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Automatic Contrast Enhancement by Transfer Function Modification
Automatic Contrast Enhancement by Transfer Function Modification
ETRI Journal. 2017. Feb, 39(1): 76-86
Copyright © 2017, Electronics and Telecommunications Research Institute (ETRI)
This is an Open Access article distributed under the term of Korea Open Government License (KOGL) Type 4: Source Indiction + Commercial Use Prohibition + Change Prohibition (http://www.kogl.or.kr/news/dataFileDown.do?dataIdx=71&dataFileIdx=2).
  • Received : October 02, 2015
  • Accepted : November 03, 2016
  • Published : February 01, 2017
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About the Authors
Tae Wuk, Bae
Sang Ho, Ahn
Yucel, Altunbasak

Abstract
In this study, we propose an automatic contrast enhancement method based on transfer function modification (TFM) by histogram equalization. Previous histogram-based global contrast enhancement techniques employ histogram modification, whereas we propose a direct TFM technique that considers the mean brightness of an image during contrast enhancement. The mean point shifting method using a transfer function is proposed to preserve the mean brightness of an image. In addition, the linearization of transfer function technique, which has a histogram flattening effect, is designed to reduce visual artifacts. An attenuation factor is automatically determined using the maximum value of the probability density function in an image to control its rate of contrast. A new quantitative measurement method called sparsity of a histogram is proposed to obtain a better objective comparison relative to previous global contrast enhancement methods. According to our experimental results, we demonstrated the performance of our proposed method based on generalized measures and the newly proposed measurement.
Keywords
I. Introduction
Histogram equalization (HE) is one of the most popular contrast enhancement techniques owing to its simplicity and effectiveness. HE uses the cumulative distribution function (CDF) of a given image to convert it into an enhanced image [1] , [2] . The entire pixel range enhanced by HE in the image follows a uniform distribution. Thus, the mean brightness of an HE output image approaches a middle gray level because HE makes the pixel density in the image uniform. In general, HE changes the original brightness of an input image and causes unnecessary visual flickers in digital video applications [3] , [4] . For example, a flicker may occur when a video is switched from a normal (general) frame to a frame with a dark subtitle, including letters. According to [4] , HE causes flickering, which is one of the most annoying problems in video enhancement. Bi-histogram equalization (BHE) was proposed to overcome this problem [3] . In BHE, the histogram of an input image is divided into two groups based on its mean brightness and the two histograms are then equalized independently. A similar method called equal area dualistic sub-image histogram equalization (DSIHE) was also proposed, where two separate histograms are created using the median brightness instead of the mean brightness [5] . However, both BHE and DSIHE may introduce some visual artifacts into darker or brighter images because the histogram is shifted to one side in order to ensure mean preservation in the image.
Minimum mean brightness error bi-histogram equalization (MMBEBHE) was proposed to further minimize the mean brightness error [6] . MMBEBHE conducts separation based on the threshold level, which yields the minimum difference between the mean input and mean output in the image. This threshold level is essentially chosen by enumeration. Another histogram-based contrast enhancement method is the successive mean quantization transform (SMQT), which is capable of conducting both nonlinear and shape-preserving stretch in the image histogram [7] [9] . The SMQT-based method obtains similar images to HE and the average of the resulting images is close to 128 gray-levels, and therefore, some visual artifacts may occur. Furthermore, another approach was proposed called recursive mean-separate histogram equalization [10] , which iteratively conducts BHE, where the mean of each sub-histogram is calculated and the sub-histograms are further divided into two parts based on their mean values. This process is repeated and the output mean converges to the input mean as the number of iterations increases. When the iteration number is infinite, the output histogram is exactly the same as the input histogram. Similar to other methods, the proposed multi-histogram equalization (MHE) [11] approach uses sub-histograms. MHE decomposes the input image into several sub-images after minimizing the within-histogram class variance, which is obtained using Otsu’s threshold selection method [12] .
The aforementioned methods focus mainly on mean preservation in an image regardless of the visual artifacts caused by large histogram bins in special gray levels, such as the background.
