Image Recognition using Bidirectional Associative Memory and Fuzzy Image Enhancement

Transcription

1 Image Recognition using Bidirectional Associative Memory and Fuzzy Image Mohammed H.Almourish (1) ABSTRACT The capability of Fuzzy Image (FIE) and Bidirectional Associative Memory (BAM) to behave as a Pattern Recognizer/Classifier of images both noisy and noise free has been investigated in this paper. This paper presents image classification and recognition with the help Fuzzy Logic (FL) model and Artificial Neural Network that exploits two techniques FIE and BAM. The proposed FIE and BAM model uses FIE to remove impulsive and smooth non impulsive noise, and to enhance the edges or other salient structures in the input image. After that the image is provided to the BAM to classify and recognize an input vector. The BAM is to store pattern pairs so that when n-dimensional vector is presented as input, the BAM recalls m- dimensional vector Y, but when Y is presented as input, the BAM recalls X, also this model allows besides correct recall of noisy patterns, perfect recall of all trained patterns, with no ambiguity and no conditions. The FIE and BAM model has been prepared in MATLAB platform. The paper evaluates the effectiveness of the model. Keywords: Image Recognition, Fuzzy Image (FIE), Bidirectional Associative Memory (BAM), Weight Matrix, Fuzzy Logic (FL), Neural Networks NN. 1. INTRODUCTION Pattern Recognition (PR) which is a science that deals with the description or classification (recognition) of measurements has turned out to be an important component of a dominant technology such as Machine Intelligence. Various approaches to pattern recognition include statistical (or decision theoretic), syntactic (or structural) and neural approaches [1]. Of the three major approaches, neural technology is emerging quickly as a powerful means to solve PR problems. FL, which has turned out to be an excellent 1 - Faculty of Engineering and Information Technology,Taiz University, Yemen mohmedalmourish@yahoo.com 71

2 computational methodology has significantly contributed to the solution of PR problems [2-6]. The fusion of Neural Networks (NN) and Fuzzy System [7] termed Neuro Fuzzy Systems have also been applied for the solution of various PR applications. This paper combines two techniques FL and NN. FL uses FIE to improve the quality of image by enhancing the minute details of the degraded image. To perform image processing using FL, three stages must occur. First image fuzzification is used to modify the membership values of a specific data set or image. After the image data are transformed from gray-level plane to the membership plane using fuzzification, appropriate fuzzy techniques modify the membership values. This can be a fuzzy clustering, a fuzzy rule-based approach, or a fuzzy integration approach. Decoding of the results, called defuzzification, then results in an output image. NN architectures that perform incremental supervised learning of recognition categories and multidimensional maps. In this last area, diverse techniques such as Multilayer Perceptron Backpropagation (MLP-BPP), matrix memories and associative memories have proved effectiveness in solving data classification problems. Among all these techniques, the associative memory paradigm is the one that best reflect the intention of emulating the associative nature of the brain. For this reason, these memories have been widely studied during the last years and, although other more expressive paradigms have emerged during the last years, in many important application fields these memories show advantages to other methods [9]. The NN model uses BAM (developed by Kosko (1988, 1992a)) for training which reads the image in the form of a matrix, evaluates the weight matrix associated with the image. A BAM stores a set of pattern associations by summing bipolar correlation matrices (an n by m outer product matrix for each pattern to be stored). The goal of a BAM is to learn mappings between input-output pairs such that the memory produces the appropriate output in response to a given input pattern. BAM are generally used to PR and categorization problems [10]. The BAM still remains the subject of intensive research. However, despite all its current problems and limitations, the BAM promises to become one of the most useful artificial neural networks. The content of this paper is organized as follows: in section 2 the fuzzy image enhancement. The proposed model of FIE and BAM in section 3. The experimental results in section 4.Conclusion is given in section 5. 72

