The objective of enhancement techniques is to process an image so that the result is more suitable than the original image for a specific application. The choice of the technique depends upon the requirement. The histogram equalization method is powerful compared to other methods. This method usually increases the global contrast of many images, especially when the usable data of the image is represented by close contrast values. Through this adjustment, the intensities can be better distributed on the histogram. This allows for areas of lower local contrast to gain a higher contrast. Various methods have been proposed for limiting the levels of enhancement most of the enhancement algorithms are based on Histogram Equalization. A comparative study is done on Brightness Preserving System with histogram equalization (BPHE) and Recursive Method of BPHE. Recursive Mean-Separate Histogram Equalization (RMSHE) is another improvement of BPHE. These algorithms clearly state that the Image enhancement using Histogram method significantly improve the visual appearance of the image.

Keywords-Contrast Enhancement; Histogram Equalization; Brightness Preserving Enhancement

I. HISTOGRAM EQUALIZATION

1.1 Introduction

Histogram equalization is a common technique for enhancing the appearance of images. Suppose we have an image which is predominantly dark. Then its histogram would be skewed towards the lower end of the grey scale and all the image detail is compressed into the dark end of the histogram. If we could `stretch out’ the grey levels at the dark end to produce a more uniformly distributed histogram then the image would become much clearer.

Histogram equalization is used to enhance contrast. It is not necessary that contrast will always be increase in this. There may be some cases were histogram equalization can be worse. In that cases the contrast is decreased.

1.1.1. Histogram function

The function used for this part is defined with the following prototype histogram(Image,nbins,min,max,display) where nbins is the number of bins chosen to perform the histogram, and min and max the two values for the range of the histogram. The display parameter is a Boolean parameter which activates the display of the input image and the associated histogram. It returns a vector containing the relative frequencies associated to the histogram. The core of the function is the computation of the histogram in number of pixels and then in relative frequency respecting the range and the number of bins. Here is the implementation of this part:

for i=1:1:size(InputIm,1)

for j=1:1:size(InputIm,2)

value=InputIm(i,j); %read input image level

if value >= minvalue && value <= maxvalue for i=1:1:nbins if value <= i*binsize+minvalue && value > (i-1)*binsize+minvalue

% original histogram in pixels

InputIm_histogram(i)=InputIm_histogram(i)+1;

% normalized histogram pdf

InputIm_normalized_histogram(i)=InputIm_histogram(i)/resolution;

end

end

end

end

end

1.1.2. Probability Mass Function (PMF)

First we have to calculate the PMF (probability mass function) of all the pixels in this image. If you do not know how to calculate PMF, please visit our tutorial of PMF calculation.

1.1.3. Cumulative Distributive Function (CDF)

Our next step involves calculation of CDF (cumulative distributive function). Again if you do not know how to calculate CDF , please visit our tutorial of CDF calculation.

% Cumulative Distribution function

for i=1:size(InputIm_normalized_histogram,2)

normalized_cumulsum=normalized_cumulsum+InputIm_normalized_histogram(i)

normalized_cumulsumvec(i)= normalized_cumulsum

output(i)=round(normalized_cumulsumvec(i)*levels) %formula: (L-1)*cdf

end

% Mapping of the original gray level to the new one

for i=1:size(InputIm,1)

for j=1:size(InputIm,2)

OutputIm(i,j)=output(InputIm(i,j)+1);

end

end

Histogram equalization aims at obtaining uniform statistical distribution of image gray levels (uniform probability density function). By histogram equalization we can get contrast enhancement and image normalization.

Figure 1. The original image and its histogram, and the equalized versions. Both images are quantized to 64 grey levels

Histogram equalization involves finding a grey scale transformation function that creates an output image with a uniform histogram.

Assume our grey levels are continuous and have been normalized to lie between 0 and 1. We must find a transformation T that maps grey values r in the input image F to grey values s = T(r) in the transformed image .

It is assumed that

T is single valued and monotonically increasing, and

for .

The inverse transformation from s to r is given by

r = T-1(s).

If one takes the histogram for the input image and normalizes it so that the area under the histogram is 1, we have a probability distribution for grey levels in the input image Pr(r).

If we transform the input image to get s = T(r) what is the probability distribution Ps(s) ?

From probability theory it turns out that

Equ.1

where r = T-1(s).

Consider the transformation

Equ.2

This is the cumulative distribution function of r. Using this definition of T we see that the derivative of s with respect to r is

Substituting this back into the expression for Ps, we get

Equ. 3

for all .

Thus, Ps(s) is now a uniform distribution function, which is what we want.