The application of histogram modification methods before equalization has been studied to overcome the issue of visual artifacts with various methods based on HE. Thus, a global HE-based enhancement method using bin underflow and bin overflow (BUBO) minimizes the gradient of the transfer function (TF) [13] . In this case, HE is conducted using a histogram clipped at the upper and lower levels. Weighted thresholded histogram equalization is conducted by clamping the original histogram at the upper and lower thresholds, and transforming all of the values between the upper and lower thresholds using a normalized power law function [14] . The gain-controllable clipped HE (GC-CHE) adaptively controls the clipped histogram using global and local gains [15] . The clipping rate of the histogram is determined based on the mean brightness, which further determines the clipping threshold. In addition, a histogram modification framework method was proposed for a bi-criteria optimization problem [4] . This method has a constraint where the modified histogram should be as close as possible to both the input histogram and a uniformly distributed histogram simultaneously. Zhang and co-workers proposed perceptual contrast enhancement with dynamic range adjustment by histogram modification [16] . This method applies a global histogram modification of a modified clipped HE after applying a modified difference of Gaussian to a local region of an image. These histogram modification methods provide enhanced images with fewer artifacts, but they do not consider mean brightness preservation in the resulting images.
Shanmugavadivu and Balasubramanian proposed the use of thresholded and optimized histogram equalization to consider brightness preservation and contrast enhancement simultaneously [17] . To classify an object and background region in an image, a histogram of the image is divided using Otsu’s method and the divided sub-histograms are then clamped independently. Four optimal parameters for histogram clamping transformation are then obtained by particle swarm optimization [18] . This method features better mean brightness preservation and contrast enhancement; however, it is not appropriate for real-time video image processing due to the iterative computations required to obtain the optimal parameters.
Recently, Huang and Yeh presented a novel HE method for automatic histogram separation and intensity transformation (HSIT) [19] , where the histogram is separated by a multiple thresholding procedure and calculating the optimum peak signal-to-noise ratio (PSNR). The intensity transformation module then enhances an image with brightness preservation for each generated sub-histogram. Arriaga-Garcia and others presented a new bihistogram equalization method called adaptive sigmoid function bihistogram equalization (ASFBHE) [20] , which involves splitting an image histogram into two parts that are equalized independently using adaptive sigmoid functions. In order to preserve the mean brightness of an input image, the parameter of the sigmoid function is selected to minimize the absolute mean brightness metric. This method improves the image contrast while preserving the mean intensity of an image. Instead of transforming the histogram into a uniform distribution, contrast enhancement is performed using sigmoid functions.
Previously proposed histogram-based global contrast enhancement techniques employ histogram modification to improve the image contrast. In contrast to these techniques, we propose an automatic contrast enhancement method based on direct transfer function modification (TFM) with HE and we demonstrate its validity. Thus, a mean point shifting (MPS) method based on TF is proposed to preserve the mean brightness of an image. MPS produces the same results as BHE. A linearization of transfer function (LTF) method, which has a histogram flattening effect, is also proposed and mathematically derived for this relationship, including a new approach where modifying the TF may transform the histogram. An attenuation factor is automatically determined using the maximum value of the probability density function (PDF) in an image to control its contrast rate. The sparsity of a histogram is proposed as a new quantitative measurement, and we demonstrated the performance of the proposed method based on generalized measurements as well as the newly proposed measurement type.
II. BHE
In contrast enhancement video applications, preserving the mean brightness is important in images because variation in the mean brightness causes flickering. BHE was proposed to overcome this problem [3] . In BHE, the histogram of the input image X is divided into two groups based on its mean brightness x m , and the two histograms are then equalized independently. The two parts of the BHE TF are defined as
(1) T ^ (x) L = x m ⋅ c ^ L (x),               0 and
(2) T ^ (x) U = x m +( x L−1 − x m )⋅   c ^ U (x),        x m as shown in Fig. 1 . The CDFs for sub-images X L and X U are
c ^ L (x)
and
c ^ U (x)
, respectively. The whole BHE TF
T ^ (x)
can be expressed as
T ^ (x)= T ^ (x) L   ∪   T ^ (x) U
and point “B” of
T ^ (x)
is located at the ( x m , x m ) coordinates.
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Transfer functions for HE and MPS (or BHE).