3 Image Recognition using of Bidirectional Associative Memory and Fuzzy Image 2. FUZZY IMAGE ENHANCEMENT 2.1 Previous Work In recent years, many researchers have applied the fuzzy set theory to develop new techniques for contrast improvement. Following, some of these approaches are briefly described see [11] Contrast Improvement with INT- Operator (Pal/King) 1. Step1: Setting the parameters (,, ) of membership function in Eq.(1). 2. Step 2: Define the membership function gray levels by the transformation G: (1) This represents the membership function maximum intensity, where for denotes the intensity of is the (m, n)th pixel, and are two positive constants (called fuzzifiers) and their values are determined from the cross-over points in the enhancement operations. 3.Step 3: Modify the membership values = (2) 4.Step 4: Generate new gray-levels = Contrast Improvement using Fuzzy Expected Value (Craig and Schneider) In this approach, the Fuzzy Expected Value (FEV) or its weighted Version (WFEV) is calculated to improve the image quality regarding to the distance of all gray-levels from FEV the algorithm can be formulated as follows: 1. Step 1: Calculate the image histogram 2. Step 2: Determine the FEV. 3. Step 3: Calculate the distance of each gray-levels from FEV (4) 1. Step 4: Generate new gray-level 73

4 (5) Contrast Improvement with Fuzzy Histogram Hyperbolization (Tizhoosh) The idea of histogram hyperbolization and fuzzy histogram hyperbolization is described in [11], respectively. Due to the nonlinear human brightness perception, this approach modifies the membership values of gray levels by a logarithmic function. The algorithm can be formulated as follows: 1. Step 1: Setting the shape of membership function (regarding to the actual image) 2. Step 2: Setting the value of fuzzifier β (a linguistic hedge) 3. Step 3: Calculation of membership values 4. Step 4: Modification of the membership values by linguistic hedge β 5. Step 5: Generation of new gray-levels by following equation: where, is the values, β is the hedge operator and the constant L denotes the maximum number of gray levels in an image Contrast Improvement based on Fuzzy If-Then Rules (Tizhoosh) The fuzzy rule-based approach is a powerful and universal method for many tasks in the image processing. We have developed a very simple inference system because the execution requirements of planned on-line implementation force us to design methods that are not expensive in computing. Our rule-based approach in this paper can be formulated as follows: 1. Step 1: Setting the parameter of inference system (input features, membership functions) see [11]. 2. Step 2: Fuzzification of the actual pixel (memberships to the dark, gray and bright sets of pixels) (6) 74

5 Fig(1): Histogram fuzzification with three membership function(adapted from: Tizhoosh, Fuzzy Image processing) 3. Step 3: Inference (e.g. if dark then darker, if gray then gray, if bright then brighter see figure 1.) 4. Step 4: Defuzzification of the inference result by the use of three singletons Locally Adaptive Contrast (Tizhoosh) In many cases, the global fuzzy techniques fail to deliver satisfactory results. Therefore, a locally adaptive implementation is necessary to achieve better results and a comparison with classical approach See [12] Image Based On Fuzzy Logic In the process of imaging and transmission, it s hard to avoid the interference of different kinds of noise. So, in the presence of noise, preprocessing steps such as image enhancement are widely used. The objectives of image enhancement are to remove impulsive noise, to smooth non impulsive noise, and to enhance the edges or other salient structures in the input image. In the techniques of image enhancement, image smoothing and image sharpening are two important methods. Images can be contaminated with different types of noise, for different reasons. For example, noise can occur because of the circumstances of recording, transmission, or storage, copying, scanning etc. Impulse noise and additive noise are most commonly found. It is a great challenge to develop algorithms that can remove noise from the image without disturbing its content. The neighborhood averaging and smoothing by image averaging are the classical image processing techniques for noise removal. Image smoothing is a method of improving the quality of images. The image quality is an important factor for the human vision point of view. The image usually has noise which is not easily eliminated in image processing. The quality of the image is affected 75

6 by the presence of noise. Many methods are there for removing noise from images. Many image processing algorithms can t work well in noisy environment. In this paper, a filter is introduced which will remove the noise and improve the contrast of the image. To achieve this goal fuzzy-logic-control based approach is used. The filter is tested on the colored images [13]. 3. THE PROPOSED MODEL OF FUZZY IMAGE ENHANCEMENT AND BIDIRECTIONAL ASSOCIATIVE MEMORY Here we propose another method for image recognition. The proposed model is divided into two phases; FIE and BAM, as shown in figure 2. In the first phase, the FIE is used to improve the quality of image by enhancing the minute details of the degraded image, in the second phase the image pattern recognition to store and recall a set of patterns even if the input vector has been corrupted by noise, The output image generated is noise-free high-contrast image. Fig(2): The block diagram of the proposed model 3.1 Fuzzy Image The technique used here makes use of modification to the brightness membership value in stretching or contracting the contrast of an image. Gray level intensities see [14] are transformed to fuzzy plane whose value range between 0 and 1. Figure 1 shows the mapping of gray level intensities to dark membership set and bright membership set after image fuzzification. Gray level Intensity values = {0,1,2,3 254,255} 76

