# Introduction

mage fusion utilises information obtained from a multi-focus images of the same scene. Image processing is one of form of signal processing for which the input is an image and the output of image processing may be either an image or a set of characteristics related to the image. For the most of the image processing techniques, images of two dimensional signals is treated as input and standard image processing techniques are applied to it. The process of image fusion is performed for multi-focus and multi-sensor images of the same scene. In multifocus images, the physical objects in the scene which are closer to the camera are in focus and the far physical object gets blurred. Adverse to it, when the far physical objects are focussed then the closer objects get blurred in the image. A hierarchical idea of image fusion has been implemented for combining significant information from multiple images into single image. The process of image fusion can be accomplished either in transformed domain or spatial domain. In spatial domain operations are performed on the pixel values. In transformed domain the images are first transformed into multiple levels of resolutions.

Information fusion can be performed at any level of the image information representation corresponding to other forms of information fusion, image fusion is usually performed at one of the three different processing levels they are Pixel, Feature and Decision Level [5]. The pixel level image fusion is also known as signal level image fusion which represents fusion at the lowest processing level, that is operations such as maximum or mean(average) are applied to the pixel values of the source images to generate the fused image. Feature level image fusion is also known as object level image fusion where fused features and object labels and information that have already extracted from individual input images. Decision level is also known as symbol level, the objects in the input image are first detected and then the suitable fusion algorithm the fused image is generated. In the field of Image Processing, image fusion has received a significant importance for medical imaging, military applications, forensic, remote sensing.

A number of image fusion techniques have been exhibited in the literature. In addition of simple pixel level image fusion techniques. We find the complex techniques such as Laplacian Pyramid [2], Morphological pyramid [6], fusion based on PCA [3], Discrete wavelet Transform (DWT) [1]. These fusion techniques have different advantages and disadvantages such as liner wavelets during image decomposition the fused image doesn't preserve the original data. Likewise due to low-pass filtering of wavelets, the edges in the image becomes smooth and hence the contrast in fused image is decreased.

In this paper, we have implemented a method for multi-focus image fusion. The implemented method is discussed in section II. In section III, the quantitative measures used to evaluate the performance of the implemented method are described. Section IV covers the experiments details and section V concludes the study.


# II.


# Implementing method

Different images are acquired from the Image Processing websites. From the acquired images consider one image, for that image generate two source images from original image that is one is left focused and right blurred other one right focused and left blurred. Every image is divided into blocks. The block size plays a significant role in differentiating the blurred 2) Spatial Frequency: Spatial frequency measure the activity level in an image, it used to calculate the frequency changes along rows and columns of the image. Spatial frequency is measured using equation ( 2).

(2)

Where and Here X is the image and p*q is the image size. A large value of spatial frequency describes the large information level in the image and therefore it measures the clearness of the image.

3) Variance: Variance is used to measure the extent of focus in an image block. It is calculated using equation ( 3)
(3)
Here is the mean value of the block image and p*q is the image size. A high value of variance shows the greater extent of focus in the image block.   
( D D D D ) ( , ) 1 ( , ) * k K i j Bk X i j CV p q ? ? ? ? ? K ? ( ) ^2 ( ) ^2 SPF RF CF ? ? 1 2 1 [ ( , ) ( , 1)] ^2 * pq i j RF X i j X i j pq ? ? ? ? ? ?? 1 2 1 [ ( , ) ( 1, )] ^2 * pq i j CF X i j X i j pq ? ? ? ? ? ?? 1 1 1 ( ( , ) ) ^2 * p q i j Variance X i j pq ? ? ? ? ? ?? ?

# Where and

Here p and q represent the dimensions of the image block. A high value of energy of gradient shows greater amount of focus in the image block.

5) Edge Information: The edge pixels can be found in the image block by using canny edge detector. It returns 1 if the current pixel belongs to some edge in the image otherwise it returns 0. The edge feature is just the number of edge pixels contained within the image block.