III. Proposed Contrast Enhancement Method Using TFM
We present three types of contrast enhancement methods using TFM. Figure 2 shows a flow chart illustrating the proposed contrast enhancement method, which includes MPS for mean preservation, LTF, and MPS/LTF. In the flow chart, MPS/LTF is established by a combination of MPS and LTF to preserve the mean brightness and prevent visual artifacts.
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Flow chart illustrating the proposed contrast enhancement method.
- 1. Type 1: MPS for Mean Preservation
We now introduce a mean preservation method using TFM, which yields the same result as the BHE method. Let us assume that p ( x ) and c ( x ) denote the PDF and CDF for input image X , respectively. In addition, we assume that the input image is divided into two sub-images, X L and X U , based on the mean x m , and p ( x ) can be divided into two groups, namely, p ( x ) L and p ( x ) U , based on the mean x m . In general, images can have an empty histogram bin group in the black and white gray part. x b and x w denote the first end point and the final start point of the empty histogram bin group, respectively. In addition, T HE ( x ) can be divided into two groups, T HE ( x ) L and T HE ( x ) U , based on x m , as shown in Fig. 1 . Point A is the crossing point between the input image mean x m and its TF output T HE ( xm ), and it is referred to as the “mean point” of T HE ( x ). The output of the HE TF T HE ( x ) has a uniform distribution, so the mean output of HE is always in the middle gray level, regardless of the input image’s brightness. Therefore, to reduce the mean error in the input and output, MPS of the TF is required. The MPS (or BHE) TF can be expressed as follows:
(3) T ^ (x)={ x m T HE ( x m )    T HE (x), 0≤x≤ x m , x m + x L−1 − x m x L−1 − T HE ( x m )  ( T HE (x)− T HE ( x m ) ) , x m  
- 2. Type 2: LTF
The HE method yields visual artifacts for an image with a highly non-uniform histogram (or PDF). Histogram flattening modification methods such as clipping have been studies to address this problem [12] [14] . Thus, to limit the change in alpha from one frame to the next in a video sequence, the calculated alpha can be smoothed using a recursive low-pass filter. In the present study, the flattened PDF
p ˜ (x)
is defined as
(4) p ˜ (x)=α ⋅ p(x)+β,   for   0≤x≤ x L−1  ,
where α (0 ≤ α ≤ 1) is an attenuation factor for equalizing the histogram and β is its bias value with a uniform brightness.
Figure 3(a) shows an example of an original PDF and its TF, and Fig. 3(b) shows a flattened PDF and its TF derived by (4). Assuming that the input image X is a continuous random variable, the CDF
c ˜ (x)
can be expressed as follows:
(5) c ˜ (x) = ∫ 0 x   p ˜ (τ)  dτ =  α ⋅ c(x)​  +β⋅ x,
where c ( x ) is the CDF of the input image. By substituting x = x L−1 into (5) and using
c ˜ ( x L−1 )=   c( x L−1 )=1,
β is derived as
(6) β= 1−α x L−1  .
From the equations (5) and (6), the modified CDF
c ˜ (x)
is expressed as
(7) c ˜ (x)=  α⋅c(x)​  +(1−α)   x x L−1 .
Thus, it is clear that
x L−1   ·   c ˜ (x)= T ˜ (x)
and x L−1 c ( x ) = T HE ( x ). Therefore, the TF of LTF is derived as follows:
(8) T ˜ (x)   =  α⋅ T HE (x)  +  (1−α)⋅ x =α⋅( T HE (x)−x )  +x,    0≤x≤ x L−1 .
Equation (8) shows that PDF (or histogram) flattening can be achieved by a simple modification of the TF using the attenuation factor α alone. Figure 3 shows the connection between PDF flattening and TF modification. As shown in (6), β is adjusted by α , so only α is controlled for the histogram distribution. If α = 0, then β = 1 / x L−1 from (6), which shows that the PDF is fully uniform and has a linear TF. If α = 1, then β = 0, which means that the PDF and TF are not modified. Thus, we can determine that as α approaches 0,
p ˜ (x)
becomes flatter and
T ˜ (x)
is more linearized.
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Transfer functions: (a) original and (b) flattened PDFs and their transfer function.
