Distribution Of Discrete Cosine Transform Coefficients Research Articles

Learning JPEG Compression Artifacts for Image Manipulation Detection and Localization

Detecting and localizing image manipulation are necessary to counter malicious use of image editing techniques. Accordingly, it is essential to distinguish between authentic and tampered regions by analyzing intrinsic statistics in an image. We focus on JPEG compression artifacts left during image acquisition and editing. We propose a convolutional neural network (CNN) that uses discrete cosine transform (DCT) coefficients, where compression artifacts remain, to localize image manipulation. Standard CNNs cannot learn the distribution of DCT coefficients because the convolution throws away the spatial coordinates, which are essential for DCT coefficients. We illustrate how to design and train a neural network that can learn the distribution of DCT coefficients. Furthermore, we introduce Compression Artifact Tracing Network (CAT-Net) that jointly uses image acquisition artifacts and compression artifacts. It significantly outperforms traditional and deep neural network-based methods in detecting and localizing tampered regions.

Fast search real‐time face recognition based on DCT coefficients distribution

The authors propose an adaptive face recognition algorithm based on the discrete cosine transform (DCT) coefficients approach. For the database's establishment, the face images are pre-processed with colour transform, hair cutting, and background removing to eliminate non-face information. The recognised kernel applied the weights of DCT coefficient distribution with the entire image transformation, to avoid position mismatch and reduce the light effect. The key coefficients of DCT are chosen from the training database by maximum variance. The fast search mode can reject 90% weak candidates with few coefficients to fasten the processing speed. The significant coefficients weighting methods are used to enhance face features. Only using 50 coefficients per picture, the recognition rate can achieve 95% for ORL face database testing. For real-time recognition, camera imaging is processed with algorithms using C-programming based on Windows system. The recognition rate can achieve 95% and the speed is about nine frames per second for real-time recognition in practice.

USAD: undetectable steganographic approach in DCT domain

ABSTRACTIn this work, we propose a new adaptive chaotic steganographic method based on the Discrete Cosine Transform (DCT) and a reversible mapping function. The mapping function is used to map the secret bits into their corresponding symbols. This mapping technique has to preserve the same dynamics, properties and distribution of the original DCT coefficients. The novelty of our approach is based on the adaptive selection phase of embedding spots. This selection is established through a blindness condition which is applied over each image of the database. The proposed embedding scheme within the middle DCT coefficients shows lower probability of detection and higher flexibility in extraction. We evaluate the detection of our method using the Ensemble Classifiers and a set of frequency and spatial domain feature extractors such as the Spatial domain Rich Model (SRM) features, Chen et al.'s 486-dimensional both inter- and intra-block Markov-based features and Liu's 216-dimensional adaptive steganography-based features.

An improved anti-forensic technique for JPEG compression

The availability of numerous powerful image processing tools or software makes it easier to manipulate the digital information without the addition of any footprints. JPEG compression based tampering detectors are generally employed in digital image forensics. An efficient anti-forensic technique is required to measure the capability of JPEG forensic detectors. In this article, an efficient JPEG anti-forensic technique is presented to hide the JPEG compression artifacts in spatial as well as Discrete Cosine Transform (DCT) domain. We initially employ shifted block DCT approach on the considered JPEG compressed image to fill the gaps in the comb-like distribution of DCT coefficients. This shifted block DCT approach led to the addition of dithering noise itself without the need of any adaptive dithering model. Therefore, the computational cost to create a JPEG forgery reduces significantly. The result of this shifted block DCT approach is further processed in the second step by TV (Total variation)-based deblocking operation to remove the blocking artifacts left during the JPEG compression in the spatial domain. The experimental results illustrate that the presented approach has better performance in comparison to the existing techniques in terms of image visual quality and forensic undetectability with highly reduced computational cost.

Blind Image Quality Assessment of Natural Scenes Based on Entropy Differences in the DCT Domain.