1.2. Transformation of Histogram

1.2.1. Normalization of a Histogram

Normalize an histogram is a technique consisting into transforming the discrete distribution of intensities into a discrete distribution of probabilities. To do so, we need to divide each value of the histogram by the number of pixel. Because a digital image is a discrete set of values that could be seen as a matrix and it’s equivalent to divide each nk by the dimension of the array which is the product of the width by the length of the image.

nkn=nklength×width=pr(rk)nkn=nklength×width=pr(rk)

Which could be written in terms of mathematical transformation:

{0,L?1?Nx?Card(x)becomes{0,L?1?0,1 x?pdf(x)=Card(x)?L?1i=0Card(xi){0,L?1?Nx?Card(x)becomes{0,L?1?0,1 x?pdf(x)=Card(x)?i=0L?1Card(xi)

Where Card means the cardinality of the set so in our case the number of pixel.

1.2.2. Equalization of a Histogram

Histogram equalization is a method to process images in order to adjust the contrast of an image by modifying the intensity distribution of the histogram. The objective of this technique is to give a linear trend to the cumulative probability function associated to the image.

The processing of histogram equalization relies on the use of the cumulative probability function (cdf). The cdf is a cumulative sum of all the probabilities lying in its domain and defined by:

cdf(x)=?k=??xP(k)cdf(x)=?k=??xP(k)

The idea of this processing is to give to the resulting image a linear cumulative distribution function. Indeed, a linear cdf is associated to the uniform histogram that we want the resulting image to have.

Figure 2. Technique to perform histogram equalization

So we are going to implement the following formula to get the new pdf:

Sk=(L?1)cdf(x)

II. LITERATURE REVIEW

Kim 2 proposed BBHE (Brightness preserving Bi-Histogram Equalization), which first segments an input histogram into two sub-histograms based on the brightness mean of the input image and then executes HE on each sub-histogram independently. Subsequently, DSIHE (Dualistic Sub-Image Histogram Equalization) was introduced by Wan et al. 3. DSIHE is conceptually similar to BBHE, but for histogram decomposition it uses the median of the input image’s brightness instead of the mean brightness. Chen and Ramli 4 developed RMSHE (Recursive Mean Separate Histogram Equalization), and Sim et al. 5 proposed RSIHE (Recursive Sub-Image Histogram Equalization). In fact, RMSHE and RSIHE are recursive versions of BBHE and DSIHE, respectively. RMSHE performs the mean-based histogram decomposition recursively and then equalizes the resulting sub-histograms individually. RSIHE acts similarly to RMSHE except that the medians are used for successive histogram decomposition.

The previous methods in the literature resolve the mean-shift problem to some extent, but tend to over-enhance or amplify background noises, thereby producing unnatural images with non-existing artifacts.

III. HISTOGRAM EQUALIZATION TECHNIQUES

There are numerous methods by which Histogram of an image can be equalized. Depending upon the area of Application, we can choose the different histogram equalization techniques. Global enhancement: The global mean and variance are measured over an entire image

Local enhancement: The local mean and variance are used as the basis for making changes

Procedures to Implement Algorithms:

1. Read the image pixel by pixel.

2. Counts the occurrence of each pixel value in the image (256 value).

3. Compute the cumulative number of pixels.

4. Multiply each un-scaled value with the scaling factor G-1/MxN to obtain the new scaled value.

where G is the maximum grey level ,

M is the number of image rows,

N is the number of image columns.

5. Assign a nearest available brightness values to the new scaled value.

We will see the following different types of Histogram Equalization methods in detail:

3.1 BBHE (Brightness Preserving Bi-histogram Equalization): It divide the image into two sub images on the basis of mean gray level. After separation these two sub images are equalized independently by using histogram equalization & the resultant image which contains the mean brightness between input mean & middle gray level but its drawback is that it cannot preserve the natural appearance of the image 7

3.2 RMSHE (Recursive mean separate Histogram Equalization): It decomposes the image recursively for generating 2r sub-image. Each sub images is independently enhanced by using HE method 7 As value of r is large it produces the output image exactly the copy of the input image and there is no enhancement at all. It is good brightness preservation technique but suffer from problem is that it decomposed the sub histogram is the power of two.

3.3. DSIHE (Dualistic sub-image histogram Equalization): It divides the image into sub images on the basis of median value. DSIHE is a term of preserving an image’s brightness and entropy. It does not present a significant change in the brightness of the input image, especially for the large area of the image with the same gray-levels but preserve the original image luminance so used in video systems but some noise may be present in output enhanced image.

3.4 MMBEBHE (Minimum mean brightness error bi-histogram equalization): It divides the image into sub images on the basis of threshold level & equalized by histogram equalization to produce output image. It preserves the mean brightness of the image & suitable for real time applications. It is superior brightness preserving method & has improved PSNR over BBHE, DSIHE, and RMSHE.

3.5. HE (Histogram Equalization): It is also called as Adaptive Histogram Equalization (AHE).It makes an adaptive selection of channels and thresholds based on the analysis of input image. It also reduces the processing time and noise. The contrast equalized image is generated by transforming the pixels’ gray levels in each input interval to the appropriate output gray-level interval according to the dominant Gaussian component and the cumulative distribution function of the input interval 3 It cannot enhance the local details of the image. Its Drawback is over enhancement of image which results in unnatural image.

