Adaptive histogram equalization based image forensics using statistics of DC DCT coefficients

DIGITAL IMAGE PROCESSING AND COMPUTER GRAPHICS VOLUME: 16 |NUMBER: 1 |2018 |MARCH Adaptive Histogram Equalization Based Image Forensics Using Statistics of DC DCT Coefficients Neetu SINGH, Abhinav GUPTA, Roop Chand JAIN Department of Electronics and Communication Engineering, Jaypee Institute of Information Technology, Sector-62, Noida, Uttar Pradesh 201309, India [email protected], abhina[email protected], [email protected] DOI: 10.15598/aeee.v16i1.2647 Abstract. The vulnerability of digital images is growing towards manipulation. This motivated an area of research to deal with digital image forgeries. The certifying origin and content of digital images is an open problem in the multimedia world. One of the ways to find the truth of images is finding the presence of any type of contrast enhancement. In this work, novel and simple machine learning tool is proposed to detect the presence of histogram equalization using statistical parameters of DC Discrete Cosine Transform (DCT) coefficients. The statistical parameters of the Gaussian Mixture Model (GMM) fitted to DC DCT coefficients are used as features for classifying original and histogram equalized images. An SVM classifier has been developed to classify original and histogram equalized image which can detect histogram equalized image with accuracy greater than 95 % when false rate is less than 5 %. Keywords CLAHE, DC DCT coefficients, Gaussian Mixture Model, image forensics. 1. Introduction Digital images are generally used to establish the occurrence of some man-made or natural incidents. These days images are one of the biggest and largest means of communication through different media and often required authenticity test. The availability of a large number of software products in multimedia devices is making creation and manipulation of digital images very cheap and convenient. Digital images can be manipulated by tampering source of information and/or the content of information. Research area which covers finding origin and authenticity of an image is known as Digital Image Forensics (DIF) [1], [2] and [3]. The forensics of source involves finding camera or source from which an image is generated or captured, and the forensics of authentication involves finding traces of manipulation in an image. To create invincible tampered images, sampling, interpolation, contrast enhancement, median filtering, addition of noise and saving in lossy compression format are some examples of the commonly involved techniques. These methods alone or chain of these methods are not tampering techniques, but they are required in order to hide any visual traces of the tampering. Therefore, detection of the presence of any such operation leads to the detail investigation of an image. In literature of contrast enhancement-based DIF, mainly two types of classical contrast enhancements, such as power-law transformation and Global Histogram Equalization (GHE), are considered [4], [5], [6], [7], [8], [9] and [10]. In our work, we have focused on detection of histogram equalization operation. The GHE increases the global contrast of an image by equally distributing intensity levels. But these days, Adaptive Histogram Equalization (AHE) [11] and [12] is getting popular due to its performance in comparison to Global Histogram Equalization (GHE). In AHE, an image is divided into tiles and thereafter, HE is applied to each tile which leads to enhancement of smaller details by increasing local contrast of the image. The equalization process is followed by bilinear interpolation to smooth out the boundaries