Image compression using Modified Fuzzy Adaptive Resonance Theory

Abstract

This research developed a software which can be used for image compression. This research proposes two methods: the first uses Joint Photographic Experts Group (JPEG),while the second uses artificial neural network (Modified Fuzzy Adaptive Resonance Theory (MFART)) algorithm. This software is applied on two types of images (jpeg and tiff). Several parameters in compression methods are tested, the results reveal that the MFART is better than the JPEG metod. The Root Mean Square Error (ERMS) for MFART method on jpeg image is equal 3.7 but it is equal to 26.09 when JPEG method implement on to the same image. MATLAB has been used in the implementation of this software. 1Introduction Data compression is the technique to reduce the redundancies in data representation in order to decrease data storage requirements and hence communication costs. The large amount of time and storage required to transmit pictorial data brings about the need of image compression. Neural network algorithms have high convergence times. Even one of the fastest neural network algorithms is the Fuzzy ARTMAP (FAM) algorithm, tends to lag in convergence time as the size of the network grows [1]. Ielaf O. abdl-majjed 152 The application of ART1 to image compression was studied, and showed that ART1 network can be a promising alternative [2]. The fuzzy ART network has several advantages over ART1 networks, these advantages are: first the ability to handle the grayscale image, second less implementation cost and processing time, and third the ability to handle both binary and analog vector. In this work we used a Modified Fuzzy ART (MFART) network which is the hybrid of ART1 and Fuzzy ART networks, as well as a second method which is the JPEG method. The rest of this research is organized as follows; it describes the architecture and the learning algorithms of Fuzzy ART networks , defines the image compression, the used methods, the used measure criteria, and the simulation results. 2The learning algorithm of MFART network The MFART network counts the grayscale difference between the input and category and picks up the category that has minimum difference instead of using fuzzy min operator as in Fuzzy ART. 2-1 The Learning Algorithm MFART [3] Step 1: Initialize the vigilance parameter (equ.1) and weight vector (equ.2) of each uncommitted node j, before presenting it to feature representation field (F) (in fig 1.) : 1 0 ≤ ≤ p ...(1) .....] 1 1 1 1 1 [ = j w ...(2) where j w and p are the 2N-dimensional weight vector and vigilance parameter respectively, and N is the dimension of input vector before transformation. Step 2: Transform the N-dimensional input vector I, whose components are in the interval [0,1], to 2N-dimensional vector ' I as follow . N N N N I I I I I I I 2 2 1 2 1 ,..., , , ,..., , + + = ′ ....(3) N i for I I i N ,.. 2 , 1 1 , 2 = − ...(4) The winning node (or category),(say j) is the node with the weight vector ( j w ) most similar to input I in terms of the minimum difference of grayscale value between the input ' I and category j, that is, ( ) ∑ = − N i ij w I 2 1 ' , in category representation field (layer C) where 2N is the dimension of ' I . In case of tie, one of them is to be selected arbitrarily. Image compression using Modified Fuzzy Adaptive Resonance Theory 153 Step 3: The selected category j is said to meet the vigilance criterion if the following inequality stand. ( ) P N w I N i ij − × ≤       − ∑ = 1 2