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Traditional two-dimensional Otsu algorithm has several drawbacks; that is, the sum of probabilities of target and background is approximate to 1 inaccurately, the details of neighborhood image are not obvious, and the computational cost is high. In order to address these problems, a method of fast image segmentation using two-dimensional Otsu based on estimation of distribution algorithm is proposed. Firstly, in order to enhance the performance of image segmentation, the guided filtering is employed to improve neighborhood image template instead of mean filtering. Additionally, the probabilities of target and background in two-dimensional histogram are exactly calculated to get more accurate threshold. Finally, the trace of the interclass dispersion matrix is taken as the fitness function of estimation of distributed algorithm, and the optimal threshold is obtained by constructing and sampling the probability model. Extensive experimental results demonstrate that our method can effectively preserve details of the target, improve the segmentation precision, and reduce the running time of algorithms.

Image segmentation is the technology and process of segmenting an image into multiple segments with characteristics and extracting regions of interest, and it is the basis of image analysis. The quality of image segmentation directly affects the results of the subsequent image processing [

Image segmentation methods mainly include threshold method [

Threshold technique is simple and effective for image segmentation, which has been widely used in computer vision and pattern recognition. There are several popular threshold methods including Otsu, maximum entropy, minimum cross entropy, and histogram [

In this paper, in order to improve the effect of segmentation and reduce computational cost of two-dimensional Otsu algorithm, a novel fast image segmentation method using two-dimensional Otsu based on estimation of distributed algorithm is proposed. Firstly, to obtain the approving performance of image segmentation, the guided filtering is employed to improve neighborhood image template instead of the mean filtering. Moreover, the probabilities of the target and background in two-dimensional histogram are exactly calculated to get more accurate threshold. Finally, in order to segment the image quickly and accurately, the estimation of distribution algorithm [

The method of two-dimensional Otsu applies the two-dimensional histogram comprising the image gray and its neighborhood image average gray to find the optimal threshold and then divides the image into the target and background. The main diagonal regions I and III of the two-dimensional histogram denote, respectively, the target and background; the subdiagonal regions II and IV present severally the edge and noise, as shown in Figure

Two-dimensional histogram.

Under the method of traditional two-dimensional Otsu, the sum of probabilities of the target and background is approximate to 1, and the sum of probabilities of the edge and noise is approximate to 0. This approximation is only satisfied under certain conditions, which has been confirmed in theory and experiment by the literatures [

In order to enhance the effect of image segmentation under two-dimensional Otsu method, we introduce the guided filtering to improve the neighborhood template, which can preferably preserve features of the edge and details [

A new neighborhood template can be constructed by using the guided filtering with preserving the edge and details of image instead of the mean filtering, which can preferably construct the image two-dimensional histogram and advance the performance of image segmentation.

Construct two tuples according to the gray values of original image and the filtered neighbor image by the guided filtering, denoted as the gray value of original image and the gray value of neighbor image. If the frequency of two tuples

Calculate accurately the probabilities

Calculate, respectively, the corresponding mean vectors

Calculate the total mean vector

Calculate the trace of interclass dispersion matrix

Calculate the optimal threshold

The improved two-dimensional Otsu algorithm suffers from a high computational cost. Consequently, we introduce the estimation of distribution algorithm with favorable global convergence ability and high computation efficiency to find the optimal segmentation threshold

As a new type of optimization algorithm in the field of evolutionary computation, the estimation of distribution algorithm proposes a new evolutionary model [

The gray value of a pixel in the image and a pixel in its neighborhood image is represented by the individual

Flowchart of image segmentation using two-dimensional Otsu based on estimation of distribution.

The current evolutionary generation

The trace of interclass dispersion matrix is regarded as the fitness function, as seen in (

Calculate the optimal fitness

If the evolutionary generation

In order to ensure that the probability model is sensitive to the search process, the individual who is used to construct the probability model must be able to accurately track the information of probability model. For the sake of preventing the algorithm into local optimal, the individual selection should have a certain randomness. Roulette is a proportion of random selection method. On the one hand, in order to ensure the tracking accuracy of probability model, the individual is selected according to the probability of alleles per gene bit. On the other hand, this method does not guarantee that the allele of large probability must be selected and has a certain randomness. In this paper, when the fitness value is the largest, the optimal segmentation threshold is obtained. Therefore, the roulette selection method based on fitness is adopted; that is, the probability that each individual is selected is proportional to its fitness. The specific steps are as follows:

Calculate the relative fitness of each individual

According to relative fitness

Simulate the roulette operation, that is, to generate a random number between 0 and 1. If

Repeat step (

Firstly, construct the Gaussian distribution function according to the excellent individual selected by Step

The sampling method depends on the probability model used by the algorithm. Therefore, the next generation population is generated on the basis of the constructed Gaussian distribution function:

In order to enhance the diversity of population and avoid the excessive effect on the population, in the first place,

On the basis of the optimal threshold

In order to evaluate the performance of image segmentation and the efficiency of the proposed method, a large number of industrial computed tomography (CT) images of different mechanical parts and many images from popular image segmentation dataset are used to test. Extensive experimental results are compared with the results of the following approaches, that is, Otsu, 2D Otsu [

Figure

Segmentation effect of various methods for different images.