# c) Artificial Neural Networks

Many Neural Network models have been implemented for tackling a diverse range of problems*, including pattern classification. The fusion we examine here can be considered as classification problem. Here we have considered a NN applications model, namely the PNN (Probabilistic Neural Network) .The basic idea underlying NN is to overlap localized receptive fields of the hidden units to create arbitrarily complex nonlinear ties. The normal architecture consists of one hidden layer and one output layer. Each hidden unit corresponding to a kernel or basis function of the input vector x, and is usually of the Gaussian form. The basic architecture of feed forward NN is shown below Here, c is the position of the hidden unit and is a user-defined width that controls is spread. For PNN a hidden unit is positioned at every training data point.


# d) Neural Network Algorithm

The algorithm first decomposes the source images into blocks. Given two of these blocks (one from each source image), a neural network is trained to determine which one is clearer. Fusion then proceeds by selecting the clearer block in constructing the final image. The fusion result of DWT is shift dependent. The use of image blocks on the other hand, avoids this problem even if there is object movement or misregistration in the source images, each object will still be in better focus in one of the source images. In detail, stepwise working of the implemented method is given under. 1) LFi is the left-focused and RFi is the rightfocused versions of the ith image in the dataset in section(II-A). 2) Divide the versions LFi and RFi of every image in the dataset into k number blocks of the size M*N. 3) Create the features file for all LFij and RFij according to the features discussed in section (II-B). Here j=1,2,3...k. For all i, there are two sets of features values for every block j named as FSLFij and FSRFij each of which contains five feature values. Subtract the features values of block j of RFi and include this pattern in feature file. Normalise the feature value between [0 1]. 4) Assign the class value to every block j of ith image. If block j is visible in LFi then assign it class value 1 otherwise give it a class value -1. In case of class value -1, block j is visible in RFi. 5) Train a neural network to determine whether LFi or RFi is clearer. Identify the clearness of all the blocks of any pair multi-focus images to be fused. 6) Fuse the given pair of multi-focus images block by block according to the classification results of the neural network. Such that Output of NN for block J If>0,select J from left-focused Image If<0,select j from right-focused Image The block diagram of the implemented method is shown in figure (2).


# III.


# Quantitative measures

There are different quantitative measures which are used to evaluate the performance of the fusion techniques. These are PSNR (Peak Signal to noise ratio), RMSE (root mean square error), Entropy, Correlation Coefficient, MAE (mean absolute error). Here R, F are the reference and fused images respectively.p*q is the image size.


# c) Entropy

Quantifies the quantity of information contained in the fused image. A bigger value shows good fusion results.
( D D D D ) 1 1 1 1 ( ^2 ^2) p q i j i j EG r r ? ? ? ? ? ? ?? ( 1, ) ( , ) i r r i j r i j ? ? ? ( , 1) ( , ) j r r i j r i j ? ?? ( ) exp( ) ^2/ ^2 Z x x c ? ? ? ? 1 1 ^2 10 1 ( ( , ) ( , ))^2 * 20 log p q i j L R i j F i j p q PSNR ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?? 1 [ ( , ) ( , )] ^2 * pq ij RMSE R i j F i j pq ?? ?? ?? 1 2 0 ( ) log ( ) L F F i H h i h i ? ? ?? ?
Here is the normalized histogram of fused image and L is the number of gray levels.


# d) Correlation Coefficient

The correlation coefficient matrix represents the normalized measure of the strength of linear relationship between variables.

Where is a data value at time step t, k is the lag.


# e) MAE

It is used to calculate the mean absolute error between reference image and fused image.

Where the predicted is fused image and is the true value fused image. 


# Experiments and results

Image fusion is performed. The implemented technique used in this paper is more efficient and useful, to highlight the efficiency. We have performed broad experimentation on this technique. We trained the feed forward neural network with different number of hidden layers and with different number of neurons on each layer  High performance.
( ) ^2 N t t k t N t t x x x x CC x x ? ? ? ? ? ? ? ? ? ? ? ? F h t x 11 1 ( , ) ( , ) * pq ij MAE R i j F i j pq ?? ?? ?? ( , ) F i j ( , ) R i j)
Texture Calculations:

V.