Blind/no-reference image quality assessment is performed to accurately evaluate the perceptual quality of a distorted image without prior information from a reference image. In this paper, an effective blind image quality assessment approach based on entropy differences in the discrete cosine transform domain for natural images is proposed. Information entropy is an effective measure of the amount of information in an image. We find the discrete cosine transform coefficient distribution of distorted natural images shows a pulse-shape phenomenon, which directly affects the differences of entropy. Then, a Weibull model is used to fit the distributions of natural and distorted images. This is because the Weibull model sufficiently approximates the pulse-shape phenomenon as well as the sharp-peak and heavy-tail phenomena of natural scene statistics rules. Four features that are related to entropy differences and human visual system are extracted from the Weibull model for three scaling images. Image quality is assessed by the support vector regression method based on the extracted features. This blind Weibull statistics algorithm is thoroughly evaluated using three widely used databases: LIVE, TID2008, and CSIQ. The experimental results show that the performance of the proposed blind Weibull statistics method is highly consistent with that of human visual perception and greater than that of the state-of-the-art blind and full-reference image quality assessment methods in most cases.

Statistical characterisation of block variance and AC DCT coefficients for power law enhanced images

The study of statistical distributions of alternating current (AC) discrete cosine transform (DCT) coefficients is one of the key techniques for digital images. In this study, we have analysed original and power law enhanced images in the logarithmic domain. The logarithmic domain linearises the otherwise nonlinear relation between original and power law enhanced images. We have experimentally proved that Gamma distribution is the best distribution for characterisation of block variance in terms of Jensen-Shannon divergence. Therefore, a composite distribution, Gaussian-Gamma, is employed for characterisation of AC DCT coefficients. We have analytically derived and experimentally verified that the scale parameters of power law enhanced image are proportional to scale parameters of the original image whereas shape parameters remain unchanged. On further experimentation, it is established that scale and shape parameters of the composite statistical distribution of AC DCT coefficients do not change if images are compressed in JPEG format after power law enhancement. Furthermore, a novel feature set of scale parameters is constructed and is applied to train decision tree to classify original, brightened, and darkened images. The comparison of achieved classification results with the state-of-the-art show the efficacy of proposed analysis.

Fast Blind Instrument Function Estimation Method for Industrial Infrared Spectrometers

Infrared (IR) spectrometers, particularly the aging ones, often suffer from the band overlap and random noise. In this paper, a blind estimation method based on discrete cosine transform (DCT) regularization is proposed for IR spectrum measured from an aging spectrometer instrument. Motivated by the observation that the DCT coefficient distribution of the ground-truth spectrum is sparser than that of the observed spectrum, an IR spectral deconvolution model is formulated in our method to regularize the distribution of the observed spectrum by total variation regularization. Then, the split Bregman method is exploited to solve the resulting optimization problem. The experimental results demonstrate an encouraging performance of the proposed approach to suppress noise and preserve spectral details. The novelty of our method lies on its ability to estimate instrument function and latent spectrum in a joint framework; thus, mitigating the effects of instrument aging to a large extent. The recovered IR spectra can efficiently capture the spectral features and interpret the unknown chemical mixture in industrial applications.

Analyzing the Effect of JPEG Compression on Local Variance of Image Intensity.

The local variance of image intensity is a typical measure of image smoothness. It has been extensively used, for example, to measure the visual saliency or to adjust the filtering strength in image processing and analysis. However, to the best of our knowledge, no analytical work has been reported about the effect of JPEG compression on image local variance. In this paper, a theoretical analysis on the variation of local variance caused by JPEG compression is presented. First, the expectation of intensity variance of 8×8 non-overlapping blocks in a JPEG image is derived. The expectation is determined by the Laplacian parameters of the discrete cosine transform coefficient distributions of the original image and the quantization step sizes used in the JPEG compression. Second, some interesting properties that describe the behavior of the local variance under different degrees of JPEG compression are discussed. Finally, both the simulation and the experiments are performed to verify our derivation and discussion. The theoretical analysis presented in this paper provides some new insights into the behavior of local variance under JPEG compression. Moreover, it has the potential to be used in some areas of image processing and analysis, such as image enhancement, image quality assessment, and image filtering.

