Brightness Preserving Weighted Dynamic Range ...

Brightness Preserving Weighted Dynamic Range Histogram Equalization for Image Contrast Enhancement Thien Huynh-The

*Thuong Le-Tien

University of Technical Education Ho Chi Minh City Ho Chi Minh City, Vietnam Email: [email protected]

*Ho Chi Minh City University of Technology Ho Chi Minh City, Vietnam Email: [email protected]

Abstract—In this paper, an effective method Brightness Preserving Weighted Dynamic Range Histogram Equalization (BPWDRHE) is proposed. Although, the Histogram Equalization (HE) is an universal method, it is not suitable for consumer electronic products because this method cannot preserve the overall brightness and the output image has unnatural looking and more visual artifacts. An extending of approach based on the Brightness Preserving Bi-Histogram Equalization method, the BPWDRHE used the weighted within-class variance as the new algorithm in separating an original histogram. Comparing with other methods using the average or the median of gray-levels, the proposed method determined a separating point based on computing the variance to minimize the total squared error of each sub-histogram corresponding to the brightness shift with HE independently. As a result, the output images obtain the comfortable visualization with preserving the overall brightness. The experimental results are presented and compared with the other brightness preserving methods. Keywords - Contrast Enhancement; Histogram Equalization; Weighted Dynamic Range; Brightness Preserving Contrast Enhancement; Within-class Variance.

I.

INTRODUCTION

Enhancing contrast of image by using Histogram Equalization (HE) is the standard technique to improve the visual image by stretching the narrow input image histogram [1]. However, it is not the appropriate method for consumer electronics, such as TV, because it changes the brightness of original image strongly and degrades the image quality in visualization. Various methods have been proposed to limit the level of enhancement based on modifying the input histogram. Brightness Preserving Bi-histogram Equalization (BBHE) [2], Dualistic Sub-Image Histogram Equalization (DSIHE) [3] and Minimum Mean Brightness Error Bi-histogram Equalization (MMBEBHE) [4] divided the input histogram into two sub-histograms by a separating point. After that, each sub-histogram is equalized independently. The BBHE method used the gray-level as the mean value of image brightness to separate histogram into two parts: the first histogram is from the minimum gray level to the mean and the second is from the mean to the maximum gray level. The DSIHE method also used the similar method to enhance the image contrast, except applying the median value of gray-level instead of the mean intensity. It is claimed that DSIHE is better than BBHE in both preserving the image brightness and conserving the

information content. The simple method to find the separating point is that testing all possible gray values form 0 to (L-1) of histogram by calculating the difference between the mean brightness of input and the mean brightness of output. After that, the separating point is chosen by enumerating as the value achieves the minimum difference in an overall brightness. Although the above methods are better than HE in keeping the brightness of image, the visualization of enhanced image is degraded seriously. Based on BBHE, Recursive Mean Separate Histogram Equalization (RMSHE) [5] and Recursive Sub-Image Histogram Equalization (RSIHE) [6] divided an original histogram into 2n sub-histograms, where n is positive integer value. RMSHE split the histogram into two parts with the average of input brightness before separating one more time on each sub-histogram. So there are 2n sub-histograms with n separated times. Unlike the RMSHE method, RSIHE divided the histogram based on the median value, rather than mean value. However, when n is too large, the output image looks like the copy of input image, i.e. there is no any enhancement here. In [7], Brightness Preserving Dynamic Histogram Equalization (BPDHE) divided a histogram into an arbitrary number of sub-histograms based on different separating points. This method used the local minima of the histogram to determine the separating points and the dynamic ranges. Based on the total number of pixels contained in each sub-histogram, the new partitions are obtained from the above dynamic ranges. After equalizing histogram to each partition independently, the brightness of image would be normalized with the original brightness to ensure that the mean of output intensity is close to the mean of input intensity. The authors in [8] proposed a contrast enhancement method using Dynamic Range Separate Histogram Equalization (DRSHE) to preserve naturalness of image and improve the overall contrast. Weighted Average of Absolute color Difference (WAAD) used in DRSHE method produces the output image having more a uniform histogram distribution. The dynamic ranges could be controlled by the adaptive scale factors to preserve the brightness. However, detecting the start and stop positions of these dynamic range is the difficult work, so this algorithm cannot be suitable for various histogram types. In [9], the authors proposed the Weighted Threshold Histogram Equalization (WTHE). This method modified a probability distribution function of an image histogram, that