# Conclusion

In this implemented technique, a feature level focus image fusion has been implemented in this paper. In this method we have trained the feed forward neural network with the block features of pairs of multi-focus images. A feature set including SF, CV, edges, variance, and EG is used to define clarity of the image block. The trained neural network was then used to fuse any pair of multi-focus images. Experimentation results show that the implemented technique performs better than the existing techniques. The fusion result of Discrete Wavelet Transform is shift dependent. The use of image block, on the other hand avoids the problem of shift dependent.
![and un-blurred regions from each other. After dividing the image into blocks, the feature values of block of all the images are calculated and feature file is generated. A comfortable number of feature vectors are used to train NN. The trained NN is then used to fuse any set of multi-focus images. Image data set, feature selection and implemented algorithm are discussed in the following sections.a) Creating Image Dataset In the implementing method, we created an image-data set of ten grayscale images. These images are acquired from the different image processing websites. For each image in the data set, we generated its two versions of the same size. In the first versions, the left half of the image is blurred and right image is focused. A similar process is performed in the right image is blurred and left image is focused. The blurred versions are generated by Gaussian blurring of radius 1.5.In implementing method experimentation, we resize all the images into 256*256 resolutions. b) Feature Extraction In feature-level image fusion, the selection of different features is an important task. The blurred objects in an image reduce its clearness. In multi-focus images, some objects are in focus and some objects are blurred. In this paper, we extract five features from each image block to represent its clearness. These are the Variance, Energy of gradient, Contrast visibility, Spatial frequency and canny edge information. From the figure (1), we calculate the blueness of Gaussian radius for source image, Left blur and Right focused ,and Left focused and Right blur. The value of features in the image against blurriness is given in table (I). If the blurriness is increased the values of energy gradient, spatial frequency and edge information are reduced. 1) Contrast Visibility : It calculates the deviation of a block of pixels from the block's mean value. Therefore it relates to the clearness level of the block. The visibility of the image block is obtained using equation (1) (1) Here and p*q are the mean and size of the block Bk respectively.](image-2.png "F")
1![Figure 1: Cameraman image (a) Original Image (b)LBRF (c)LFRB](image-3.png "Figure 1 :")
![a) PSNR Determines the degree of resemblance between reference images fused image and fused image. A bigger value shows good fusion results. L denotes to number of gray level in the image. b) RMSE Calculate the deviation between the pixel values of reference image and fused image. A lesser value shows the good fusion results.](image-4.png "")
2![Figure 2: Block Diagram of the Implementing method](image-5.png "Figure 2 :")
![. The results of the implementing technique are compared with different existing methods including DWT, PCA, Laplacian pyramid, Morphological processing based image fusion techniques. To calculate the performance of the implementing technique, the results for two different pairs of multi-focus images are obtained including Pepsi, balloon, and cameraman images. a) Difference between DWT based Image fusion and the Implementing Technique Gonzalo pajares, implemented a DWT based image fusion technique to perform multi-focus image fusion. The fusion result Discrete Wavelet Transform is shiftdependent. The use of image block, on the other hand avoids the problem of shift dependent. We have used five different features like (SPF, EG, CV, Variance, Edge) to calculate the clearness of a block more accurately as compared to DWT. Even though if there is object misregistration or movement in the input images, each object will still be in finer focus in one of the input images. Thus, in the fused result, all the blocks covering a particular object will come from the same input image and its clarity will not be affected due to any misregistration problem. b) Visual Comparison Assessments The visible comparisons has shown in below figures (3) for Pepsi images, figure (4) for balloon images, figure (5) for cameraman images. All the images are of size 256*256.](image-6.png "")
1© 2012 Global Journals Inc. (US) Global Journal of Computer Science and Technology Volume XII Issue X Version I 18
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			© 2012 Global Journals Inc. (US)
		
		
			
			
			

				


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