due to the tiling of images. Although, this provides better enhancement than global counterpart, enhancement of noise content in homogeneous regions of background is a major concern. Generally, various versions of AHE are available to suppress the enhanced noise [11]. The most popular and acceptable variation of AHE is contrast limited AHE (CLAHE) [12], [13], [14], [15] and [16]. The c 2018 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 125 DIGITAL IMAGE PROCESSING AND COMPUTER GRAPHICS VOLUME: 16 |NUMBER: 1 |2018 |MARCH 0 1000 2000 3000 0 0.5 1 1.5 10-3 (a) Original Image (ucid00005.tif). 0 500 1000 1500 2000 0 0.5 1 1.5 10-3 (b) GHE Image. 0 500 1000 1500 2000 0 0.5 1 1.5 10-3 (c) AHE Image (no clipping). Fig. 1: Characterization of I0,0using GMM. CLAHE suppresses enhancement of noise by limiting the highest value in image histogram known as Clip Limit (CL). The CL can be defined as highest value allowed in a bin of histogram of an image tile. The density values which are greater than CL in a given image tile are redistributed. The CL and number of tiles (T) are two important parameters of CLAHE. In literature, it is stated that different probability density functions (pdf)s (uniform, exponential, Rayleigh, etc.) for image histograms in HE for CLAHE are considered based on applications. In addition to natural images [16] and [17], CLAHE also found its application in enhancement of medical images [13] and [14] and underwater images [15]. Since the use of CLAHE is spreading, the tools to detect the presence of AHE are also required. In this paper, the statistical characterization of block DC coefficient of 2D 8×8DCT coefficients is employed to classify original and HE images. HE images include GHE, AHE and CLAHE images. The block DC coefficient of 2D 8×8DCT coefficients is defined as an array made up of all DC coefficients from 8×8block of DCT coefficients. In image forensics, the DCT coefficient analysis is employed to detect tampering in JPEG compressed images [18] and [19]. Further, the statistical characterization of DCT coefficients has been popular for improvements in encoder/decoder for JPEG standard [20], [21], [22] and [23]. It may be noted that statistical characterization of block variance and AC DCT coefficients are recently employed to detect global contrast enhancement (or power-law transformation) [24]. In this work, a tool is developed using statistical parameters obtained from fitting of block DC coefficient by Gaussian Mixture Model (GMM). The estimated parameters with other statistical parameters are applied to train a 10-fold cross-validation Support Vector Machine (SVM) [25]. The trained SVM classifier can be used to classify original and HE images. The proposed tool is independent of Tand can detect the presence of HE for a large set of CL, all considered pdfs (uniform distribution, exponential distribution, Rayleigh distribution ) for image histograms and range of gray levels ("full" and "original") used for equalization. By means of Receiver operating curves (ROC), the efficacy of the proposed tool for the classification of original and HE images is shown. Additionally, the performance of the tool in detection of CLAHE images for different CLs, Ts, image histogram equalization pdfs, and range of gray levels used in equalization is also discussed. The paper is divided into four sections. Section 2. describes the statistical characterization of block DC DCT coefficients by GMM. The HE detection system and its detection algorithm with ROC curves of developed classifiers are explained in Sec. 3. Section 4. concludes the paper. 