Design and Implementation of an Integrated Fuzzy and Shannon Entropy System for Edge Detection from

Global Perspectives on Geography (GPG) Volume 1 Issue 2, May 2013

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Design and Implementation of an Integrated Fuzzy and Shannon Entropy System for Edge Detection from High Resolution Remotely Sensed Images Abbas Kiani1, Hamid Ebadi2, Farshid Farnood Ahmadi*3 Geomatics Engineering Faculty, K.N.Toosi University of Technology, Tehran, Iran

1,2

Department of Geomatics Engineering, University of Tabriz, Iran

3

abbasekiani@yahoo.com; 2 ebadi@kntu.ac.ir; *3 farshid_farnood@yahoo.com

1

Abstract In this study, a new technique using Shannon entropy and based on the fuzzy logic is used for the edge detection from aerial/satellite images. In the proposed technique, different information layers are determined by the input image based on different values of threshold and using Shannon entropy, and then the appropriate edges are automatically detected and extracted using the combination of information layers.

In order to evaluate the algorithm, the results from the proposed technique are compared with that from LOG, Sobel, Prewitt edge detectors and a fuzzy edge detector technique. The results show that the hybrid system presents higher reliability for the detection of image brightness and contrast variations, curve-shaped features and sharp corners.

Keywords Hybrid Edge Detection; Entropy, Fuzzy Logic; Threshold

Introduction The edge is a prominent feature in high resolution images; which can be defined as the boundary between two regions separated by two relatively distinct gray levels. An effective and useful feature for object recognition is the shape and edge information of the objects; thus, the use of edges is common in machine vision applications. Edges with significant information about the image represent the shape property of the objects. The importance of the edges is such that the human visual system also uses a preprocess step for the edge detection.

Majority of the classical mathematical algorithms for edge detection is based on the derivative of the original image pixels such as Gradient, Laplacian and Laplacian of Gaussian operators. Gradient based edge detection methods, such as Roberts, Sobel and

Prewitts use two separate 2-D linear filters to process vertical and horizontal edges. The Laplacian edge detection method employs a 2-D linear filter to approximate second-order derivative of pixel values.

In addition to the mentioned methods, other approaches have been used for edge detection, including cellular neural network techniques, ant colony algorithm, fuzzy techniques, bacterial foraging technique, etc. Because of the uncertainties in many aspects of image processing, fuzzy processing is desirable. These uncertainties include: cumulative and non-cumulative noises in the low level of the image processing, inaccuracy in the assumptions of the algorithm, and interpretative ambiguous interpretation in high-level image processing.

Edges are generally modeled as intensity boundaries and ridges. Fuzzy image processing, a tool for the formulation of the edge, is a combination of imprecise information from different sources. In most approaches presented for edge detection based on fuzzy logic, the fuzzy rule base technique is utilizedd.

In these methods, the neighboring points of each point are considered as classes, and the fuzzy inference system is implemented using the proper membership functions defined for each class. In (Liang and Looney 2003), for example, it was tried to detect the edges by considering the neighboring points as 3Ă—3 kernels around the central points and defining predetermined membership functions to detect the discontinuities in the gray level (or intensity level of color) of different classes. Its fuzzy classifier detects classes of image pixels corresponding to gray level variations in the various directions. This technique uses rules and constant membership functions for the determination 21

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Global Perspectives on Geography (GPG) Volume 1 Issue 2, May 2013

of the edge points, in which the discontinuity in the gray level of the points around the central point is considered as the edge. Moreover, Mansouri et al. presented similar methods for the fuzzy edge detection. In their approach, the neighboring points of each pixel are considered as 6 sets. A value between zero and one is assigned to each class by proper membership functions (normal functions in this method). Then, based on the membership degree of each class and using the fuzzy rules, the fuzzy rule base system is used to decide on the existence of the edge and its direction. In 2008, Chaira et al. presented an algorithm for edge detection using the Attanassov’s intuitionistic fuzzy set theory. A distance measurement technique, called fuzzy intuitionistic divergence, having also been suggested, was applied to images for edge detection. It was tried in this approach to detect dominant edges and to remove undesired ones. Experimental studies showed that the edge detection was solely dependent on the choice of the uncertainty constant.

Renu Dhir applied an adaptive neuro-fuzzy inference system (ANFIS) for edge detection. Fuzzy logic enables us to use the uncertainty in the classifier design and consequently increase the credibility of the system output. This technique involved training the ANFIS edge detector for Edge detection. Their technique used the edge strength information based on strong fuzzy if then rules to avoid detection of spurious edges corresponding to noise, which is often the case with conventional gradient-based techniques (i.e., Sobel and Roberts). The internal parameters of the ANFIS edge detector have been optimized.