The black and white level stretch concept can be applied using the LTF method in (8). The generalized TF of the LTF with a stretch is given as follows:
(9) T ˜ (x)={ 0, x< x b  , α⋅{ T HE (x)− T ¯ (x) }+ T ¯ (x),   x b ≤x≤ x w , x L−1 , x> x w  ​,
where
(10) T ¯ (x)= x L−1 x w − x b ⋅(x− x b ),    x b ≤x≤ x w .
- 3. Type 3: MPS/LTF
Both MPS and LTF are required to preserve the mean brightness and prevent visual artifacts. We propose a combined method based on MPS and LTF. The TF of MPS/LTF can be expressed by
(11) T ˜ (x)={ 0, x≤ x b  , α⋅{ T ^ (x) L − T ¯ (x) L }+ T ¯ (x) L , x b    x w ,
where
  T ^ (x) U = T HE (x)⋅ y P T HE ( x m ) ,    x b Figure 4 illustrates the relationships among
T ^ (x)
,
T ¯ (x)
, and
T ˜ (x)
, as derived by (11). In the case of the attenuation factor α = 1,
T ˜ (x)= T ^ (x)
, which is equivalent to BHE TF. For α = 0,
T ˜ (x)= T ¯ (x)
, and we denote
T ¯ (x)
as a bi-linear stretching (BLS) TF for the two divided straight lines based on point B, and the resulting image will be stretched because it has two piecewise linear TFs,
T ¯ ( x ) L
and
T ¯ (x) U .
Point B represents point x m , where the averages of the input and output are equal. For α = 1, the TF becomes
T ^ (x)
(equal to MPS or BHE) in Fig. 1 , and T HE ( x ), the TF of HE, is transformed into
T ^ (x)
. In addition, the TF becomes MPS/LTF when 0 < α < 1.
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Transfer function of MPS/LTF.
- 4. Summary of Proposed Automatic Contrast Enhancement Method
Table 1 summarizes the proposed automatic contrast enhancement method. The proposed method directly modifies HE-TF, T TH , for an image, and controls its functions simply via the attenuation factor α . Figure 5(a) shows an example of the change in LTF-TF according to α . In the case where α = 0, the TF of the proposed method acts as an image-stretching function, whereas it operates as an image HE function when α = 1. Figure 5(b) shows an example of the change in MPS/LTF-TF according to α . The TF operates as BLS when α = 0, whereas it operates as BHE if α = 1.
Summary of the proposed automatic contrast enhancement method.
Proposed method Equation Parameter Function
MPS Eq. (3) None Bi-histogram equalization (BHE)
LTF Eq. (9) 0 ≤ α ≤ 1 α = 0 Stretching
α = 1 Histogram equalization (HE)
MPS/LTF Eq. (11) 0 ≤ α ≤ 1 α = 0 Bi-linear stretching (BLS)
α = 1 Bi-histogram equalization (BHE)
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Example of (a) LTF-TF and (b) change in MPS/LTF-TF according to α.
- 5. Automatic Attenuation Factor Control
The LTF and MPS/LTF algorithms include an attenuation factor α , which can control the contrast enhancement rate for an image. The contrast enhancement rate increases with α , but the possibility of visual artifacts also increases due to the increase in the gradient of TF. By contrast, visual artifacts decrease with α and the rate of contrast enhancement also decreases. Therefore, automatic selection of the attenuation factor is proposed as follows:
(12) α={ 0, p max > θ max , θ max − P max θ max − θ min ,   θ min ≤  p max  ≤   θ max , 1,       p max < θ min ,
where p max is the maximum value of the PDF (or histogram), θ max is the maximum threshold, and θ min is the minimum threshold. If p max is greater than θ max , such as in a cartoon image or a non-uniform illuminated image, then α is reduced to zero to prevent visual artifacts. When many pixels are concentrated in a few levels (the maximum amplitude of the histogram is very high) such as in a cartoon, the image is processed with less contrast enhancement ( α is close to zero). This is similar to using a bi-linear stretched TF
T ¯ (x)
. However, when p max is small, that is, the histogram is flattened such as with a natural image, then α assumes a larger value to increase the contrast enhancement rate and the value of α is limited to 1, which is equivalent to BHE TF. If the PDF is uniform over all gray levels, then p max = 1 / x L−1 . Hence, the range of the minimum threshold θ min is 1 / x L−1 θ min < 1 . To determine this feature automatically, a simple linear control rule is proposed that uses the two boundary values in the histogram. We only consider an example and the user can employ various defined nonlinear control rules. In the present study, θ max = 0.05 and θ min = 0.004 based on analyses of various test images.