is, each original probability density value could be replaced by a new value based on probability density function (pdf) threshold value. Nevertheless, the disadvantage of this method is that determining threshold value through a scale parameter for the good visualization with no any conditions to ensure the sum of probability density value conserved. To solve this problem, Recursively Separated and Weighted Histogram Equalization (RSWHE) [10] normalized the modified pdf. Before that, each sub-histogram is smoothed by changing the corresponding original pdf. Brightness Preserving Weight Clustering Histogram Equalization (BPWCHE) [11] assigned each non-zero bin of the input histogram for the clusters and computed its weights. After using three criteria to merge pairs of neighbor clusters, the sub-histograms are then equalized independently. The authors in [12] proposed the Global Contrast Enhancement Histogram Modification Algorithm by adjusting linear operations of the input histogram and utilizing the Back & White stretching to obtain the visually pleasing, artifact free and natural looking images. Recently, the authors in [13] proposed Adaptive Gamma Correction with Weighting Distribution (AGCWD) method to enhancement the image contrast. This method improved the brightness of dimmed image via the gamma correction and probability density function of luminance pixels. The enhanced image obtained the high contrast, however the overall brightness could be not preserved. In this paper, the Brightness Preserving Weighted Dynamic Range Histogram Equalization (BPWDRHE) is proposed as an efficient contrast enhancement method. The authors separated the input image histogram based on the Otsu method [1] for determining the separating points. The purpose of this separation method is minimizing of the each sub-histogram error corresponding to its mean brightness with histogram equalization independently. To be suitable to various histogram types, the dynamic range can be resized by scale factor. After that, the HE-based histogram is smoothed and normalized for both getting the comfortable visualization and preserving the overall brightness. This paper is organized as follow. Section II, BPWDRHE is described in detail. Then, the experimental results and discussions conclusion are given in section III. Finally, the section IV presents the conclusion of this work.

Frequency

t1

0 DR1

Fig. 1.

t2 DR2

t3 DR3

255 Gray level DR4

The dynamic range separation using Otsu method (n=2).

sub-histogram and it is corresponding to its mean brightness. The threshold used in histogram dividing is determined as the minimum-variance gray-level. In our application, the threshold can be seen as the separating point and computed through the weighted sum of variance of the two classes σω2 : σω2 (t) = ω1 (t)σ12 (t) + ω2 (t)σ22 (t)

(1)

where the weights ω1 and ω2 are the probabilities of two classes separated by a threshold t. σ12 and σ22 are the variances of these classes. It can be seen that the histogram will be separated into 2n parts with n times in separation. However, actually when n is too large, the enhancement influence on the output image is very slight. In this paper, four sub-histograms are generated with two times in separating. Let denote t1 , t2 , t3 as the gray-levels corresponding to the separating points. There are four sub-histogram ranges here, denoted as follow: [0, t1 ], [t1 + 1, t2 ], [t2 + 1, t3 ], [t3 + 1, L − 1]. Fig 1 shows the result of separation process based on Otsu method into four dynamic ranges, called DR1, DR2, DR3, DR4 with the lengths of them (t1 + 1), (t2 − t1 ), (t3 − t2 ), (L − 1 − t3 ), respectively. The total length of these sub-histograms is still L with L = 28 gray-levels. B. Adaptive scale factor to resize the range of sub-histogram

II. BRIGHTNESS PRESERVING WEIGHTED DYNAMIC RANGE HISTOGRAM EQUALIZATION The contrast enhancement method is proposed in this paper consists of four steps: • Step1: Define the break points and determine sub-histogram ranges. • Step2: Resize the sub-histograms by adaptive scale factor. • Step3: Implement HE for each resized sub-histogram. • Step4: Smoothing HE histogram and preserving the overall brightness. A. Determination of break points and separation In this step, the authors proposed the algorithm to divide the image histogram into sub-histograms based on the Otsu method [1]. This separation scheme preserves the overall brightness and natural looking of an image thanks to minimizing the brightness change with HE to each sub-histogram independently. The minimization of the within-class variance is as similar as the minimization of the total squared error of each