2. Statistical Characterization of DC DCT Coefficients The block DC DCT coefficients obtained by employing type - II DCT are characterized using GMM in order to classify original and HE images. 2.1. Gaussian Mixture Model A GMM is a pdf which is the weighted sum of densities of Gaussian components defined as p x|µi,X i , wi!= K X i=1 wig x|µi,X i!,(1) where xis D-dimensional continuous-valued data vector, wifor i= 1,2,3, ..., K are the weights of mixture and Kis the number of components. In Eq. (1), g is a D-dimensional Gaussian density which can be expressed as g x|µi,X i!=1 2π(D/2) Pi (1/2) exp (−1 2X0 −1 X i X),(2) where X= (x−µi),µiis mean vector, and Piis covariance matrix. It may be observed from Eq. (1), the sum of mixture weights (wi) for all components c 2018 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 126 DIGITAL IMAGE PROCESSING AND COMPUTER GRAPHICS VOLUME: 16 |NUMBER: 1 |2018 |MARCH 0 500 1000 1500 2000 0 0.5 1 1.5 10-3 (a) 0 500 1000 1500 2000 0 0.5 1 1.5 10-3 (b) 0 500 1000 1500 2000 0 0.5 1 1.5 10-3 (c) 0 500 1000 1500 2000 0 0.5 1 1.5 10-3 (d) 0 500 1000 1500 2000 0 0.5 1 1.5 10-3 (e) 0 500 1000 1500 2000 0 0.5 1 1.5 10-3 (f) 0 500 1000 1500 2000 0 0.5 1 1.5 10-3 (g) 0 500 1000 1500 2000 0 0.5 1 1.5 10-3 (h) 0 500 1000 1500 2000 0 0.5 1 1.5 10-3 (i) 0 500 1000 1500 2000 0 0.5 1 1.5 210-3 (j) 0 500 1000 1500 2000 0 0.5 1 1.5 210-3 (k) 0 500 1000 1500 2000 0 0.5 1 1.5 210-3 (l) Fig. 2: Characterization of I0,0of CLAHE images using GMM with varying CL and T(a), (e) and (i) CL = 0.005, (b), (f) and (j) CL = 0.01, (c), (g) and (k) CL = 0.05, (d), (h) and (l) CL = 0.1. (a)-(d) T=8×8, (e)-(h) T=16 ×16, and (i)-(l) T =32 ×32, represents number of tiles used in CLAHE with uniform pdf and "full" range of gray levels. is equals to 1. The parameters of GMM are: mean vector, covariance matrix, and mixture weights. These parameters can be collected to form a feature set (θ) given by, θ=(wi, µi,X i), i = 1,2,3, ..., K. (3) The model settings, like the number of components, type of covariance matrix, and sharing of parameters, depends on the size of available data for estimation of parameters and application. In our work, the diagonal covariance matrix for all components is used, and the parameters in Eq. (3) are estimated using Maximum Likelihood Estimation (MLE). 2.2. Statistical Characterization The DC coefficients of images are calculated in grayscale domain by employing type - II 8×8block DCT of JPEG standard. The type-II DCT is defined as Ib u,v =αu(u)αv(v) 7 X x=0 7 X y=0 ix,y cos π(2x+ 1)u 16 cos π(2y+ 1)v 16 ,(4) where x, y and u, v represent spatial and frequency domain variables, respectively. The value of αu(u)and αv(v)at u= 0, v = 0 is 1/√8. The DCT coefficient at u= 0, v = 0 is known as DC coefficient which is defined in type - II DCT as Ib 0,0=1 8 7 X x=0 7 X y=0 ix,y,(5) where Ib 0,0is the DC coefficient of an image block, b represents number of the block. It may be noted that Ib 0,0is eight times of the mean value of 8×8block of an image. The block DC coefficient I0,0can be defined as I0,0=I1 0,0, I2 0,0, ..., IB 0,0,(6) c 2018 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 127 DIGITAL IMAGE PROCESSING AND COMPUTER GRAPHICS VOLUME: 16 |NUMBER: 1 |2018 |MARCH 0 500 1000 1500 2000 0 0.5 1 1.5 10-3 (a) 0 500 1000 1500 2000 0 0.5 1 1.5 210-3 (b) 0 500 1000 1500 2000 0 0.5 1 1.5 10-3 (c) 0 500 1000 1500 2000 0 0.5 1 1.5 210-3 (d) Fig. 3: Characterization of I0,0of CLAHE images using GMM for (a) T=8×8, exponential distribution (b) T=8×8, Rayleigh distribution, (c) T=16 ×16, exponential distribution and (d) T=16 ×16, Rayleigh distribution with CL = 0.01 and "full" range of gray levels. 