9th IEEE/ACIS International Conference on Computer and Information Science
A Novel Fuzzy Ant System For Edge Detection Om Prakash Verma1, Madasu Hanmandlu2, Ashish Kumar Sultania3, Dhruv4 1,3,4. Department of Information Technology, Delhi Technological University, Delhi(Formerly Delhi College of Engineering) 2. Department of Electrical Engineering, Indian Institute of Technology, Delhi
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[email protected], , Abstract:- A new approach for edge detection is presented in this paper using fuzzy derivative and Ant Colony Optimization (ACO) algorithm to reduce the discontinuities presented in the image filtered by Sobel operator. The number of ants are calculated and placed at the endpoints of the edges in the image filtered by Sobel Edge detector. Fuzzy Derivative Technique gives fuzzy probability factor. This probability factor is used to decide the next most probable pixel to be edge. The Ant colony optimization (ACO) technique is taken from the behavior of some species of ants which uses certain chemicals (known as pheromone) to inform other ants about the appropriate path. The intensities of the pheromones help ants for making decision for the right path. This concept is used by placing artificial ants on the image and edges are calculated by considering intensity difference as heuristic information. Two rules are also proposed for reducing movement of ant. Keywords:- Ant colony optimization, fuzzy derivative, pheromone, heuristic information, Sobel Edge Detector.
I. INTRODUCTION Edge detection is a fundamental problem in image analysis. Edges in the image may be regarded as a boundary between two dissimilar regions. Edges may even contain other edges, when look closer. An edge is easy to detect since differences in pixel values between regions are relatively easy to calculate. Over the years, many approaches have been proposed to extract the contours features in an image. For example, the Sobel edge detector[2] used local gradient operators, which were capable of detecting edges having high spatial frequencies and certain orientations only. The Sobel edge detector produces poor results in blurred and noisy images. The Prewitt operator [3,14] was proposed to extract contour features by fitting a least-squareerror (LSE) quadratic surface over a 3*3 image window. The Canny detector [15] defines edges as zero-crossing of second derivatives in the direction of greatest first derivative. The Canny edge detector works in multistage. Marr et al [17] proposed an algorithm that finds edges at the zerocrossings of the image Laplacian. Non-linear 978-0-7695-4147-1/10 $26.00 © 2010 IEEE DOI 10.1109/ICIS.2010.145
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filtering techniques [18] for edge detection also saw much advancement through the SUSAN method, which works by associating a small area of neighboring pixels with similar brightness to each center pixel. The nature of the image data is indeterminate and the edges of an object in an image are not very clear and occasionally scene pixel to object ones occurs moderately, so fuzzy reasoning is able to extract useful attributes from the approximate and incomplete data and improve the task of edge detection. Different algorithms for fuzzy based edge detection [6, 16, 19, 20,] have been proposed. In most of these methods, adjacent points of pixels are assumed in some classes and then fuzzy system inferences are implemented using appropriate membership function, defined for each class. Fuzzy logic by the local approach has been used by Bloch [19] for morphological edge extraction method. Ho et al [20] used both global and local image information for fuzzy categorization and classification based on edges. Abdallah et al [4] propose a fuzzy logic reasoning strategy for edge detection in digital images without determining the threshold value. The first ACO algorithm proposed by Dorigo et al. Since then a number of ACO algorithms such as ant colony system [10], Max-Min ant system [6], ant colony algorithm for Solving continuous optimization problem [14], an improved ACO for solving the complex combinatorial optimization problem [7,8], has come in the fore. ACO has inspired from foraging behavior of some ant species. Ants deposit pheromone (a type of chemical) on the ground in order to communicate between the members of their community which also increases the probability that the other ants will follow the same path. The proposed approach drives the number of ants on the image by the discontinuities present in the edge detected by the Sobel edge detector. This paper is organized as follows: In Section II, brief introduction to ACO is presented. In Section III a method for Edge detection using Fuzzy Derivative is describe. A Fuzzy Derivative and ACObased discontinuities removal approach is proposed
in Section IV. Section V deals with Result & Discussion. The conclusions are drawn in Section VI.
2) Initialize the positions of total K ants, as well as the pheromone matrix τ(0). 3) For the construction-step index n = 1 : N and for the ant index k = 1 : K. Consecutively, move the kth ant for L steps, from the node i to the node j according to a probabilistic transition matrix P(n)
II ANT COLONY OPTIMIZATION Ant Colony Optimization (ACO) is a populationbased approach first designed by Marco Dorigo and co-workers [11,12] and inspired by the foraging behavior of ant colonies. In ACO, a number of artificial ants build solutions to an optimization problem and exchange information on their quality via a communication scheme that is reminiscent of the one adopted by real ants [13]. Individual ants are simple insects with limited memory and capable of performing simple actions. However, the collective behavior of ants provides intelligent solutions to problems such as finding the shortest path from the nest to the food source. Ants foraging for food lay down quantities of a volatile chemical substance, named pheromone, marking their path that it follows. The ants can carry on indirect communication through a chemical substance. The ants travel a shorter path on which the pheromone trail accumulates faster than on the longer one. Therefore, the faster the pheromone [7] trails increase on the short path, the greater is the probability that the other ant has travelled that path. Artificial ants [8] are like real ants with some major differences:1) Artificial ants have memory, 2) They aren't completely blind, 3)They live in a discrete time environment. However they have some adopted characteristics from the real ants, like 1) They probabilistically prefer path with a larger amount of pheromone, 2)Shorter path is true path, larger is the rate of growth in the pheromone concentration, 3)They communicate to each other by means of the amount of pheromone laid on each path.