In video applications, α should be calculated for each frame. Different frames may have different PDFs, so the value of α may exhibit high temporal variation. The variation in α can also causes visual disturbances such as flickering. To resolve this problem, α is derived using a recursive low-pass filter, which can be applied to a video sequence.
As a special case of the automatic MPS/LTF method, the automatic LTF method alone can also be used without the MPS method. The LTF method is simpler than the MPS/LTF method because the MPS method is avoided. The LTF method can be used in applications where preserving the mean brightness is not important, such as video surveillance systems.
IV. Experiments and Results
Traditionally, quantitative measurements of image enhancement have employed the absolute mean brightness error (AMBE) and discrete entropy H [21] . The AMBE is the absolute difference between the input and output mean brightness and it is used to measure the mean preservation. Discrete entropy H is used to measure the content of the image, where a higher value indicates a flatter histogram. This method is used mostly for relative comparisons of the histogram flatness. In addition, we present a new measure based on the quantitative sparsity of a histogram to express the absolute number of visual artifacts.
- 1. Sparsity of Histogram
Sparsity is a criterion for evaluating the performance of a global contrast enhancement method based on HE. In HE, the sparsity of the histogram bin is increased more when the slope of the TF is larger. The resulting image of a histogram has greater sparsity, so histogram modification methods such as the histogram clipping method have been proposed for flattening the original histogram. These methods are employed to reduce the sparsity. Artifacts cannot be evaluated using the sparsity itself, but it may be useful for relative evaluations of histogram transformation methods [21] . Thus, we propose a new quantitative sparsity of a histogram method. Sparsity of a histogram is a quantitative method that expresses the extent of the visual artifacts in an image. Visual artifacts are introduced during global contrast enhancement based on HE due to the high slope of the TF, which yields a sparse histogram of the output image. A set of non-zero histogram (PDF) bins, Ak is defined as
(13) A k ={  j |p( x j )>0,   0≤j where p ( xj ) is the PDF of gray level xj and the maximum element of the set elements, mk , is expressed as follows:
(14) m k = ​max​​ { A k }  for  k=0, 1,  ...  ,L−1.
The number of zero histogram bins between two adjacent non-zero histogram bins, Nk is derived as
(15) N k = { (k− m k −1)⋅I[p( x k )>0],       k=1, 2,  ...  ,L−1, 0,                                        A k =ϕ  or   m k =k−1, 
where I [∙] is the indicator function. If the [∙] condition is true, then I [∙] = 1; else, I [∙] = 0. Figure 6 shows an example of the number of zero histogram bins, where Nk = 3 indicates that there are three adjacent zero histogram bins between p ( x k−4 ) and p ( xk ).
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Example showing the number of zero histogram bins.
We define the sparsity of a histogram using (15) as follows:
(16) S= ∑ k=0 L−1 p( x k )+p( x k− N k −1 ) 2 ⋅ N k .
If the number of zero histogram bins between two adjacent non-zero histogram bins is high and the probabilities of their gray levels are elevated, then S has a high value. A higher S value means that the image is not clear and it contains visual artifacts. Therefore, the value of S can be used as a quantitative measure to express the extent of visual artifacts present in an image.
The sparsity S is obtained by multiplexing the number of zero-histogram bins and the mean of the probability of both sides, p ( x k–4 ) and p ( xk ). We can see that the following two examples have the same S value: p 1 ( xk ) = {0.01, 0, 0, … , 0, 0.99} and p 1 ( xk ) = {0.99, 0, 0, … , 0, 0.01}. If L = 256 (for 8-bit images), then S ( p 1 ) = S ( p 2 ) = 253 × (0.01 + 0.99)/2 = 126.5.