Applying the HE for these dynamic sub-histograms do not assure a good enhancement because a sub-histograms with small ranges are not enhanced significantly. So the small-range sub-histograms could be resized by the controllable scale factor and the fixed range to ensure that the sum of resized ranges has been conserved. The length of fixed range, called FR, depends on the number of sub-histograms that are generated in the first step: F R = 2Ln = 64 with n = 2 in this paper. The lengths of resized dynamic ranges, denoted RDR, of new sub-histograms are defined as [8] RDRi = F R + α (DRi − F R)

(2)

Where α is a scale factor that has the value between 0 and 1. It is noted that proposed separation in previous step is invalid when decreasing to zero. The example of original DR and new RDR after applying scale factor are shown in Fig . 2. Let the range of the new sub-histogram is [0, RDRi − 1] for the first one, and [mini , maxi ] for ith one (with i > 1). Calculating

DR1

DR2

FR RDR1

RDR2

DR3

Finally, to minimize the difference between the mean brightness of the output image and the original image, the modified histogram is normalized by below equation [7]:

DR4

FR

FR

RDR3

Fig. 2.

more similar to uniform histogram when λ increases. When holding the uniform parameter at constant value, the overall contrast of image is reduced when γ increases.

FR

fn (x) =

RDR4

Resize the dynamic range by scale factor α = 0.85 for k = 4

the range of ith sub-histogram through the below equations: mini =

i−1 X

RDRi

(3)

k=1

maxi =

i X

RDRi − 1

(4)

k=1

C. Equalize each new sub-histogram independently With the same concept of BBHE, the next step in BPWDRHE is applying the HE for each sub-histogram independently. With the gray-level k belongs to ith new sub-histogram (k ∈ [mini , maxi ]), the mapping function is given as:  x P  nk  (i = 1)  (RDRi − 1) N1 ; k=0 fhe (x) = (5) x P nk    (mini − 1) + RDRi Ni ; (i > 1) k=mini

Where nk is the number of pixels with gray-level k, and Ni is the total pixels contained in ith sub-histogram (such as, N1 denotes for the first sub-histogram). D. Smoothing HE and normalize the image brightness

The weakness of HE-based methods is that the HE histogram distribution is very scattered, that is, the distance between two non-zero pixel bins is large. It can be explained that there are a few non-zero bins distributed on the huge range of the histogram. Because of the over-enhancement since this behavior, the output image is unnatural and easily gets visual artifacts. To deal this problem, the HE histogram can be altered so that the modified histogram is closer to a uniform distributed histogram u. Using the algorithm for histogram smoothing is suggested in [12], the mapping function is defined as: fhe + λu fs (x) = (1 + λ) I + 2γDT D Where λ is the uniform parameter and γ is parameter and the difference matrix D with 255 × 256 is bi-diagonal " −1 1 0 .. 0 0 : : : .. : : D= 0 0 0 .. 0 −1

0 : 1

#

III.

RESULTS AND DISCUSSIONS

In our simulation, the authors implemented BPWDRHE and eight other methods, which are Global HE [1], BBHE [2], DSIHE [3], MMBEBHE [4], WTHE [9], BPDHE [7], RSWHE [10] and AGCWD [13] on various images to demonstrate the performance of proposed method. The tests of significant of the quantitative measures are performed on 40 gray-images [14] and 10 color-images [15] of Kodak database set. For the proposed method, the parameters and factors have been set as follow, k = 4 for separation, α = 0.85 for resizing sub-histogram, λ = 1 and γ = 10 for smoothing HE. Assessment of image enhancement is not easy task. Although it is desirable to have an objective assessment approach to compare contrast enhancement techniques, unfortunately there is not any accepted objective criterion in the literature to give meaningful results for every image. However, it is usually desired to have some quantitative measures and subjective assessments. In this research,the authors use Absolute Mean Brightness Error (AMBE) [5], Discrete Entropy (DE) [12] and Measure of Enhancement (EME) [16] as the quantitative measures. For the color images, the contrast enhancement is quantified by applying these measures on its luminance channel only. For the input image X and output Y image, the AMBE is defined as AM BE = |E(X) − E(Y )|

(9)

where E(X) and E(Y) are the mean brightness of X and Y, respectively. The lower value of AMBE, the better is the preservation of original image brightness. The DE of an image is defined as: DE(X) = −

255 X

p (xi ) log p (xi )

(10)

i=0

where p (xi ) is the probability of pixel intensity xi , which is estimated from the normalized histogram. A higher value of DE indicate that the image has richer details. Let dividing the image into k1 k2 non-overlapping sub-blocks Xi,j of size w1 × w2 , in this paper, its size is 8 × 8. EME is computed as

(7)

In ( 6), when λ and γ are zero, the smoothed histogram is equal to the HE histogram, that is, there is no any smoothing effect. In the case γ is zero, the smoothed histogram becomes

(8)

Where B and Bs are the mean brightness of original and modified image after using smoothing algorithm, respectively. The output image is not only preserved the overall brightness but also obtained the comfortable visualization by applying the mapping function as giving in (8).