,
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∑
, ,
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(1)
where τi,j(n−1) is the pheromone information value and ηi,j represents the heuristic information of the arc linking the node i to the node j; the constants α and β represent the influence of pheromone information and heuristic information, respectively. 4) Update the pheromone matrix τ(n) after the movement of each ant within each construction step. ,
1
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if i, j belongs to the best tour, otherwise
where ρ is the evaporation rate. 5) Make the solution decision according to the final pheromone matrix τ(N). performed after the move of all K ants within each construction-step; and the pheromone matrix is updated as τ 1 ψ .τ ψ. τ (3) where ψ is the pheromone decay coefficient. III. EDGE DETECTION USING FUZZY DERIVATIVE TECHNIQUE Fuzzy technique [5] is based on the observation that a small fuzzy derivative are mostly caused by noise, while a large fuzzy derivative are mostly caused by an edge in the image. Fuzzy rules depend on the intensity of the eight neighbors. Fuzzy rules are applied to all the pixels of the image. Fuzzy derivative method gives fuzzy probability factor which is used as heuristic function. The heuristic function is used to represents the edge information at each pixel location of the image. The neighborhood of a pixel(x,y) can be displayed as in Fig.1.
Parameters defined in the procedure of ACO are as follow: 1) Pheromone matrix: This matrix contains the value of pheromone intensity which attract the ants to follow paths traversed by other ants. Pheromone matrix are updated twice, once after the movement of each ants and secondly after movement of all the ants. 2) Probabilistic transition matrix: The value of probability for the ant's movement from one pixel to another is stored in probability transition matrix. The procedure of ACO can be summarized as follows: 1) Let total K ants are applied to find the optimal solution in a space χ that consists of M1× M2 nodes.
Fig.1: Pixel (x,y) with its neighborhood pixel
The derivative at the central pixel position (x,y) in the direction D (D Є dir {NW,W,SW,S,SE,NE,E,N}) is defined as the difference between intensity of the pixel at (x,y) and its neighbor in the direction D. This derivation is denoted by ∇D(x,y). The derivative at the central pixel position (x,y) in the direction N is defined as the difference between intensity of the
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(2)
pixel at (x,y) and its neighbor in the direction N as in given by ,
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Similarly, all the , set of fuzzy derivatives in the eight directions are calculated which is used to calculate the fuzzy probability factor (FPF) for deciding edge pixel.
(4)
The principle of fuzzy derivative is based on the following observation. Consider an edge passing through the neighborhood of a pixel in SE-NW direction. The derivative value of SW direction will be large, but also the derivative values of neighboring pixels perpendicular to the edge’s direction can be expected to be large. So if there is an edge passing through SE-NW direction through the pixel (x,y) then derivative values in the direction SW for the pixels at positions (x,y),(x+1,y+1) and (x-1,y-1) should be high. A direct estimate of intensity variation due to the pixel is calculated which is used to calculate the fuzzy derivative as average of two highest valued absolute derivatives out of three found for a particular direction. For the edge in the direction of SE-NW the three fuzzy derivatives can be defined as:
IV. PROPOSED METHOD USING FUZZY DERIVATIVE AND ACO The number of endpoints in the image filtered by Sobel Edge Detector is calculated. These endpoints defined at the discontinuities present in the image. A central pixel position (x,y) is the endpoints if only one (out of eight) of the neighboring pixel is white and the central pixel itself is also white. The central pixel position is (x,y) for which only one of the neighboring pixel P ( P Є { (x-1,y-1), (x-1,y), (x1,y+1), (x,y-1), (x,y+1), (x+1,y-1), (x+1,y), (x+1,y+1) } is white shown in fig 3.
Fig 3 Central edge pixel(x,y)
The number of ants are equal to the number of endpoints calculated and are placed at the position of endpoints detected after applying the Sobel edge detector in the image. The fuzzy derivative in the image gives fuzzy probability factor. The fuzzy probability factor is used to find the next probable pixel for the movement of ant. For reducing the movement of ants the rules used by [21] are reduced and devised as follow: Rule 1) The movement of the ant is stopped when it touches the track already traversed by another ant. Rule 2) When all the neighboring pixels (8 pixels in 3*3 grid) are already traversed by the ant, then the movement of ant stops. These rules are shown in fig 4(a) and 4(b) respectively
Fig 2: Showing the Fuzzy Derivative across all directions
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(5) , (6)
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(7) , for the The value of fuzzy derivative pixel at (x,y) in the direction of NW can be calculated by applying following rules: If (( , ( then
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