7 Bright membership degree (BMD) is calculated using following formula: BMD = intensity/255; BWD ={0,0.0039,..,1} Dark membership degree (DMD ) is calculated using following formula: DMD = 1- (intensity/255); DWD={1,0.9960,,0}. To effectively improve the enhancement effect, we combine the following procedures: Primary enhancement of an image, denoted by E1 Smoothing algorithm, denoted by S Subsequent final enhancement, step E2 The object of contrast enhancement is to process a given image so that the result is more suitable than the original for a specific application in pattern recognition. As with all image processing techniques we have to be especially careful that the processed image is not distinctly different from the original image, making the identification process worthless. The technique used here makes use of modifications to the brightness membership value in stretching or contracting the contrast of an image. Many contrast enhancement methods work as shown in Figure.3, where the procedure involves a primary enhancement of an image, denoted by E1 in the figure, followed by a smoothing algorithm, denoted by S, and a subsequent final enhancement, step E2 to accomplish the primary and final enhancement phases shown in Figure [3]. Fig(3): Diagram of the enhancement model The fuzzy operator defined in Eq.(7), called intensification [15], intensify α = (7) Figure[4] illustrate the operation of intensification for fuzzy linguistic hedges on a typical fuzzy set. 77

8 Fig.(4): Fuzzy intensification. The function [15] of the smoothing portion of this method (the S block in Fig.3) is to blur (make more fuzzy) the image, and this increased blurriness then requires the use of the final enhancement step, E2. Smoothing is based on the property that adjacent image points (points that are close spatially) tend to possess nearly equal gray levels. Generally, smoothing algorithms distribute a portion of the intensity of one pixel in the image to adjacent pixels. This distribution is greatest for pixels nearest to the pixel being smoothed, and it decreases for pixels farther from the pixel being smoothed. The contrast intensification operator, Eq. (7), on a fuzzy set generates another fuzzy set, = INT( ), in which the fuzziness is reduced by increasing the values of that are greater than 0.5 and by decreasing the values of that are less than 0.5. If we define this transformation T1, we can define T1 for the membership values of brightness for an Eq.(8), as ( ) = (8) In general, each in X may be modified to enhance the image X in the property domain by a transformation function in Eq.(9), Tr, where = (9) And ( ) represents the operator INT as defined in Eq. (7). The transformation Tr is defined as successive applications of T1 by the recursive relation in Eq.(10), { ( )} r = 1, 2,... (10) 78

9 From modification of membership function using square function and cube function that pixel that is dark has been made darker by decreasing its fuzzy bright membership degree and the one in the middle is not altered much and the pixel that is bright is made brighter by increasing its fuzzy bright membership degree. Algorithm for modifying bright membership degree function [14] using cube operation if (BMD<=0.5) MBMD = 4*(BMD else MBMD = 1-4*(1-BMD end We can conclude cube operation gives better contrast than square operation Image Smoothing: A useful smoothing algorithm is called defocusing see figure 6. Fig (6): Pixels required around center pixel to use smoothing algorithm The (m, n) the smoothed pixel intensity is found [Pal and King, 1981] from = (11) where = 1 1 > > > 0 (i, j) (m, n) In Eq. (11), represents the (m, n) the pixel intensity, expressed as a membership value; denotes a set of N1 coordinates (i, j) that are on or within a circle of radius R1 centered at the point (m, n); denotes a set of Ns coordinates (i, j) that are on or within a circle of radius Rs centered at the (m, n) the point but that do not fall into ; and so on. For example, Q = {(m, n + 1), (m, n 1), (m + 1, n), (m 1, n)} is a set of coordinates that are on or 79