0 500 1000 1500 2000 0 0.5 1 1.5 10-3 (a) 0 500 1000 1500 2000 0 0.5 1 1.5 10-3 (b) 0 500 1000 1500 2000 0 0.5 1 1.5 10-3 (c) 0 500 1000 1500 2000 0 0.5 1 1.5 10-3 (d) Fig. 4: Characterization of I0,0of CLAHE images using GMM for (a) T=8×8, "full" range (b) T=8×8, "original" range, (c) T=16 ×16, "full" range and (d) T=16 ×16, "original" range with CL = 0.01 and uniform distribution. where B is number of 8×8non-overlapping blocks in the input image. The histograms of I0,0of original image, histogram equalized image, and adaptive histogram equalized image are characterized by GMM as shown in Fig. 1. The statistical characterization of I0,0 of CLAHE images for different values of CL and Tis shown in Fig. 2. The statistical characterization of I0,0 of CLAHE images for different pdfs of histograms is shown in Fig. 3. The effect of the range of gray levels on characterization of I0,0is shown in Fig. 4. In the legend of Fig. 4, "full" represents the entire available range of gray levels (i.e., 256 for 8-bit image), and "original" represents the range of gray levels in original image. The characterizations shown in Fig. 1, Fig. 2, Fig. 3 and Fig. 4 are obtained with optimum number of components found using Akaike Information Criterion (AIC) [26]. Further, to measure the efficacy of characterization, we have employed Jensen-Shannon (JS) divergence [27] and [28] and Kolmogorov-Smirnov (KS) statistic [29] and [28]. The values of JS and KS in different cases of HE for a UCID [30] image are shown in legends of Fig. 1, Fig. 2, Fig. 3 and Fig. 4. A consistency in values of JS and KS concludes GMM as a good model of fit across original and different types of HE images. 2.3. Parameter Analysis of CLAHE To find the optimum number of components (K) for GMM, we have calculated the mean JS and KS values with varying K(1,3,5,...,10) for all 1338 images of UCID database. It is worth mentioning that KS hypothesis test is performed with α= 0.01. The efficacy of GMM for characterization of I0,0can be observed from Tab. 1, Tab. 2, Tab. 3, Tab. 4 and Tab. 5. Effect of CL: With an increase in the value of CL from 0.005 (large clipping) to 1 (no clipping), the shift in skewness from right to left of p(I0,0)is observed (Fig. 2 and Fig. 3). Lower values of CL represent low contrast, and higher values of CL represent higher contrast. Additionally, a decrease in kurtosis among distributions can also be observed in Fig. 3. The effect of CL in characterization of p(I0,0)is tabulated in Tab. 1, Tab. 2, Tab. 3 and Tab. 4 for different values of T. Effect of T: The effect of the number of tiles Tused in CLAHE is shown in Fig. 2. It may be observed from Fig. 2 that kurtosis of p(I0,0) increases with increase of T. The Tab. 1, Tab. 2, Tab. 3 and Tab. 4 show variation of up to 2 % in mean JS and KS statistic values with varying T. c 2018 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 128 DIGITAL IMAGE PROCESSING AND COMPUTER GRAPHICS VOLUME: 16 |NUMBER: 1 |2018 |MARCH Tab. 1: Mean values of JS and KS and KS Hypothesis result for T=8×8(Org = Original). 1C 3C 5C 10C CL JS KS KS Hypo JS KS KS Hypo JS KS KS Hypo JS KS KS Hypo Org 0.0606 0.1683 2.39 0.0122 0.0395 71.52 0.0110 0.0441 80.12 0.0203 0.0813 75.86 0.005 0.0371 0.1185 7.55 0.0129 0.0439 85.13 0.0134 0.0497 86.62 0.0210 0.0816 76.83 0.01 0.0267 0.0944 14.72 0.0117 0.0412 89.24 0.0173 0.0603 89.61 0.0265 0.0919 87.44 0.05 0.0113 0.0528 40.96 0.0155 0.0528 94.25 0.0254 0.0829 92.83 0.0322 0.1046 91.33 0.1 0.0084 0.0438 52.84 0.0192 0.0644 93.2 0.0319 0.1028 92.53 0.0392 0.1258 90.66 10.0067 0.0378 63.45 0.0254 0.0834 93.2 0.039 0.1243 92.15 0.0448 0.1421 90.96 Tab. 2: Mean values of JS and KS and KS Hypothesis result for T=16 ×16. 