deviation Vector Median Filter [9], the impulse noise detection mechanism does not require the distance calculation and subsequent ordering of the vectors of a kernel. The algorithm deals with the difference values of the red (R) and the green (G) intensities denoted by ? RGi (say), and the difference values of the green (G) and blue (B) intensities denoted by ? GBi (say), (where 1 ? i ? N, N=9).

In a 3×3 kernel, it has been observed empirically that ?  Step 2: Calculate the mean of Î?" RGi and Î?" GBi denoted by
? i = ? ? N j 1 ?(X i , X j ? 1 ? ? 2 ? ? 3 ?, ...,? ? X (1) ? X (2) ?, ...,? X (9) X VMF = X (1) X RCVMF = X VMF , if r c > r k = X C otherwise D = ?( X c , X (k) ) X RCTVMF = X VMF , if r c > r k and D > ?"¨ = X c otherwise W=[W 1 .W 2 ?..W N ] Y = vectormedian [W 1 *X 1 , W 2 *X 2 ,Î?" 1
RGi and Î?" 1 GBi . Where i=1,2?9 and i?5.

Step 3: Calculate the absolute deviation between Î?" and
Î?" 1 .(12)
Step 4 : Calculate the mean of DRGi and DGBi denoted as
D 1
RGi and D 1 GBi . where i=1,2?.9 and i?5.

Step 5 : Now

Step 6 :
If D RGc > D 1
RGi or D GBc > D 1 GBi where i=1,2?9 and i?5. central vector is corrupted, hence central vector is replaced by Vector Median of kernel.

IV.


# IMAGE FUSION ALGORITHM

The block diagram for multi-sensor image fusion is shown in figure 1. The algorithm for the multisensor image fusion using quality assessment of spatial domain is as follows:

The images captured by different sensors are filter using five different filtering algorithms. These five filtered images are fused into a single image having all objects in focus without producing details that are nonexistent in the given images. The algorithm consists of the following steps:

1. Let I 1 , I 2 ,......, I 5 be the noisy images of an object or scene captured by sensors S 1 ,S 2 ,......,S 5 respectively. Let I i be of size NXN where i =1,2,?,5. 2. Filter the noisy images using five different filtering algorithms. The filtered images are denoted as R i . 3. The recovered images R i for i=1,2,..,5 are divided into non-overlapping rectangular blocks (or regions) with size of mxn . The j th image blocks of R i are referred by R i j 4. Quality assessment value (?) of R i j is calculated and the results of R i j are denoted by ? i j . Quality Assessment value ? is given by ? i j .

Quality Assessment value ? is given by ( 14) where (15)

The covariance matrix of the gradient vectors for all b 2 sites in this block is given by ( 16)

In order to determine the sharper image block, the quality assessment value of image blocks from 5 recovered images are sorted in descending order and the same ordering is associated with image blocks. The block with the maximum quality assessment is kept in the fused image. The fusion mechanism is represented as follows:

If ? i j is the quality assessment value of block R i j , the ordering of assessment values is given by (17) and this implies the same ordering to the corresponding blocks Where the subscripts are the ranks of the image blocks. Since the block with the largest quality assessment value is in the fused image, it will correspond to rank 1 of the ordered blocks ie; 
? RGi = X(i, R) -X(i,G) ? GBi = X(i,G) -X(i,B)
Where i= 1?9
D RGi = | ? RGi -? 1 RGi | D GBi = | ? GBi -? 1 GBi | where i= 1,2,?9 D RGc = | ? RGc -? 1 RGi | D GBc = | ? GBc -? 1
GBi | where i= 1,2,?9, i? 5 and c is the central vector .
?=? 1 -? 2 ? 1 = ? ? ? ? ? ? J J trace J trace det 4 ) ( 2 1 ? ? ? 2 = ? ? ? ? ? ? J J trace J trace det 4 ) ( 2 1 ? ? J= s B s T s g g b ? ? 2 1 = ? ? ? 21 11 j j ? ? ? 22 12 j j ? (1) > ? (2) >??..> ? (5) R (1) > R (2) > ? > R (5) Fused Block = R (1)
V.