With the advancement of aerial/satellite imaging techniques, especially the appearance of digital aerial/satellite images, edge detection is necessary to extract spatial information. Most remote sensing applications such as image registration, image segmentation, region separation, data compression and recognition have utilized edge detection as a preprocessing step for feature extraction. Land cover/land use classification of urban areas setting its own requirements for feature extraction, typically consist of regions with various sizes and shapes depicted in remotely sensed images. In this case, edge detection can help to extract many different types of potentially suitable features. Remote sensing images have their own characteristics such as rich texture, intense illegibility, and huge data quantity. In addition,

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dispersion of atmosphere, radiation and reflection of earth surface make the captured images blurred. Even in the same position, the images captured by different satellites in different times are discrepant. Many current algorithms are not effective for edge detection of remote sensing images. So, it is necessary to design a new algorithm which can be applied to various kinds of remote sensing images.

In this research, an integrated fuzzy and Shannon entropy techniques are used for optimal edge detection. After the determination of the intensity value properties for the pixels of each region in the image using the entropy, these values are considered as our fuzzy system inputs under several different information layers. A significant issue in the edge detection using the entropy method is to determine the appropriate threshold. Variable thresholds are used in this study to detect edges with different details.

Finally, by means of the use of the fuzzy logic and the combination of different information layers, the output of our fuzzy system is the desired optimal edges.

Theory of the Proposed Algorithm Fuzzy logic is a form of reasoning which replaces the simple machine patterns by various methods of conclusion in the human brain. In the crisp sets, an object definitely belongs to a set: µA(x) = {0,1} or not.

In fuzzy sets, however, an object can be a member of a set to an extent: µ(x): X  [0,1] Where the membership function is a real number 0≤ µA ≤1 meaning that the object relatively belongs to the set.

The partial value of the membership function is called the membership degree.

The fuzzy system provides an appropriate tool to code the knowledge. The fuzzy combination is categorized into two parts: the linguistic part which is shown to the user, and the numerical part which is automatically processed by the system. The linguistic part is related to the input descriptions. The linguistic terms are related to their numerical worlds by the membership functions. The general system of the fuzzy image processing methods is as shown in FIG. 1.

The input image must be first fuzzified after entering the system, and then other processes can be performed on the image.

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Expert knowledge

Input image

Image fuzzification

Membership modification

Image Defuzzication

Results

Fuzzy logic Fuzzy set theory FIG. 1 THE GENERAL SYSTEM FOR THE FUZZY IMAGE PROCESSING TECHNIQUES (TIZHOOSH 1997)

.In 1948, Shannon redefined entropy of Boltzmann/Gibbs as a measure of uncertainty regarding the information content of a system. It is an uncertainty measure of a set of random variables which is defined in terms of probabilistic behavior of a source of information.

pixels of each image section using Shannon entropy and determines the Shannon entropy values as the inputs for the fuzzy system. Then, it detects the desired edges using fuzzy inference by defining membership functions and the considered logic.

Flowchart of the procedure is illustrated in FIG. 2.

Let X be a discrete random variable on a finite set X={x1,…,xn}, with probability distribution function p(x)=Pr(X=x) containing I(x) units of information defined by: I(A) =

[1/ P(A)] = -

[P(A)]

Input image

Determination of the proper thresholds

(1)

The amount I(A) is called the self-information of event A. The base of logarithm, n, determines the unit which is used to measure the information. Thus, if we use bits, the base of this algorithm is 2. If the probability mass function is presented as the self-information of X, then the Shannon entropy of X is the expected value of self-information. The entropy H(X) of X is defined as:

Create binary Layers from input image by applying the thresholds.

Binary image 2

Binary image i

Binary image 1

Compute the Shannon entropy values for each binary image, and create information layers.

I’th layer evaluated using Shannon entropy

2’th layer evaluated using Shannon entropy

1’th layer evaluated using Shannon entropy

Fuzzy combination of the different layers

(2) It is a measure of average information content per source symbol.

Proposed Algorithm The main aim of this study is to develop a new technique for the edge detection. The edge is defined as the boundary between an object and the background or the boundary between the overlapping objects in an image. In an ideal case, assuming that the intensity of each object is uniform and different from the intensity of its neighboring objects, any significant variation in the intensity values can be considered as an edge. The proposed technique investigates the

Defuzzifying

Edge image

FIG. 2 THE FLOWCHART OF THE PROPOSED APPROACH.