Algorithm:

1. Read the Input Image

2. Calculate the Cumulative Frequency Distributive Function (CFD)

3. Compare the CFD with the Equalized Histogram

4. Find the intensity of each with the transformed Image

5. Design the Mapping with new Intensity value

3.6 AWMSHE (Automatic Weighting Mean separated Histogram Equalization): Used for gray scale images. In this method an input image is separated into several sub images. It can be determined on the basis of local and global histogram. It involves the stages are as follows

(i) Automatic histogram separation: Separate the input image on the basis of weighted mean function and automatic determine the recursion level

(ii)Piecewise Transform function: By equalizing sub histograms we achieve contrast enhancement. Drawback is that it cannot be applied to consumer electronic products that produce color images.

3.7. DHE (Dynamic Histogram Equalization): It divides the image histogram based on local minima and a specific gray level is assign before equalization. It can be done on the basis of their dynamic range in input image and cumulative distribution (CDF) on histogram values. It cannot produce any side effects but cannot preserve the mean brightness of the image. It can be used for gray scale & color images, maintain the input brightness which overcomes the drawback of previous techniques but suffers from brightness preservation.

3.8. Description of cumulative histogram equalization

In this section the general approach for cumulative histogram equalization is described.

Here are the steps for implementing this algorithm.

1. Create the histogram for the image.

2. Calculate the cumulative distribution function histogram.

3. Calculate the new values through the general histogram equalization formula.

4. Assign new values for each gray value in the image.

Figure 3. Flow Diagram

4. EXPERIMENTAL RESULTS AND DISCUSSION

Practical results of the techniques explained previously applied to popular images in image processing can be found in this chapter, divided by grayscale and color images. The histograms can also be found here. All the images are obtained with MATLAB.

4.1. Brightness Preserving Bi-Histogram Equalization

4.3 Dualistic sub-image histogram Equalization

4.2. Recursive mean separate Histogram Equalization

4.4. Recursive Separated sub-image histogram Equalization

V. CONCLUSION

In this paper we have analyzed different techniques of histogram equalization for Image Contrast and Brightness preserving Enhancement. Each of the techniques have advantage and as well as disadvantages. Depending on the application of Image processing the technique can be selected for the best Image Enhancement. The Implementation and the results were verified under MATLAB -2014 R. Also different application of images was illustrated to obtain the best results.

HE works on the four main elements of images: saturation, contrast, sharpness and brightness. We focus on these four parameters and thus, enhance the quality of images. We obtain the desired contrast levels, along with preservation of brightness and not only this, the natural look of the input image is maintained. Future applications include photos obtained from satellite communications – since we obtain images from satellite that are distorted due to space interference and dispersion losses. Other application fields are Medical field- X-Rays, Meteor descriptions.

Finally, as conclusions, we can prove that Histogram equalization algorithm is the simplest of all, it has a wide variability of grey levels and it is not suitable for color images.

Future Enhancement

We all are in midst of revolution ignited by fast development in computer technology and imaging. Against common belief, computers are not able to match humans in calculation related to image processing and analysis. But with increasing sophistication and power of the modern computing, computation will go beyond conventional, Von Neumann sequential architecture and would contemplate the optical execution too. Parallel and distributed computing paradigms are anticipated to improve responses for the image processing results.

VI. BIBILOGRAPHY

1. Gonzalez, R., Woods, R.: Digital Image Processing, 2nd edn. Prentice Hall, New Jersey (2002)

2. Kim, Y.: Contrast enhancement using brightness preserving bi-histogram equalization. IEEE Trans. on Consumer Electronics 43(1), 1–8 (1997)

3. Wan, Y., Chen, Q., Zhang, B.: Image enhancement based on equal area dualistic sub-image histogram equalization method. IEEE Trans. on Consumer Electronics 45(1), 68–75 (1999).

4. Chen, S., Ramli, A.R.: Contrast enhancement using recursive mean-separate histogram equalization for scalable brightness preservation. IEEE Trans. on Consumer Electronics 49(4), 1301–1309 (2003)

5. Sim, K.S., Tso, C.P., Tan, Y.: Recursive sub-image histogram equalization applied to gray-scale images. Pattern Recognition Letters 28, 1209–1221 (2007)

6. Wang, C., Ye, Z.: Brightness preserving histogram equalization with maximum entropy: A variational perspective. IEEE Trans. on Consumer Electronics 51(4), 1326–1334 (2005).

7. Haidi Ibrahim, Member, Nicholas Sia Pik Kong,” Brightness Preserving Dynamic Histogram Equalization for Image Contrast Enhancement”, IEEE Transactions on Consumer Electronics, Vol. 53, No. 4, November 2007