(6) the smoothing size of length

B fs (x) Bs

EM E(X) =

k1 X k2 max (Xi,j ) 1 X 20 ln k1 k2 i=1 j=1 min (Xi,j )

(11)

where max (Xi,j ) and min (Xi,j ) are the maximum and minimum gray levels, respectively, in block Xi,j . High contrast

sub-blocks give a high EME value, whereas for homogeneous sub-blocks, the EME value should be close to zero. It is worth to note that the EME is highly sensitive to noise. However, for the contrast enhancement application, this value is expected that EM E(Y ) > EM E(X).

(a) Original

(b) Global HE

(c) BBHE

(d) DSIHE

(e) MMBEBHE

(f) WTHE

(g) BPDHE

(h) RSWHE

(i) AGCWD

(j) BPWDRHE

A. Subjective Assessment 1) Gray Image: Some example contrast enhancement results for gray-scale images are shown in Fig. 3 - Fig. 8. With each example image, the cropped version is also represented to analysis in detail. For the T oy image shown in Fig. 3, due to the overcontrast enhancement occurred unusually in Global HE, it is hardly to identify the plastic balloons. The BBHE, DSIHE, MMBEBHE and WTHE method provide the similar-contrast images, but there are the degradations on the background. The photometric difference between some regions of the background is significant and unacceptable because the viewer can confuse the brighter regions with the balloon shadows in these images. This occurrence is severe in the output image of WTHE method. Therefore, the output images of these methods have many artifacts and look unnatural. Although getting the better visual quality result, the enhancement of AGCWD is not powerful enough to distinguish the detail on the balloon in Fig. 4. The weakness of this method is no ensuring the overall brightness. Only BPDHE, RSWHE and BPWDRHE do not distort the original image; however, the brightness of RSWHE is darker in general. For the Aircraf t image shown in Fig. 5 and their cropped in Fig. 6, it can be seen that the Global HE, BBHE, MMBEBHE, WTHE method enhanced the overall brightness excessively. So the texture on aircraft body cannot be observed. Although the DSIHE and BPDHE method perform better than the above methods, they also enhanced the unnecessary details of background unexpectedly. It is difficult to know the contrast enhancement on RSWHE image because of slight effect. For the AGCWD, the enhanced image looks brighter with no brightness preservation and so many bright-pixel details have been removed, such as, the take-off trail. The output image of BPWDRHE method is enhanced in moderate level enough to observe the parts of aircraft and take-off trail clearly while overall brightness hardly ever change. For the P entagon image shown in Fig. 7 and Fig. 8, the Global HE, BBHE, MMBEBHE and WTHE method improved the contrast of image in the 2-side extension way, that is, the bright pixels to be event brighter and the dark pixels to be even darker. However, brightness enhancement only occurred with bright pixel in DSIHE and AGCWD. Therefore, the AMBE values of two above methods are larger than the AMBE values of others. Only three methods BPDHE, RSWHE and BPWDRHE still maintain the general brightness. However, some detail of enhanced image of the BPDHE method is dimmed unexpectedly with medium brightness pixels while enhancement of the RSWHE method is not strong enough to recognize the change in brightness. It can be considered in detailed through results in Fig . 8 which represents the smallcropped area from P entagon. Except the fan-shaped object in the square detected by the very dim thin boundary in Fig. 8(b)−(f) images, the BPDHE image also get the same problem

Fig. 3.

The test image T oy

(a) Original

(b) Global HE

(c) BBHE

(d) DSIHE

(e) MMBEBHE

(f) WTHE

(g) BPDHE

(h) RSWHE

(i) AGCWD

(j) BPWDRHE

Fig. 4.

