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The mathematical model that aims at determining points in an image at which the image brightness suddenly changes is called edge detection. This study aims to propose a new hybrid method for edge detection. This method is based on cellular learning automata (CLA) and stochastic cellular automata (SCA). In the first part of the proposed method, statistic features of the input image are hired to have primary edge detection. In the next step CLA and SCA are employed to amplify pixels situated on edge and castrate those pixels which are part of the image background. The simulation results are conducted to prove proposed method performance and these results suggest that the proposed method is more efficient in finding edges and outperforms the existing edge detection algorithms.

The various applications in image processing, such as medical, military and engineering science, cause to promote techniques in feature extraction of image [

To have high quality edge detection method, an algorithm with four stages is employed. In the first stage standard deviation is calculated using Moore neighborhood [

This paper is divided into five parts. In Section 2, basic concepts of CLA and SCA and their structures are introduced. Section 3 discusses the proposed model and all details of the algorithm. The simulation results and comparison are presented in Section 4. Finally, the conclusion is derived in Section 5.

In this section preliminaries information about learning automata (LA) and SCA will be defined.

Narendra et al. [

Learning automata are represented by a four-tuple

After an automaton receives the reinforcement signal, it updates the state probability vector, applying Equation (1) for favorable response and Equation (2) otherwise.

where

Stochastic cellular automata locally interacting Markov chains [

There are few edges in a uniform image, like image of the sea and there are many edges in image including many different objects. From statistical point of view it means standard deviation in image with the low number of edges is low and vice versa. The number of edges in each image can be determined with the help of this feature.

The proposed method is divided in to 3 main steps as follows:

Step 1: At first for each pixel, standard deviation is calculated using Moore neighborhood. This value is placed instead of pixel. This procedure is repeated for all pixels of image.

Step 2: After applying standard deviation, all detected edges have good quality; however the main weakness of this method is disability to remove the waste pixels from the background of image. To solve this problem, an optimum function is defined in Equation (3) to makes edges pixel stronger and background pixels weaker.

where

Normally, the value of

Step 3: To improve the optimum function (Equation (3)) performance, value of

Before defining rules, we assume that variable Similarity_Count save numbers of pixel in Moore neighborhood of each pixel which have same gray level with the central pixel. Mentioned rules are represented in

Rule 1 | Rule 2 | Rule 3 | Rule 4 | Rule 5 | Rule 6 | Rule 7 | Rule 8 | Rule 9 | |
---|---|---|---|---|---|---|---|---|---|

Similarity_Count | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |

Edge_Probability (%) | 0 | 85 | 95 | 85 | 80 | 55 | 40 | 20 | 5 |

To determine the value of

where

Step 4: In the last step of the proposed method our aim is to reinforce the edges pixel and remove the pixels which are belong to background. To obtain the mentioned goal a learning automaton with following rules is employed.

1) Dedicate a learning automaton with two actions (edge, non edge) to each pixel.

2) Each action initial probability is measured using Equation (5).

3) Action edge in each automaton will be awarded and action non edge will be punished if two rules were satisfied simultaneously:

a) Numbers of automaton in the Moore neighborhood of mentioned automaton which choose action edge are between 2 and 4.

b) Mentioned automaton chooses action edge.

In rest of states action edge will be punished and action non edge will be awarded.

4) The proposed method will be terminated if the entropy of two sequential stages is lower than the

5) Now, each automaton has its final action and if the action is edge the corresponding pixel is the part of edge and vice versa.

In the current section, various experiments have been tested to identify and validate the proposed method’s performance.

A MATLAB 7 platform on a PC with an Intel Core i7, 2.3 GHz CPU, 8 GB memory and 500 GB hard disk with a Windows 7 Professional operating system is utilized to perform the introduced method. In this research all images are gray level with dimensions

In the first experiment, the proposed method is applied on three images with dimension

In the second experiment, the effect of parameter

In this experiment computational time of the four well-known edge detection methods are represented in

To compare our proposed method with two basis edge detection methods namely Robert and Sobel [

Sobel | Robert | CNN-PSO | SCA-CLA | |
---|---|---|---|---|

16 (ms) | 27 (ms) | 194 (ms) | 92 (ms) | |

53 (ms) | 92 (ms) | 569 (ms) | 348 (ms) | |

174 (ms) | 341 (ms) | 1994 (ms) | 1274 (ms) |

This paper conducted to present a new method for edge detection based on a hybrid model of cellular learning automata (CLA) and fuzzy cellular automata (FCA). In the first part of algorithm, standard deviation is applied to obtain the initial edges. Although in the second step an optimum function with the constant power is used to improve the edges quality, this power is constant for all the pixels and causes those non edge pixels to blur. To solve this problem, a hybrid model of SCA and CLA is used. The main advantage of the proposed method is using SCA and CLA for adjusting optimum function to reinforce edge pixels and castrate those non edge pixels. The numerical experiments and comparisons with the well-known existing methods justify the superior performance and efficiency of our proposed method.

Nasim Vatani,Rasul Enayatifar, (2015) Gray Level Image Edge Detection Using a Hybrid Model of Cellular Learning Automata and Stochastic Cellular Automata. Open Access Library Journal,02,1-8. doi: 10.4236/oalib.1101203