- 2. Experimental Results
Next, we present some results obtained by our proposed method, MPS/LTF, using various smoothing factors. Figure 7 shows the five original images ( U2 , F16 , Pen , Pentagon , and Arctic hare ) and their corresponding PDFs. The U2 image is an example of a dark image, and the F16 and Arctic hare images are examples of bright images. The Pen image has outlier histogram bins at special gray levels. The Pentagon image has a normal brightness level but a low contrast rate.
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Original test images and their PDFs for: (a) U2, (b) F16, (c) Pen, (d) Pentagon, and (e) Arctic hare.
Figure 8 shows the TFs according to the attenuation factor α in MPS/LTF for the U2 , F16 , and Pen images. The images obtained are shown in Figs 9 and 10 . The quantitative measurement results for these images are listed in Tables 2 4 . In the tables, H denotes the discrete entropy and S denotes the sparsity of the histogram. As shown in Fig. 9 , an image with a large number of visual artifacts, such as an image obtained by HE, has a highly sparse histogram, whereas an image with no visual artifacts has a high density histogram. Previously proposed HE-based methods lead to severe mean brightness errors and visual artifacts in a very bright image such as U2 . Thus, we can see that a very dark ( U2 ) or bright ( Arctic hare ) image should be enhanced using a lower histogram modification for contrast enhancement.
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Transfer functions of MPS/LTF for: (a) U2, (b) F16, and (c) Pen.
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Resulting images and PDFs for U2: (a) LTF α = 1.0 (HE), (b) MPS/LTF α = 1.0 (BHE), (c) MPS/LTF α = 0.5, and (d) MPS/LTF α = 0.0 (BLS).
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Examples of the images obtained for F16 and Pen: (a) LTF α = 1.0 (HE), (b) MPS/LTF α = 1.0 (BHE), (c) MPS/LTF α = 0.5, and (d) MPS/LTFα = 0.0 (BLS).
Quantitative measurement forU2(mean = 32.52,pmax= 0.051).
U2 image LTF MPS/LTF
α = 1.0 (HE) α = 0.5 α = 0.0 (LS) α = 1.0 (BHE) α = 0.5 α = 0.0 (LBS)
AMBE 0.00 98.56 49.07 0.13 16.30 8.47 0.51
H 5.64 5.38 5.57 5.61 5.24 5.53 5.61
S 0.00 6.90 3.64 0.41 2.01 1.12 0.42
Quantitative measurement forF16(mean = 178.68,pmax= 0.030).
F16 image LTF MPS/LTF
α = 1.0 (HE) α = 0.5 α = 0.0 (LS) α = 1.0 (BHE) α = 0.5 α = 0.0 (BLS)
AMBE 0.00 49.84 19.16 12.01 0.76 3.66 6.36
H 6.71 6.41 6.60 6.67 6.36 6.59 6.67
S 0.00 2.80 1.54 0.27 1.21 0.74 0.41
Quantitative measurement forPen(mean = 105.25,pmax= 0.021).
Pen image LTF MPS/LTF
α = 1.0 (HE) α = 0.5 α = 0.0 (LS) α = 1.0 (BHE) α = 0.5 α = 0.0 (LBS)
AMBE 0.00 23.40 4.02 14.93 7.20 5.31 3.33
H 6.58 6.39 6.49 6.53 6.31 6.48 6.53
S 0.00 2.33 1.21 0.11 2.15 1.16 0.20
Based on the analysis of the three test images, we can see that visual artifacts are obtained when the value of S is greater than 1. Therefore, to remove visual artifacts, we can deduce that α should have a very small value. To use the proposed automatic α selection method in the equation (12), two parameters are needed, θ max and θ min , and we determined that θ max = 0.05 and θ min = 0.004 by analyzing various test images.
The quantitative measurement results obtained for the five test images using the automatically determined smoothing factor are listed in Table 5 . We compared the proposed MPS/LTF method with BUBO, GC-CHE, HSIT, and ASFBHE which are representative histogram modification methods, as well as with the basic HE method.
Quantitative measurement results obtained for the test images using the automatically determined attenuation factor for MPS/LTF (*αis the automatic determined smoothing factor for MPS/LTF).