10 within a circle of unit radius from a point (m, n). Hence, in this smoothing algorithm, a part of the intensity of the (m, n) the pixel is being distributed to its neighbors. The amount of energy distributed to a neighboring point decreases as its distance from the (m, n) the pixel increases. The parameter represents the fraction retained by a pixel after distribution of part of its energy (intensity) to its neighbors. The set of coefficients is important in the algorithm, and specific values are problem-dependent [15]. 3.2 Bidirectional Associative memory The BAM of the net consists of two layers of neurons [16], connected by directional weighted connection paths. The net iterates, sending signals back and forth between the two layers until all neurons reach equilibrium (i.e., until each neuron's activation remains constant for several steps). BAM neural nets can respond to input to either layer. Because the weights are bidirectional and the algorithm alternates between updating the activations for each layer, we shall refer to the layers as the X-layer and the Y-layer (rather than the input and output layers). The BAM works when the input vector X(p) is applied to the transpose of weight matrix to produce an output vector Y(p), as illustrated in Figure 7(a). Then, the output vector Y (p) is applied to the weight matrix W to produce a new input vector X(p+1), as in Figure 7(b). This process is repeated until input and output vectors become unchanged, or in other words, the BAM reaches a stable state. The basic idea behind the BAM is to store pattern pairs so that when n-dimensional vector X from set A is presented as input, the BAM recalls m-dimensional vector Y from set B, but when Y is presented as input, the BAM recalls X. The BAM is unconditionally stable (Kosko, 1992). This means that any set of associations can be learned without risk of instability. This important quality arises from the BAM using the transpose relationship between weight matrices in forward and backward directions. The BAM algorithm can be presented an unknown vector (probe) X to the net and retrieve a stored association [16]. The probe may present a corrupted or incomplete version of a pattern from set A (or from set B) stored in the BAM see Figure 7(c). 80

11 Fig (7): BAM operation: (a) forward direction; (b) backward direction; (c) schematics of the process done in the direction from x to y and y to x Algorithm The algorithm for training the network and testing it is given below. Training the Net Step1: The image [S] is read in the form of square matrix [S] [m * m]. Step2: The image is changed to grayscale if it is in RGB format. Step3: The matrix may be reduced to suitable size for quicker result. Step4: The Gray scale image has been converted to binary (0,1) image (A) by using a user defined Threshold ( ) parameter. The Gray value >= is converted to 1 in original image. The gray value < t converted to 0. Step5: Convert binary to bipolar Step6: For binary input vectors, the weight matrix W = { } is given by 81

12 Image Recognition using of Bidirectional Associative Memory and Fuzzy Image = (12) For bipolar input vectors, the weight matrix W = { = } is given by, where, (13) - is the training input vector and is the target matrix. Testing the Output The BAM should be able to receive any vector from set A and retrieve the associated vector from set B, and receive any vector from set B and retrieve the associated vector from set A. The BAM testing algorithm can be presented as follows. Step1: Various images are taken as input in form of matrix [x] and changed it to grayscale. The matrix (B) is then changed in terms of 0 and 1 using the previous threshold function as stated above. The matrix may be reduced to the size as given in training process i.e. [m * m] matrix for quicker result. Step2: Weight matrix [W] as evaluated by equation 12, is provided to the network. Step3: Output is calculated as: *,n=1,2, 3, (14) Y= where [Y] is the output matrix and is the test matrix. Step4: The output is passed through the activation function [10]. For bipolar input vectors, the activation function (by using Threshold ( )) for the Y-layer is (15) where, is the net input to unit Yj. And the activation function for the X-layer is where, is the net input to unit Xi. Step5: For i=1 to m For j=1 to m If = Then display the Y and S and stop; otherwise, continue. 82

13 4. EXPERIMENTAL RESULTS We have run two types of tests to verify that our solution is feasible. First, we have applied fuzzy image enhancement to obtain an improved test images are operated on different intensities of noise as salt and pepper (0.02, 0,25 and 0.90). The performance is compared based on the parameter Peak Signal-to- Noise Ratio (PSNR).This ratio is often used as a quality measurement between the original and a compressed image. To higher the value of PSNR, better the quality of output image. Different of the PSNR is calculated for image with different noise intensities. The program generates positive PSNR around 21dB which is considered to be the best ratio. The overall execution time which the program takes is approximately seconds. After first phase images are fed in to the second phase BAM to recall images. As each image was presented, the model network was required to identify it. Response on each trial could be one of the following: image1, image2, image3, image4 see figure 9. Because an image was always presented, though it might be distorted by 100 percent noise, the response other image was always counted as an error. The four histograms in figure 11 show the percentage of correct responses for each of the four images as the level of visual noise increased from 0 to 100 percent. In each case, there were no errors in recognition until visual noise exceeded at least 30 percent. Performance remained better than 50 percent until noise exceeded 60 percent. The stepwise result of the image recognition algorithm for image shown in Fig.9 is shown by Fig. 10 (a) to Fig. [10 (f)]. 83

