An Efficient Image Contrast Enhancement Method using Sigmoid Function and Differential Evolution

Image enhancement is an adjusting process to make an image more appropriate for certain applications. The contrast enhancement is one of the most frequently used image enhancement methods. In this study, we introduce a new image contrast enhancement method using a link between sigmoid function and Di erential Evolution (DE) algorithm. DE algorithm is performed to identify the parameters in sigmoid function so that they can maximize the measure of contrast. The experimental results show that the proposed method not only retains the original image features but also enhances the contrast e ectively.


Introduction
The rst attempt towards digital image recognition was the color-based algorithm (color his-togram or color distributive features) [1]. Therefore, the color contrast enhancement is a very important step in image processing. It is applied in medical image processing, remote sensing, and other areas [24]. shaped that can be given as To deal with the image contrast enhancement problem, we put x = f (x, y) then we have the modied sigmoid function including the contrast and threshold value as follows.
where g(x, y) is the enhanced pixel value, c is the contrast factor, th is the threshold value and f (x, y) is the original image pixel value. In summary, given a color image with RGB scale, the algorithm for image contrast enhancement using a modied sigmoid function is proposed as follows. Algorithm 1.
Step 1. Input the image f (x, y).
Step 2. Extract R, G, B planes of the image.
Step 3. Re-scale the color planes to the range of [0, 1].
Step 4. For each plane, apply the equation to get the enhanced pixel values.
Step 5. Finally concatenate the enhanced R, G, B planes to get the enhanced output image.
In the above algorithm, by adjusting the contrast factor and threshold value, it is possible to tailor the amount of lightening and darkening to control the overall contrast enhancement.
The threshold value th is between in 0 and 1 and reaches the optimal value between 0.3 and 0.5, according to Kannan. Similarly, c is identied by 10, it is not completely exact in fact.
According to our experiment presented below, the value of c is between 9.8 and 10 and cannot be identied unless using the evolutionary algorithm.

Image enhancement quality 1) Root Mean Square (RMS)
The contrast of an image is calculated by the luminance dierence between its pixels. The high contrast image always has more luminance difference than low contrast image. This paper uses the RMS contrast [36] as the objective function for maximizing. Given the image of size M × N , the RMS contrast is computed as follows.
where L ij is the luminance of the pixel (i, j), L is the mean of luminance in the image. RMS contrast can be considered as the standard deviation of the pixel luminance in the image. For instance, in Fig. 1, it is clearly seen that the more contrast image, a larger standard deviation in histogram, and vice versa. Therefore, to enhance the image contrast, the RMS value needs to be maximized.

2) Eective Measure of Enhancement
(EME) The EME [39], a measure of image enhancement, is based on the Weber's and Fechner's laws. Let an image f (x, y) be split into a number of blocks and using the equation 3) Absolute Measure of Enhancement (AME) The AME [40] uses the relationship between the spread and the sum of the two luminance values found in a small block and the average value of the measured results of all blocks in the whole image. Let an image f (x, y) be split into a number of blocks and using the equation

The proposed method
As mentioned before, the major drawback in image contrast enhancement method using the sigmoid function is that its parameters as the con- • current-to-best/1: where integers r 1 , r 2 , r 3 , r 4 , r 5 are randomly selected from {1, 2, . . . , N P } and must satisfy r 1 = r 2 = r 3 = r 4 = r 5 = i; F is the scale factor and randomly chosen within [0, 2]; x best is the best individual in the current population.
After mutation, in the case of the j th component v ij of mutant vector v i violates its boundary constraints, it will be reected back to allowable region as described in following formula: otherwise.
where i ∈ {1, 2, . . . , N P }; j ∈ {1, 2, . . . , 6}; j rand is the integer selected in range [1,6]; and CR is the crossover control parameter chosen within Selection Finally, each trial vector u i is compared to its target vector x i . The better one with lower objective function value will serve as a new target vector x i in the next generation.
The DE stop searching when the absolute difference between the current optimum objective function and the mean of objective functions is less than a xed value of tolerance. The whole process of image contrast enhancement using the sigmoid function and the DE is illustrated in Fig. 2

Conclusion
This paper proposes a method for contrast enhancement using sigmoid function and DE algorithm. In particular, DE is utilized to search the optimal threshold th and optimal contrast factor c in each color plane. The numerical examples show that the DE-Sigmoid outperforms the other comparative algorithms in terms of RMS contrast, and competes the others in terms of EME and AME. The proposed method has a disadvantage when the improved performance is (a) Rank in terms of RMS.
(b) Rank in terms of EME.
(c) Rank in terms of AME.