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Quantitative measurement results obtained for the test images using the automatically determined attenuation factor for MPS/LTF (*α is the automatic determined smoothing factor for MPS/LTF).
The BUBO method clips the histogram using the upper and lower levels to minimize the gradient of the TF. The BUBO method also uses a clipping parameter α BB , the contrast rate of which can be controlled from a minimum HE of α BB = 0 to a maximum HE of α BB = ∞. As α BB approaches zero, it produces a detailed image, but with a reduced contrast. BUBO is a non-automatic method, so the parameter α BB was fixed at 0.8 in our simulation.
The GC-CHE method clips an input image histogram, where the clipped histogram is controlled with one global and two local gains. In our simulation, the gray levels defining the black and white level regions for local gain control were determined as k B = 63 and k W = 192.
In the HSIT method, the optimum recursion level was determined when the increase in the PSNR was lower than a particular value of 0.1, which may saturate sub-histograms generation by separating an image histogram. The ASFBHE method used the common sigmoid function proposed by Verhulst in 1838 in the context of a population to split an image histogram into two parts, which were equalized independently.
A comparison of the AMBE values listed in Table 5 shows that the MPS/LTF method outperforms the HE, BUBO, GC-CHE, HSIT, and ASFBHE methods. A comparison of the H values shows that the performance of the proposed method, MPS/LTF, is similar to that of the BUBO, GC-CHE, HSIT, and ASFBHE methods, and all of these methods outperform the HE method. However, a comparison of the S values shows that MPS/LTF outperforms the HE, BUBO, GC-CHE, HSIT, and ASFBHE methods. Therefore, we can deduce that the S values are more easily distinguished than the H values for performance comparisons.
Using the simulation parameters listed in Table 5 , the images obtained for Pentagon and Arctic hare are shown in Fig. 11 . For the Pentagon image in Fig. 11 , all of the methods produced images with good contrast enhancement and they preserved the mean brightness. However, the Arctic hare image in Fig. 11 has increased brightness and a high p max value, so the images produced by the BUBO, GC-CHE, and HSIT methods are darker than the original image as well as containing some visual artifacts. Similarly, using the MPS/LTF method with α = 0.0 (BLS), the image obtained has a smaller amount of contrast enhancement. However, it has no visual artifacts and the mean brightness is preserved. Thus, mean brightness preservation can be achieved using the BUBO and GC-CHE methods if the mean brightness of the input image is close to 128. The image produced by the ASFBHE method is much brighter than the original image, but the local details are decreased.
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Examples of the image results obtained for Pentagon and Arctic hare: (a) original, (b) BUBO, (c) GC-CHE, (d) HSIT, (e) ASFBHE, and (f) MPS/LTF.
The outstanding performance of the MPS/LTF method in terms of the AMBE is because the MPS of the TF is used to preserve the mean brightness. The difference in the performance according to S between the MPS/LTF method and the BUBO and GC-CHE methods is attributable to the automatic control of the smoothing factor.
For the F16 or Pentagon images, a reasonable parameter value in BUBO is α BB = 0.8. However, for the U2 and Arctic hare images, due to the high p max value, α BB must assume a smaller value to reduce the visual artifacts. To address this problem, the BUBO method can apply automatic parameter control according to p max , which is similar to our proposed method. However, the parameter range for BUBO is 0 ≤ α BB ≤ ∞ , whereas the smoothing factor range for the proposed method is 0 ≤ α ≤ 1 , s oa nonlinear decision rule is required.
For the GC-CHE method, the clipping rate is determined automatically based on the mean brightness, thereby leading to deduction of the clipping threshold. However, it is not easy to determine the clipping threshold based on the clipping rate.
In the HSIT method, the recursion level is determined by a particular PSNR value, so it may be difficult to apply contrast enhancement to images with various image brightness levels. In addition, the performance of the ASFBHE method is affected by the parameter value selected for the sigmoid function based on the AMBE of an image, which may not ensure the sparsity of the histogram for the image obtained.