In digital image processing, an image in the real world is a function of two real variables, e.g. f(x,y) or the gray level value, as a function of the pixel position (x,y). On the other hand, the threshold values are used to transform a dataset containing different values (here, brightness degrees of the image pixels) into a new dataset. When a threshold value is applied to the input data, the input values below the threshold are replaced by an output value and the input values

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FIG. 3 THE EFFECT OF APPLYING THE THRESHOLD.

above the threshold are replaced by another output value. In other words, the threshold classifies the pixels into two categories (FIG. 3).

In the proposed technique, some proper thresholds are first automatically defined based on the radiometric properties of the input. The number of these thresholds (n) can be increased or decreased corresponding to the details of the image. Based on the experimental tests, two thresholds (n=2) for conventional images and three thresholds (n=3) for more complex images lead to desirable results, although the designed system can hold more number of thresholds.

In the next step, a Mask filter w(x,y) of the size u×v is defined where v=2b+1 and u=2a+1 (a and b are nonzero positive integers). The smallest significant size for the mask is 3×3. The region the mask covers is shown in FIG. 4. f(x-1,y-1)

f(x-1,y)

f(x-1,y+1)

f(x,y-1)

f(x,y)

f(x,y+1)

f(x+1,y-1)

f(x+1,y)

f(x+1,y+1)

FIG. 4 COVERED PIXELS IN AN IMAGE PATCH UNDER A THREE-BY-THREE MASK.

Then the entropy of each central pixel is determined as follows, H(central Pixel) = -p × log(p) 24

(3)

Where p is the probability of the central pixel of the image under the application of the above mask.

Up to this step, a number of information layers are produced for the selected number of thresholds (n) with pixels containing the Shannon entropy values for each region of the image, and the layers are saved in the knowledge base (FIG. 3). In fact, each information layer is a new image created from the original image; and these information layers are the inputs to the fuzzy system.

As stated before, the crisp inputs for the fuzzy system used are the information layers produced above, which contain the entropy values of the original image pixels with sizes equal to the original image. A proper method is described below to combine these information layers and extract the appropriate edges.

According to Equation 3, by computing the Shannon entropy values for all cases in a 3×3 kernel, the graph of FIG. 5-a is obtained. The abscissa shows the probability values, and the ordinate shows the Shannon entropy values. Given the computed values, the range for the fuzzy system inputs is considered from 0 to 0.5.

The fuzzifier converts the precise, unambiguous and non-fuzzy data into a linguistic variable. In the proposed algorithm, three variables, namely Zero, Weak and Strong, are defined as linguistic variables (FIG. 5-b).

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programming in MATLAB (version 7.0) for the test images which used in this study includes a simple image with .jpg format (FIG. 6a) and an aerial digital image taken from the city of Anzali (north of Iran) (FIG. 7a). Comparison of the results with that of the LOG, Prewitt, Sobel detectors and a fuzzy technique presented by Aditya Irawan in the University Negeri Jakarta in 2011 clearly approves the better performance of the proposed edge detection operator for the test image. (a)

(b) FIG. 5 (a) ENTROPY VALUES FOR A THREE-BY-THREE KERNEL. (b)MEMBERSHIP FUNCTIONS AND LINGUISTIC VARIABLES DEFINED FOR THE INPUTS OF THE FUZZY SYSTEM.

The database contains information about the membership functions of the fuzzy sets and the variable domains. In the proposed method, membership functions are defined as Gaussian type.

The rule base contains a set of inference rules (set of ifthen’s), and the number of which depends on the selected number of threshold values (n) and the number of linguistic variables to different extents. In this research, three linguistic variables are defined. As discussed above, the proposed algorithm investigates the input images in the cases of 2 and 3 thresholds for which 8 and 27 rules are defined in the rule base, respectively.

The defuzzifier converts the inference unit result which is a linguistic variable, into a precise number.

The output of our fuzzy system is indeed the desired edge. In all the above steps, the center average defuzzifier, the AND method and the multiplication inference engine are used.

In the first test, the non-remote-sensing image is investigated. This image has been selected to demonstrate the ability of the algorithm for edge detection based on a non-remote-sensing image. This image containing different curvatures with various thickness can be a challenge to estimate the ability of the algorithm. The fuzzy system applied is the Sugeno method, and the input membership functions are of the Gaussian type. The rule base is defined in which 8 rules are considered for the 2 thresholds used, and the AND operator is applied to relate them. The extracted edge is eventually obtained as shown in FIG. 6f, which shows that the proposed algorithm has extracted the edges appropriately. One of the most important features of this technique is the complete extraction of the curved edges, while these edges have not been extracted by Sobel and Prewitt methods. LOG technique has some problems to extract the sharp edges, which has caused discontinuities in the extracted edges. Irawan’s fuzzy technique has been successful in extracting the thick edges in this image, but it fails to show a good performance for the weak edges. However, due to the use of different information layers as the inputs for the fuzzy system, our proposed technique has been successful in detecting the strong edges as well as in extracting the weak ones. It has then combined them in a fuzzy system, and has extracted most edges present in the image.