1C 3C 5C 10C CL JS KS KS Hypo JS KS KS Hypo JS KS KS Hypo JS KS KS Hypo Org 0.0606 0.1683 2.39 0.0121 0.0395 71.52 0.0098 0.0408 79.82 0.0176 0.0728 75.26 0.005 0.0409 0.1216 8 0.0105 0.0366 85.35 0.0126 0.0472 85.8 0.0215 0.0792 82.29 0.01 0.0311 0.0993 14.5 0.0096 0.0341 90.06 0.0123 0.0444 88.94 0.0218 0.0774 85.65 0.05 0.0132 0.0561 45.52 0.0186 0.0630 92.9 0.0264 0.0868 92.38 0.0301 0.0985 91.55 0.1 0.0089 0.0431 60.24 0.0235 0.0782 92.97 0.0319 0.1038 91.85 0.0393 0.1269 90.21 10.0057 0.0322 76.46 0.0329 0.1075 93.27 0.0391 0.1256 92.08 0.0473 0.1507 90.28 Tab. 3: Mean values of JS and KS and KS Hypothesis result for T=32 ×32. 1C 3C 5C 10C CL JS KS KS Hypo JS KS KS Hypo JS KS KS Hypo JS KS KS Hypo Org 0.0606 0.1684 2.39 0.0121 0.0388 71.52 0.0098 0.0408 79.82 0.0229 0.0899 74.89 0.005 0.0482 0.1247 8.45 0.0148 0.0532 73.84 0.0192 0.0750 76.08 0.0321 0.1231 71.52 0.01 0.0413 0.1087 15.02 0.0135 0.0493 80.57 0.0224 0.0839 80.42 0.0324 0.1186 76.83 0.05 0.0201 0.0642 39.69 0.0202 0.0676 93.05 0.0280 0.0925 92.3 0.0368 0.1216 90.58 0.1 0.0130 0.0515 51.05 0.0271 0.0897 92.3 0.0321 0.1049 91.63 0.0421 0.1373 90.21 10.0063 0.0333 70.7 0.0418 0.1357 90.88 0.0474 0.1529 89.46 0.0522 0.1676 87.74 Tab. 4: Mean values of JS and KS and KS Hypothesis result for T=64 ×64. 1C 3C 5C 10C CL JS KS KS Hypo JS KS KS Hypo JS KS KS Hypo JS KS KS Hypo Org 0.0606 0.1683 2.39 0.0125 0.0396 71.75 0.0107 0.0424 80.49 0.0237 0.0927 75.11 0.005 0.0438 0.1157 12.03 0.0164 0.0559 83.93 0.0234 0.0825 85.5 0.0339 0.1204 82.81 0.01 0.0438 0.1157 12.03 0.0164 0.0553 83.71 0.0244 0.0853 85.8 0.0313 0.1116 83.41 0.05 0.0332 0.0903 23.54 0.0199 0.0662 92.68 0.0286 0.0950 92.08 0.0401 0.1329 90.28 0.1 0.0252 0.0757 36.62 0.0255 0.0849 92.68 0.0338 0.1117 90.73 0.0411 0.1353 89.39 10.0129 0.0513 53.36 0.0307 0.1018 91.78 0.0392 0.1284 89.39 0.0444 0.1449 87 Tab. 5: Mean values of JS and KS and KS Hypothesis result for image HE pdfs (D1= uniform distribution, D2= exponential distribution and D3= Rayleigh distribution) and range of gray levels (R1= "full" and R2= "original"). 1C 3C 5C 10C JS KS KS Hypo JS KS KS Hypo JS KS KS Hypo JS KS KS Hypo D1 R10.027 0.094 14.72 0.012 0.041 89.24 0.017 0.060 89.61 0.026 0.092 87.44 R20.028 0.1 12.11 0.013 0.045 88.12 0.017 0.060 88.49 0.023 0.082 86.17 D2 R10.028 0.102 9.72 0.01 0.036 89.61 0.017 0.059 89.01 0.026 0.089 87.14 R20.029 0.108 8.37 0.012 0.0419 87.37 0.018 0.064 87.59 0.027 0.093 85.28 D1 R10.025 0.092 13.83 0.015 0.0514 92.08 0.023 0.075 92 0.029 0.095 89.91 R20.025 0.094 13.38 0.014 0.0465 92.08 0.021 0.071 91.93 0.033 0.1081 89.24 c 2018 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 129 DIGITAL IMAGE PROCESSING AND COMPUTER GRAPHICS VOLUME: 16 |NUMBER: 1 |2018 |MARCH (a) For analysis and detection. (b) Feature extraction block. Fig. 5: The system model. Effect of image HE pdfs: As may be observed from Tab. 5, the maximum number of KS hypothesis tests is passed when the image histogram equalization pdf is a Rayleigh distribution. Effect of range of gray levels in HE: The mean values of JS and KS statistic are the smallest (Tab. 5) when the chosen gray levels are in full range with uniform and exponential distribution. But in case of Rayleigh distribution, the chosen ranges of gray levels have no effect on the mean values of JS and KS statistics. One can observe from Tab. 1, Tab. 2, Tab. 3, Tab. 4 and Tab. 5 that the optimum values of JS and KS statistic are obtained with K=3and 5. In our work, we have chosen K= 5 because the maximum number of KS hypothesis tests for original images is passed with K= 5. It is noteworthy that the mean values of JS and KS statistic are calculated after removing 5 % outliers from the original images database. 