The experimental results are shown in Figure

The computational cost of two-dimensional Otsu based on intelligent algorithm is mainly reflected in calculation of the fitness of individual. In the case of the same population size, the computational cost of different algorithms are qualitatively evaluated by comparing the evolutionary generation of population when the algorithms reach convergence state.

The maximum fitness convergence curves of the aluminum part are obtained by using two-dimensional Otsu methods based on intelligent algorithm, as shown in Figures

The highest fitness convergence curve based on 2D Otsu-FSA.

The highest fitness convergence curve based on 2D Otsu-GA.

The highest fitness convergence curve of our method.

According to the above experimental results and analyses, for solving the optimal threshold of two-dimensional Otsu, the estimation of distribution algorithm requires fewer population size and few number of iterations than the genetic algorithm and the fish swarm algorithm. In other words, the estimation of distribution algorithm can effectively reduce the computational cost.

Moreover, in order to compare the efficiencies of the proposed method and the existing methods, objectively and precisely, the mean time of image segmentation under different methods is counted. Table

Comparison of segmentation time under different methods (s).

Image | Our method | Traditional 2D Otsu | 2D Otsu-FSA | 2D Otsu-GA |
---|---|---|---|---|

Cylinder head | 0.23 | 2.53 | 1.25 | 0.92 |

Carburetor | 0.28 | 2.66 | 1.31 | 0.97 |

Nuts | 0.24 | 2.58 | 1.27 | 0.94 |

Aluminum part | 0.30 | 2.71 | 1.39 | 1.02 |

Bearing | 0.29 | 2.68 | 1.37 | 0.99 |

In this section, we compare our method with Otsu, 2D Otsu, 2D Otsu-FSA, 2D Otsu-GA, ME + PPD, LCK, and LSD on a host of images that come from popular image datasets. As an example, we select a grain image and a tire image from the general image library, a duck image and a bird image from the BSD500 image dataset, and a motorcycle image from the VOC image dataset to demonstrate the comparative results, as illustrated in Figure

Comparisons of image segmentation under various methods.

The computational costs of the above methods on the five images in Table

Comparisons of computational costs (s).

Method | Image | ||||
---|---|---|---|---|---|

Rice | Tire | Duck | Bird | Motorcycle | |

Otsu | 0.011 | 0.012 | 0.013 | 0.015 | 0.018 |

2D Otsu | 1.46 | 1.41 | 2.01 | 1.71 | 1.52 |

2D Otsu-FSA | 0.62 | 0.64 | 1.16 | 1.05 | 0.68 |

2D Otsu-GA | 0.46 | 0.51 | 0.86 | 0.79 | 0.53 |

ME + PPD | 0.32 | 0.38 | 0.28 | 0.22 | 0.27 |

LCK | 5.63 | 13.25 | 22.36 | 23.50 | 19.72 |

LSD | 4.52 | 9.64 | 19.45 | 16.37 | 15.21 |

Our | 0.14 | 0.18 | 0.12 | 0.09 | 0.13 |

In this paper, we present a fast image segmentation method using two-dimensional Otsu based on estimation of distribution algorithm. The proposed method can preferably preserve the edges and details of the object because the guided filtering template is replaced with the mean filtering template. Furthermore, compared with other existing image segmentation methods, our method has desirable segmentation performance and computational cost for image with simple scene. However, similar to other threshold-based image segmentation methods, our method is preferable for the images with the same gray scale range; it has a limitation to the object with large gray scale distribution. In addition, the actual segmentation effect of our method is not perfect in complex scene.

In the future, we plan to preprocess the object so that our segmentation method can perform well for special objects as well as handle more complex images.

The authors declare that they have no conflicts of interest.

This paper is supported partly by Chongqing Natural Science Foundation of China (Grant no. cstc2016jcyjA0353) and National Key Scientific Instrument and Equipment Development Projects of China (Grant no. 2013YQ030629).