In the second test, the aerial digital image has been investigated. Since there are several features and many details in this image, 3 thresholds and correspondingly 27 rules are used in the rule base. Some of these rules are listed below:

Results and Discussion



The performance of the results obtained from the proposed approach was evaluated through

If (input1 is zero) and (input2 is zero) and (input3 is zero) then (output1 is zero) (1)



If (input1 is zero) and (input2 is weak) and

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(input3 is weak) then (output1 is weak) (1) 

If (input1 is strong) and (input2 is strong) and (input3 is zero) then (output1 is zero) (0.8)



If (input1 is strong) and (input2 is weak) and (input3 is strong) then (output1 is zero) (0.4) …

The results obtained from the application of different

edge detection algorithms are shown in FIG. 7. As it can be seen from this figure that Prewitt and Sobel techniques have been successful in extracting the buildings, but not in extracting the curve-shaped features in the image center and some fine details of the image. Irawan’s fuzzy technique extracts the dominant features of the image. Thus, in a general

(a)

(b)

(c)

(d)

(e)

(f)

FIG. 6 THE RESULTS OBTAINED FROM APPLYING EDGE DETECTION OPERATORS. (a) THE CONVENTIONAL IMAGE; (b) SOBEL TECHNIQUE; (c) PERWITT TECHNIQUE; (d) IRAWAN’S FUZZY TECHNIQUE; (e) LOG TECHNIQUE; (f) The Proposed TECHNIQUE.

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view, most image features are obvious, and the image noise is small; however, the fine features and details of the image are not clearly obvious as in FIG. 7d. The LOG technique has been relatively successful in extracting trees and curve-shaped features in the image center, but it shows a weak performance in detecting the building areas. In particular, the LOG has caused some noises in the image by extracting

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many unnecessary features.

Our proposed technique has properly extracted the building areas and the curved features present in the image center. It has also extracted most dominant edges in the image by extracting some fine details like trees, as well as suitably removing the unnecessary and noise-like edges from the extraction procedure.

(a)

(b)

(c)

(d)

(e)

(f)

FIG. 7 THE RESULTS FROM APPLYING EDGE DETECTION OPERATORS. (a) THE CONVENTIONAL IMAGE; (b) SOBEL TECHNIQUE; (c) PERWITT TECHNIQUE; (d) IRAWAN’S FUZZY TECHNIQUE; (e) LOG TECHNIQUE; (f) THE PROPOSED TECHNIQUE.

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Global Perspectives on Geography (GPG) Volume 1 Issue 2, May 2013

Conclusions

detection." Applied soft computing 8(2): 919-927.

In this research, a new technique was developed for the edge detection from high resolution images, which efficiently identified and detected the edge pixels in the images using the fuzzy logic and Shannon entropy.

The designed fuzzy rules were good solutions to improve the edge qualities as far as possible. A drawback of the conventional fuzzy edge detection algorithms is that they need high loads of computation; which has been solved by the combined proposed method. According to the obtained results, it can be concluded that the integrated approach introduced presents a higher reliability for determination of the brightness and contrast variations. Furthermore, the system performed well for curve-shaped lines, and the sharper corners of the image were well identified and detected as edges.

Deshmukh, N. K., A. B. Kurhe, et al. (2011). "Edge detection technique for topographic image of an urban/peri-urban environment

using

Authors would like to thank Akram Eftekhary and Salim Masoumi for their collaboration in this research.

functions

and

morphological filter." International Journal of Computer Science and Information Technologies 2: 691-693.

Dhir, R. (2012). "Novel Adaptive Neuro-Fuzzy based Edge Detection Technique." International Journal of Computer Applications 49(4): 23-27.

Gang, L., Y. Fan, et al. (2008). An algorithm for remote sensing image edge detection based on fuzzy sets.

Intelligent Information Technology Application, 2008.

IITA'08. Second International Symposium on, IEEE. He, Q. and Z. Zhang (2007). "A new edge detection algorithm for image corrupted by White-Gaussian noise."

AEU-International

ACKNOWLEDGMENT

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Journal

of

Electronics

and

Communications 61(8): 546-550.

Li, H., X. Liao, et al. (2011). "Edge detection of noisy images based on cellular neural networks." Communications in

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