Related methods were proposed in [3] [6] and [10] [17] to preserve the mean brightness and reduce the visual artifacts as much as possible in order to enhance the image contrast. In the case where α = 1, TF is the same as HE. This condition enhances the contrast of an image, but the mean brightness is fixed at 255 gray-levels and this may cause visual artifacts. For α = 0, the contrast enhancement effect may be reduced, but AMBE and the sparsity value are also reduced. Our aim is to make this process automatic. Moreover, α = 0 indicates that stretching or BLS may not be performed, as shown in Fig. 5 . For the U2 and Arctic hare images in Figs 9 and 11 with very dark and bright mean brightness levels, respectively, the AMSE and sparsity value are decreased with low contrast enhancement. However, in the case of a general image, for example, the Pentagon image in Fig. 11 , a better result can be obtained using high contrast enhancement.
We also tested the proposed method using video sources that comprised moving images containing several colors. Thus, we tested both the proposed method and the BUBO method, which uses a real-time implementable algorithm, in video simulations. Figure 12 shows an image captured from a video simulation as well as the images and TFs obtained by the BLS (MPS/LTF α = 0.0) and BUBO methods. The videos obtained by the two methods and the TF per frame are displayed in real-time. A video simulator was implemented using Open-CV and the contrast enhancement process was conducted in real-time. For color video processing, the contrast enhancement process was applied to the luminance component ( Y ) only, and the chrominance components ( C b and C r ) were multiplied by the ratio of their input and output luminance values to ensure hue preservation.
PPT Slide
Lager Image
Videos and transfer functions obtained using the proposed BLS (MPS/LTF α = 0.0) and BUBO.
According to the video simulations, we deduced that the proposed method achieved satisfactory brightness preservation and obtained natural-looking images. Hence, its performance is better than that of the BUBO method. The proposed method can be implemented easily for field programmable gate arrays, application-specific integrated circuits, or video streaming because it features a real-time implementable algorithm and low-computational complexity.
V. Conclusions
In this study, we proposed an automatic contrast enhancement method using a TFM based on HE. By applying the MPS method, the mean of an image is preserved and the brightness is controlled easily. The image contrast is enhanced without visual artifacts by the LTF. The contrast rate is controlled automatically using the maximum value of the image PDF. The performance of the proposed method was determined based on the AMBE, the discrete entropy H , and the proposed sparsity of a histogram S . The MPS/LTF method is suitable for consumer electronics such as TVs because of the mean preservation technique employed in this method, and the LTF method is suitable for surveillance video systems such as closed-circuit television, where preserving the mean is not very important.
Acknowledgements
This study was supported by the ETRI R&D Program (16ZC3110, Local-based medical device/robot development & medical IT convergence for small and medium enterprise revitalization project) funded by the Government of Korea.
BIO
twbae@etri.re.kr
Tae Wuk Bae received his BS, MS, and PhD degrees in electrical engineering from Kyungpook National University, Daegu, Rep. of Korea, in 2004, 2006, and 2010, respectively. Since 2014, he has been working at the Daegu-Gyeongbuk Research Center, ETRI, Daegu, Rep. of Korea. His research interests include medical devices and medical signal processing.
Corresponding Author elecash@inje.ac.kr
Sang Ho Ahn received his BS, MS, and PhD degrees in electronic engineering from Kyungpook National University, Daegu, Rep. of Korea, in 1986, 1988, and 1992, respectively. Since 1995, he has been with the Electronic Engineering Department, Inje University, Gimhae, Rep. of Korea. His research interests include robot vision, infrared image processing, and infrared countermeasures.
yucel@ece.gatech.edu
Yucel Altunbasak is a professor in the School of Electrical and Computer Engineering at Georgia Institute of Technology, Atlanta, USA. He joined Hewlett-Packard Research Laboratories in July 1996. In addition, he taught at Stanford and San Jose State Universities CA, USA as a consulting assistant professor. He joined Gatech in 1999. He serves as the technical program chair for ICIP-2006. He was an associate editor for IEEE Transactions on Image Processing, Signal Processing, Signal Processing: Image Communications, and for the Journal of Circuits, Systems and Signal Processing. He serves as the vice-president for the IEEE Communications Society Multimedia Communications Technical Committee. He has been elected to the IEEE Signal Processing Society IMDSP, MMSP, and BISP Technical Committees.
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