The small area is cropped from T oy

with medium gray-level. In this method, the brightness of pixels of the object is decreased to the background brightness. Only with RSWHE and BPWDRHE, the object can be known easily due to the high contrast. 2) Color Image: Contrast enhancement can be easily extended to the color images. The most obvious way to extend the gray-scale contrast enhancement to the color images is applying the methods to the luminance component. The simulation is implemented on 10 color images from Kodak For the Hats image shown in Fig. 9 and the cropped version in Fig. 10, the result of the Global HE, BBHE, DSIHE and WTHE method shown that the hues of output image are changed seriously. These methods darkened some areas of wood plank and the hat shadows and brightened some regions of the cloud and the top of yellow hat. Therefore, many details in these regions are lost. The degradations of MMBEBHE, WTHE and BPDHE are not as severe as the result of above methods. The AGCWD method produced the brighter image both in overall and detail and so the bright-pixel detail on the

(a) Original

(b) Global HE

(c) BBHE

(d) DSIHE

(e) MMBEBHE

(f) WTHE

(g) BPDHE

(h) RSWHE

(i) AGCWD

(j) BPWDRHE

Fig. 5.

The test image Aircraf t

(a) Original

(b) Global HE

(c) BBHE

(d) DSIHE

(a) Original

(b) Global HE

(c) BBHE

(d) DSIHE

(e) MMBEBHE

(f) WTHE

(g) BPDHE

(h) RSWHE

(i) AGCWD

(j) BPWDRHE

(e) MMBEBHE

Fig. 11. (f) WTHE

Fig. 6.

(g) BPDHE

(h) RSWHE

(i) AGCWD

The small area is cropped from Aircraf t

(a) Original

(b) Global HE

(c) BBHE

(d) DSIHE

(a) Original

(b) Global HE

(c) BBHE

(d) DSIHE

(e) MMBEBHE

(f) WTHE

(g) BPDHE

(h) RSWHE

(i) AGCWD

(j) BPWDRHE

(e) MMBEBHE

Fig. 12. (f) WTHE

Fig. 7.

(g) BPDHE

(h) RSWHE

(i) AGCWD

The test image P entagon

top of the yellow hat is not clear. For the proposed method and RSWHE, the details enhanced expectantly with no hueddistortion, for instance, the texture of wood plank looks clearly.

(b) Global HE

(c) BBHE

(d) DSIHE

(e) MMBEBHE

(f) WTHE

(g) BPDHE

(h) RSWHE

(i) AGCWD

(j) BPWDRHE

The small area is cropped from P entagon

(a) Original

(b) Global HE

(c) BBHE

(d) DSIHE

(e) MMBEBHE

(f) WTHE

(g) BPDHE

(h) RSWHE

(i) AGCWD

(j) BPWDRHE

Fig. 9.

The test image Hats

(a) Original

(b) Global HE

(c) BBHE

(d) DSIHE

(e) MMBEBHE

(f) WTHE

(g) BPDHE

(h) RSWHE

(i) AGCWD

(j) BPWDRHE

Fig. 10.

The small area is cropped from Hats

The small area is cropped from W all

(j) BPWDRHE

(a) Original

Fig. 8.

The test image W all

(j) BPWDRHE

Finally, the W all image shown in Fig. 11 and the smallcropped areas from output images shown in Fig. 12. The results of Global HE, BBHE, DSIHE, MMBEBHE and WTHE have the similar contrast enhancement with cold overall hue while BPDHE has the better visual result. The characteristic of AGCWD is that it usually produces the output image looks brighter than the original, so there are some bright-pixel detail have low-contrast will be lost or realized in difficulty. In Fig. 15, the object behind the glass window in Global HE, BBHE, DSIHE and WTHE are brightened so much that it is hardly to be observed. Except RSWHE and BPWDRHE, the remains of method get the same drawback in slight level. It can be seen that the enhancement of RDWHE is very slight through the chroma of the door. The proposed method not only improves the image contrast but also preserves the overall brightness while the details in the image are also clearer. B. Objective Assessment Computed quantitative measures AMBE, DE and EME are listed in TABLE. I, II and III, respectively. Comparison of AMBE values shows that the proposed method outperforms the other methods used in simulation, except BPDHE. Two methods BPDHE and BPWDRHE utilized brightness normalization to obtain the good brightness preservation. For the AGCWD method, it can be seen that the AMBE value is largest. This method only focuses on improving the brightness of dimmed images while brightness preserving is ignored. In additions, some enhanced images are unnatural look with the small AMBE values because the bright pixels to be even brighter and the dark pixel to be even darker. Through comparison DE values, the proposed method performed similar to the RSWHE method. Both of them are better than the other methods with high discrete entropy. Many original histogram bins grouped

TABLE I.