1. It x,y ←grayscale Itwhere, x= 0,1, ...7, y = 0,1, ...7, represents spatial domain. 2. Compute 8×82D block DCT, It u,v ←DCT (It x,y) where, u= 0,1, ...7, v = 0,1, ...7, represents frequency domain. 3. Compute the block DC Coefficient, It 0,0. 4. Estimate parameters by fitting block DC Coefficient, It 0,0to GMM (Eq. 2). 5. Create features set, F(Eq. 7). 6. ghe ←SVMClassifier (F) here, he = 0 =⇒original and he = 1 =⇒HE. Fig. 6: Proposed HE detection algorithm. 3. Histogram Equalization Detection 3.1. System Model for Analysis and Detection The system model used for analysis and detection is shown in Fig. 5. The GHE, AHE and CLAHE operations are performed in spatial domain with 256 gray levels and saved in TIFF format. For CLAHE, the T are 8×8,16 ×16,32 ×32 and 64 ×64 and the CL are 0.005,0.01,0.03,0.05,0.07,0.09,0.1,0.3. Additionally, the CLAHE images are also generated with exponentially and Rayleigh distributed histograms for all considered Ts and CLs. For the range of gray levels in enhanced images, both "original" and "full" ranges are considered. For feature extraction (Fig. 5), the 2D 8×8block DCT of the grayscale image is computed. The DC DCT coefficient of each block is collected to generate I0,0(Eq. 6). It is observed (Fig. 1, Fig. 2, Fig. 3, Fig. 4 and Fig. 5) that p(I0,0)is varying with histogram equalization operations. Therefore, statistics of I0,0can be used as features for classification. Construction of the feature set involves the calculation of 10 −fold cross-validation accuracies of SVM classifiers for respective feature set. The accuracies corresponding to different feature sets for classification between original and GHE, original and AHE, original and CLAHE (CL = 0.05, D= D1, D2, D3, T=8×8, R1) images are shown in Tab. 6. After experimentation, a 56dimensional feature set FEq. (7) is constructed and used for classification between original and all types c 2018 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 130 DIGITAL IMAGE PROCESSING AND COMPUTER GRAPHICS VOLUME: 16 |NUMBER: 1 |2018 |MARCH Tab. 6: 10 −fold cross-validation accuracies of SVM classifiers for different feature sets. Features Number of features Org vs. GHE Org vs. AHE Org vs. CLAHE (D1) Org vs. CLAHE (D2) Org vs. CLAHE (D3) θ(Eq. 3) 15 86.7 % 88.7 % 86.1 % 83.8 % 87.6 % S(Eq. 8) 11 98.8 % 97.0 % 93.8 % 92.0 % 93.1 % p(I0,0)30 95.7 % 97.4 % 93.0 % 91.9 % 93.6 % θ+S26 97.4 % 97.4 % 93.7 % 92.0 % 94.0 % F(Eq. 7) 56 97.7 % 98.6 % 95.4 % 94.3 % 96.1 % of histogram operations. The estimated parameters from GMM are combined with mean, median, mode, variance, skewness, kurtosis, minimum, maximum, entropy, energy of I0,0, number of peaks in I0,0and empirical p(I0,0). The feature set Fis defined as F={θ, p(I0,0), S},(7) where S=nµ(I0,0), var(I0,0), Sk(I0,0), Ku(I0,0), min(I0,0), max(I0,0), median(I0,0), mode(I0,0), energy(I0,0), entropy(I0,0), peaks(I0,0)o.(8) The feature set Eq. (7) is applied to 10 −fold crossvalidation SVM with Radial Basis Function (RBF) kernel for training. 3.2. Detection Algorithm and Results The proposed detection algorithm for classifying original and histogram equalized images is shown in Fig. 6. To test the efficacy of the proposed algorithm with important parameters of GHE, AHE and CLAHE, we have created different simulation environments. The used database is UCID (TIFF format) with 1338 images. The performance of proposed classifiers is shown in Fig. 7, Fig. 8, Fig. 9, Fig. 10 and Fig. 11 using 10 −fold cross-validation ROC curves. The images are passed through GHE and AHE operation, and for preparation of feature matrix for each classification, the original images are mixed with corresponding HE images. The obtained ROC curves