# EXPERIMENTAL RESULTS

The proposed method of image fusion for impulse noise reduction in images was tested on the true color remote sensing image with 290x290 pixels. The images are captured by five different sensors with different noise densities. The noisy images are filtered using five different vector median filtering algorithms. The filtered images are fused into a single image using the Image fusion method based on the quality assessment in spatial domain.. The experimental results are shown in Figure 2. Table (1) shows the PSNR value of fused image with different noise densities of input images with respect to original image. 
2011![Global Journals Inc. (US) Global Journal of Computer Science and Technology Volume XI Issue XXI Version I 29 2011 December zero or 255 with probability p y ij =](image-2.png "D © 2011")
![RGi and ? GBi values closely correspond to each other. Thus the mean absolute deviation D' RG and D' GB i.e. the mean of D RGj and D GBj (where 1 ? j ? N, Multi-Sensor Image Fusion for Impulse Noise Reduction in Digital Images © 2011 Global Journals Inc. (US) Global Journal of Computer Science and Technology Volume XI Issue XXI Version I 30 2011 December X VMF = vectormedian (window)](image-3.png "")
99![and j ?c, c = (N+1)/2, N = 9) has small values. D RGj and D GBj are the absolute deviation values of ? RGj and ? GBj from ?' RG and ?' GB respectively. ?' RG and ?' GB denote the mean of ? RGj and ? GBj (where 1 ? j ? N, and j ? c, c = (N+1)/2, N = 9 ).The absolute deviation of the central vector ? RGc and ? GBc values from ?' RG and ?' GB is obtained respectively as D RGc and D GBc .If the absolute deviation D RGc and D GBc of the central vector pixel exceeds the value of D' RG or D' GB respectively for a 3X3 kernal, the central vector pixel is to be replaced by the vector median of the kernel. The algorithm is represented as follows.In a 3X3 kernel,Step 1: Find the difference values of red(R) and the green(G) intensities denoted by Î?" RGi and the difference values of the green(G) and blue(B) intensities denoted by Î?" GBi .(11)](image-4.png "?,W 9 *X 9 ]")
![Image Fusion for Impulse Noise Reduction in Digital Images © 2011 Global Journals Inc. (US) Global Journal of Computer Science and Technology Volume XI Issue XXI Version I 31 2011 December](image-5.png "")
12![Figure 1 : Block Diagram of multisensor Image fusion](image-6.png "Figure 1 :Figure 2")
			© 2011 Global Journals Inc. (US)
			© 2011 Global Journals Inc. (US) Global Journal of Computer Science and Technology Volume XI Issue XXI Version I 34 2011 December
			December
		
		
			

VI.


## CONCLUSION

This paper presents the multi-sensor image fusion method for impulse noise reduction in digital images. This technique can be used in military, remote sensing and medical applications. The experimental results show that our fusion algorithm works better in removal of impulse noise in digital images. The proposed method is simple and can be used for realtime imaging applications.  


## Global Journal of Computer
			
			

				


* 
	
		Tri-state median filter for image Denoising
		
			TaoChen
		
		
			Kai-KaungMa
		
		
			Li-HuiChen
		
	
	
		IEEE Transactions on Image Processing
		
			8
			12
			
			December 1999
		
	




* 
	
		Adaptive nonlinear filters for simultaneous removal of different kinds of noise in images
		
			ReihardBerstein
		
	
	
		IEEE Trans on circuits and systems
		
			34
			11
			
			1987
		
	




* 
	
		Image sequence fusion using ashift invariant wavelet transform
		
			ORockinger
		
	
	
		IEEE transactions on image processing
		
			3
			
			1997
		
	




* 
	
		Fusion performance measures and a lifting wavelet transform based algorithm for image fusion
		
			ChaveliRamesh
		
		
			TRanjith
		
	
	
		Proc. 5th International conference on image fusion
				5th International conference on image fusion
		
			july 2002
			
		
	




* 
	
		A noise fading technique for images corrupted with impulse noise
		
			SIndu
		
		
			ChaveliRamesh
		
	
	
		Proceedings of ICCTA07
				ICCTA07
		
			IEEE
		
	




* 
	
		Vector Median Filters
		
			JAstola
		
		
			PHaavisto
		
		
			YNeuro
		
	
	
		Proc. of IEEE
				of IEEE
		
			April 1990
			78
			
		
	




* 
	
		Express Letters -Two-Dimensional Rank-Conditioned Median Filter
		
			SLl. Alparone
		
		
			RBaronti
		
		
			Carla
		
	
	
		IEEE Trans. On Circuits and Systems-II: Analog and Digital Signal Processing
		
			42
			2
			
			February 1995
		
	




* 
	
		Adaptive Vector Median Filter for Removal Impulses from Color Images
		
			KMSingh
		
		
			PKBora
		
		II-396 -II-399
	
	
		Proc. of Int.Symposium on Circuits and Systems
				of Int.Symposium on Circuits and Systems
		
			May 2003
			2
		
	




* 
	
		Removal of Impulse Noise from Color Image
		
			RHLaskar
		
		
			BBhoowmick
		
		
			RBiswas
		
		
			SKar
		
		
			2009
			TENCON IEEE
		
	




* 
	
		Block Diagram of Multi Sensor Image Fusion