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To process the traffic monitoring image, a local Histogram Equalization method based on fuzzy mathematics was proposed in this paper. In this paper, firstly, we define a function to measure the similarity degree of two images. Then, a suitable Gaussian fuzzy distribution function was chose to generate a 3 × 3 matrix of influential factors. In order to reduce the artificial boundaries, we combined the 3 × 3 influential matrix with a 3 × 3 smooth filter matrix to get the final smooth-influ- ence matrix. Finally, the smooth-influence matrix was used to process the center block image. The simulation results demonstrated that the proposed method can reduce time consumption while improving the image contrast and can get satisfactory results.

With the rapid development of IoT (Internet of thing), traffic monitoring technology has been more and more widely used. But due to various reasons, the traffic monitoring image cannot be applied directly. Among them, the device, environments, and the intensity of light are all the factors that influence the image quality. In order to make secondary use, we have to process the image and enhance the image contrast. As an important step in image processing, contrast enhancement has becoming more widely used.

Currently, there are many methods of contrast enhancement; among them, histogram equalization is a well- known method because of its less complexity and high efficiency [

In recent years, many researchers have tried different ways to improve the traditional histogram equalization algorithm, and have acquired some great achievements. Among them, BHE (bi-histogram equalization) method firstly divided the input image gray level into two parts by the average gray value [

To process the traffic monitoring image [

The rest of this paper is organized as follows: Section 2 is to describe our method, Section 3 is to show the simulation and comparison results, Section 4 is to analyze our method, and Section 5 is to conclude this whole paper.

During the process of Histogram Equalization, the discrete transformation function is as follows [

where,

In order to simplify the analysis the continuous form of formula (1) is figured out as follows [

As the Formula (2) shows, there are differential relationships between

We use the difference of the pixels amount of the same gray level between two sub-block images to measure the similarity degree of them. In order to simplify the process of the measurement, firstly, the normalization preprocessing of each gray level was implemented. The similarity degree varies between 0 and 1, especially, when the two sub-block images are the same, the similarity degree is 1. Therefore, the similarity function is defined as follows:

where,

Defined in this way, the similarity function not only can decrease the computational complexity but also is suitable for sub-blocks of different sizes [

The domain of the similarity degree is defined as

where,

After several tests, the arguments of the three membership functions are determined, on the condition that

In order to simplify the description, we number the sub-blocks of the split image, which can be shown in

Because we have divided the input image into a series of sub-blocks before the processing, there are some in

evitable artificial boundaries in the processed image, In order to decrease the computational complexity and reduce the quantity of artificial boundaries, the 3 × 3 smoothing filter matrix is combined with

Define operator

where,

According to the operator defined in Formula (7), the 3 × 3 smoothing filter matrix is combined

where,

According to the smooth-influence matrix, we compute the histogram of the center block and get the transformation function to process the center block image. In this way, the process can retain the information of the center block and peripheral sub-blocks, meanwhile reducing the artificial boundaries.

The proposed method can be divided into the following steps [

Step 1: Color transformation (RGB- > HSV);

Step 2: Extract the V component, and divide it into a series of sub-blocks;

Step 3: Compute

Step 4: Implement the equalization process of the center block;

Step 5: Revert the V component and color transformation (HSV- > RGB), then output the image.

In the proposed method, the processing of each sub-block needs the auxiliary processing of the 8 peripheral blocks. So we have to do some additional processing on the edge blocks. The results of additional processing is showed in

For the edge blocks, we copy their reflectional symmetrical blocks as the filled blocks (as the

Then two traffic monitoring images of low contrast were chose (such as a dawn image and a fog image) to do experiments:

We have tested HE, BHE, AHE and POSHE methods respectively. The results of the experiment are showed in

In order to have a more objective understanding of the proposed method, we compared HE, BHE, AHE, POSHE and the proposed method from following three aspect: pre-processing, artificial boundaries process and average time. The results of the comparison are shown in

As

In the process of our method, the peripheral sub-blocks A, B, C, D, E, F, G and H affect the histogram equalization of the center block. The main time consumption concentrates on the computation of

where,

If the image is divided into

Method | Pre-processing | Artificial boundaries process | Average time |
---|---|---|---|

Proposed | Divide | Using smooth filter | 0.270552 |

HE | NULL | NULL | 0.256914 |

BHE | NULL | NULL | 0.256914 |

AHE | Divide | Bi-linear interpolation | 0.293260 |

POSHE | Divide | Detect and eliminate | 0.289349 |

a. Experimental environment: Matlab 7.06, Intel (R) Celeron (R) CPU, 4.00 GB RAM; b. Experimental data: 720 P traffic monitoring images.

So the total execution time of processing an image can be written as:

From the Formula (10), we know the total execution time is proportional to the number of sub-blocks, that is, when the value of

As the

In this paper, there are two reasons why do we choose Gaussian function as the membership function. On one hand, the Gaussian function is suitable for describing the phenomenon of nature, human society, psychology and education; On the other hand, the Gaussian function’s arguments are relatively simple compared to the other intermediate types of distribution fuzzy function, it only needs two arguments to control the position and shape of the function.

Form the subject point, on the condition that the shape controlling parameter

As the

From the experimental results, we know the more suitable arguments are

With the rapid development of traffic monitoring technology, the conventional image processing method is no longer suitable for the traffic monitoring images. In this paper, three features of traffic monitoring images have

been analyzed. On the basis of these features, a local histogram equalization method based on fuzzy mathematics was proposed. This method is suitable for contrast enhancement of traffic monitoring images. The contrast of the processed images is stretched, meanwhile the time consumption of our method is relatively low. In order to reduce artificial boundaries, we use a 3 × 3 smooth filter. But when observed carefully, some slight artificial boundaries will be found. Because the artificial boundaries and the image content are closely related, the method of reducing artificial boundaries completely and quickly is more challenging. So one of the focuses of future research is to eliminate the artificial boundaries.

Jia Shi,Kejian Yang, (2015) An Improved Histogram Equalization Method in the Traffic Monitoring Image Processing Field. Journal of Computer and Communications,03,25-32. doi: 10.4236/jcc.2015.311005