for classification between original and each GHE and AHE are shown in Fig. 7. The simulation environments used for CLAHE are tabulated in Tab. 7. The achieved TPR is >95 % with FPR <5 % in most of the cases. The CL = 0.005 represents less contrast. Thus, the results at CL = 0.005 fall to 90 % with exponential distribution. In case of GHE and AHE, detection accuracy is more than 99 % with false alarm less than 1 %, which is comparable to existing methods [6] and [9], as shown in Tab. 8. The detection results for AHE and CLAHE are not reported in [6] and [9]. The proposed method is applicable with high efficacy for all types of histogram equalization operations. 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Fig. 7: ROC curves for GHE and AHE classifier. Tab. 7: Simulation environments of CLAHE. (D= distribution, D1= uniform distribution, D2= exponential distribution and D3= Rayleigh distribution) and R= range of gray levels, R1= "full" and R2= "original", "All" represents considered values of Tand CL as described in Sec. 3.1. Cases Parameters ROC varying constant T CL D R Case 1 TAll D1 R1 Fig. 8(a) D2Fig. 8(b) D3Fig. 8(c) Case 2 CL All - D1 R1 Fig. 9(a) D2Fig. 9(b) D3Fig. 9(c) Case 3 DAll All - R1Fig. 10 Case 4 RAll All All - Fig. 11 Tab. 8: Accuracy (TPR, FPR) of proposed method and existing methods in HE based image Forensics. Methods GHE AHE and CLAHE Stamm[6] 100 %,3 % NA Y uan[9] 100 %,1 % NA P roposed 99 %,1 % 99 %,1 % and 95 %,5 % 4. Conclusion The histogram equalization is a commonly used contrast enhancement technique. Its adaptive and contrast limited variant CLAHE is also spreading its footprint in application based image enhancements. We have developed a novel method to detect the presence of three commonly found c 2018 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 131 DIGITAL IMAGE PROCESSING AND COMPUTER GRAPHICS VOLUME: 16 |NUMBER: 1 |2018 |MARCH 0 0.2 0.4 0.6 0.8 1 False positive rate 0 0.2 0.4 0.6 0.8 1 True positive rate ROC (a) Uniform. 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 ROC (b) Exponential. 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 ROC (c) Rayleigh. Fig. 8: ROC curves: HE detection for enhancement with varying Tfor all CL. 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 ROC (a) Uniform. 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 ROC (b) Exponential. 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 ROC (c) Rayleigh. Fig. 9: ROC curves: HE detection for enhancement with varying CL for all T. 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 ROC Fig. 10: ROC curves for different pdfs used in CLAHE. histogram equalization variants using statistical features. The proposed method employs statistical features of block DC coefficient to classify original and histogram equalized images. With few exceptions, the proposed tool achieves higher accuracy 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 ROC Fig. 11: ROC curves for different ranges used in CLAHE. with all variants of histogram equalization. This tool does not involve image histograms based methods for detection of contrast enhancement and involves DC DCT coefficients, which is least affected by JPEG compression after enhancement. c 2018 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 132 DIGITAL IMAGE PROCESSING AND COMPUTER GRAPHICS VOLUME: 16 |NUMBER: 1 |2018 |MARCH References [1] FARID, H. Image forgery detection. IEEE Signal Processing Magazine. 2009, vol. 26, iss. 2, pp. 16–25. ISSN 1053-5888. DOI: 10.1109/MSP.2008.931079. [2] REDI, J. A., W. TAKTAK and J. L. DUGELAY. Digital image forensics: a booklet for beginners. 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