ABSOLUTE MEAN BRIGHTNESS ERROR - AMBE & AVERAGE OF AMBE S - AAMBE

METHOD

Toy

Aircraft

AMBE Pentagon

Hats

Wall

AAMBE (50 images)

Global HE[1] BBHE[2] DSIHE[3] MMBEBHE[4] WTHE[9] BPDHE[7] RSWHE[10] AGCWD[13] BPWDRHE

29.38 5.48 1.27 3.16 27.13 0.15 7.70 26.14 0.08

47.82 1.46 15.42 6.51 55.61 0.05 3.48 58.45 0.01

11.04 6.89 28.65 1.37 12.36 0.02 0.80 35.46 0.09

7.81 23.77 0.03 1.25 22.25 0.02 0.76 33.52 0.02

10.19 17.19 10.19 1.00 23.62 0.007 0.45 38.33 0.07

30.49 12.29 11.98 2.99 29.62 0.26 2.19 36.75 0.05

TABLE II.

TABLE III.

MEASURE OF ENHANCEMENT - EME & AVERAGE OF EME S - AEME

METHOD

Toy

Aircraft

EME Pentagon

Hats

Wall

AEME (50 images)

Original Global HE[1] BBHE[2] DSIHE[3] MMBEBHE[4] WTHE[9] BPDHE[7] RSWHE[10] AGCWD[13] BPWDRHE

4.81 13.94 10.99 9.40 11.06 10.34 7.18 6.60 4.61 6.29

3.14 25.64 18.99 8.09 8.72 15.39 5.68 3.37 1.98 4.85

8.59 40.57 36.44 21.62 23.96 32.5 14.71 10.16 8.56 12.28

5.42 15.64 15.85 15.91 14.28 12.89 12.76 7.03 5.55 7.62

14.65 39.87 42.56 39.86 38.07 34.92 19.55 16.65 14.44 20.87

14.34 28.86 26.04 23.88 24.27 22.44 21.09 15.12 14.19 15.62

DISRETE ENTROPY - DE & AVERAGE OF DE S DENOTED ADE

METHOD

Toy

Aircraft

DE Pentagon

Original Global HE[1] BBHE[2] DSIHE[3] MMBEBHE[4] WTHE[9] BPDHE[7] RSWHE[10] AGCWD[13] BPWDRHE

4.19 3.48 4.09 4.03 4.07 3.35 4.07 4.19 3.61 4.15

2.78 2.60 2.72 2.74 2.71 2.74 2.75 2.78 2.78 2.77

4.66 4.01 4.61 4.57 4.59 4.64 4.47 4.66 4.62 4.64

Hats

Wall

ADE (50 images)

4.79 4.66 4.1 4.67 4.65 4.68 4.60 4.79 4.74 4.77

4.83 4.75 4.11 4.75 4.74 4.70 4.58 4.83 4.79 4.81

4.52 3.84 4.42 4.40 4.41 4.27 4.32 4.51 4.30 4.48

into one bin after enhancement can be the reason wherever DE value decrease for over-enhancement images. It is not difficult to know that the details of these images are reduced clearly. The comparison of EME values in Table. III shows that the Global HE, BBHE, DSIHE, MMBEBHE and WTHE method usually get higher EME values than remain methods. Since EME measures a form of contrast, it is no surprise that these methods give the highest values even though they hardly ever produced the most visually pleasing images. For the AGCWD method, increasing the brightness in overall can be the cause of depressing the local contrast, corresponding to EME value.

IV.

CONCLUSION

In this work, the authors proposed and experimented the new contrast enhancement method for both gray-scale and color image, called BPWDRHE. The BPWDRHE method not only enhanced the contrast but also preserved the overall brightness to generate the natural looking images without visual artifacts. At first, the BPWDRHE method used the sum of weighted within-class variance for dividing histogram to minimize equalization-based brightness shift. Then, the sub-histograms are resized with the scale factor. After that, histogram equalization is applied to each partition independently. Finally, the histogram is smoothed and normalized to obtain the comfortable visualization. The experiment results demonstrated that the BPWDHE method is better than the other methods in many quantitative measures, such as the overall brightness, the discrete entropy and the local contrast.

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