14 Fig(9): input images (1, 2, 3 and 4) show the input patterns and testing image shows input patterns distorted and corrupted with different intensities of noise. The bottom finding image shows the FIE and corresponding recalled. Fig(10(a)): Input image Fig.(10(b)): Distorted image Fig.(10(c)): Add noise to distorted image (0.6) 84

15 Fig.(10(d)): Remove noise Fig(10(e)):Recall original image Fig.(10(f)): Final enhancement 85

16 Fig(11): Recognition performance for each of four test stimuli as function of level of visual noise 5. CONCLUSION Fuzzy logic and neural networks theory is a new research area for defining new algorithms and solutions in mathematical morphology environment. Fuzzy morphology approach to image enhancement gives better results than various existing enhancement approaches. In the present study, we have used fuzzy morphological methods to enhance the contrast of images. The proposed FL and NN model, that utilizes two techniques FIE and BAM able to classify and recognize of images. This paper presents performance of FIE suppress salt & pepper noise. Moreover, it is also able to preserve fine image details, edges and textures as were of the original image. The FIE method proves the best approach for enhancing the corrupted images. After FIE the image is provided to the BAM includes ability of the network to recall noisy (10, 50, 90%).The result also concludes that the FIE and BAM implemented in this method presents greater robustness to distorted image. It is recommended for the future work to test the Real Time Image Processing Application to give more effective results and to mange with a variety of images. 86

17 6. References [1.] J. C. Bezdek and S. K. Pal (eds.), Fuzzy Models for Pattern Recognition, IEEE Press, Piscataway, NJ, [2.] G. A. Carpenter and S. Grossberg, Pattern Recognition by Self Organizing Neural [3.] Networks, MIT Press, Cambridge, MA, [4.] G. A. Carpenter, S. Grossberg, N. Markuzon, J. H. Reynolds and D. B. Rosen, Fuzzy ARTMAP: a neural network architecture for incremental supervised learning of analog multidimensional maps, IEEE Trans. Neural Networks 3, 5 (1992) [5.] G. A. Carpenter, S. Grossberg and J. H. Reynolds, ARTMAP: supervised real time learning and classification of non stationary data by a self organizing neural network, Neural Networks 4 (1991) [6.] A. Kandel, Fuzzy Techniques in Pattern Recognition, Wiley, NY, [7.] T. Kasuba, Simplified fuzzy ARTMAP, AI Expert,November(1993) [8.] B. Kosko, Neural Networks and Fuzzy Systems: A Dynamical Systems Approach to Machine Intelligence, Prentice Hall, Englewood Cliffs, NJ, [9.] Tizhoosh, Fuzzy Image Processing,1997, Springer,Berlin.. [10.] Laurene Fausett, Fundamentals of Neural Networks: Arquitectures, Algorithms, and Applications, Pearson Education, [11.] [12.] Gonzalez R.C., Woods R. E., Digital Image Processing,Addison-Wesley Publishing Group, Massachusetts etc.,1992. [13.] Mr. Harish Kundra, Er. Aashima, Er. Monika Verma Image Based On Fuzzy Logic,IJCSNS International Journal of Computer Science and Network Security, VOL.9 No.10, October 2009 [14.] Prof. Mrs. Preethi S.J, Prof. Mrs. K. Rajeswari, Membership Function modification for Image using fuzzy logic, International Journal of Emerging Trends & Technology in Computer Science (IJETTCS), March April 2013 [15.] Timothy J. Ross. Fuzzy Logic with Engineering Applications, Second Edition Third edition. McGraw-Hill, [16.] Michael Negnevitsky, Artificial Intelligence: A Guide to Intelligent Systems, 2nd edition. Pearson Education, 87