Detection of shifted double JPEG compression by an adaptive DCT coefficient model

In many JPEG image splicing forgeries, the tampered image patch has been JPEG-compressed twice with different block alignments. Such phenomenon in JPEG image forgeries is called the shifted double JPEG (SDJPEG) compression effect. Detection of SDJPEG-compressed patches could help in detecting and locating the tampered region. However, the current SDJPEG detection methods do not provide satisfactory results especially when the tampered region is small. In this paper, we propose a new SDJPEG detection method based on an adaptive discrete cosine transform (DCT) coefficient model. DCT coefficient distributions for SDJPEG and non-SDJPEG patches have been analyzed and a discriminative feature has been proposed to perform the two-class classification. An adaptive approach is employed to select the most discriminative DCT modes for SDJPEG detection. The experimental results show that the proposed approach can achieve much better results compared with some existing approaches in SDJPEG patch detection especially when the patch size is small.

Analysis of the spatial layer discrete cosine transform coefficient distribution and its application to rate model for H.264/SVC encoder

Knowledge of the discrete cosine transform coefficient distribution (DCT-DIST) is important for the encoder design. For example, rate control relies on this knowledge to estimate a possible bit rate and then decide proper coding parameters before the actual encoding task is performed. Therefore the rate control performance is fairly dependent on how accurately the DCT-DIST is modelled. The spatial enhancement layer (SL) DCT-DIST for H.264 scalable video coding (SVC) is studied in this Letter. SL DCT-DIST knowledge is furthermore used to derive a novel rate model. Our results can help design a proper rate control module for the H.264/SVC encoder.

A Cauchy distribution-based ternary hypothesis testing for bipolar additive watermark detection in H.264/AVC video

The statistical distribution of discrete cosine transform (DCT) coefficients is important for video watermarking since they are the main carriers for watermark embedding. For the statistical distribution of intra-coded DCT coefficients in the H.264/AVC video stream, non-parametric hypothesis test is utilised to verify that Cauchy distribution is better than generalised Gaussian distribution (GGD). Moreover, ternary hypothesis test is introduced into the detection of bipolar additive watermarks. By adjusting the watermark strength parameter, the detector performance can be guaranteed. Experimental results show that for those bipolar additive watermarks in the H.264/AVC stream, the proposed approach can achieve a detection accuracy of more than 80% on average.

No-reference peak signal to noise ratio estimation based on generalized Gaussian modeling of transform coefficient distributions

We present a no-reference peak signal to noise ratio (PSNR) estimation algorithm based on discrete cosine transform (DCT) coefficient distributions from H.264/MPEG-4 part 10 advanced video codec (H.264/AVC) bitstreams. To estimate the PSNR of a compressed picture without the original picture on the decoder side, it is important to model the distribution of transform coefficients obtained from quantized coefficients accurately. Whereas several conventional algorithms use the Laplacian or Cauchy distribution to model the DCT coefficient distribution, the proposed algorithm uses a generalized Gaussian distribution. Pearson's χ 2 (chi-square) test was applied to show that the generalized Gaussian distribution is more appropriate than the other models for modeling the transform coefficients. The χ 2 test was also used to find optimum parameters for the generalized Gaussian model. It was found that the generalized Gaussian model improves the accuracy of the DCT coefficient distribution, thus reducing the mean squared error between the real and the estimated PSNR.

スラント変換を用いたグラデーション領域に対する高画質符号化手法

We propose a new coding method by applying slant transform (SLT) to gradation areas instead of discrete cosine transform (DCT). A contour in a gradation area, which is often caused by the coding process for high compression, is one of the typical artifact noises for subjective evaluation. Since the pixel value changes linearly in a gradation area, DCT is not always suitable for its transformation. In our proposed method, although only traditional DCT is utilized in the encoding process to avoid increasing computational complexity, the inverse SLT (ISLT) instead of IDCT is performed in the area that is estimated as a gradation area in accordance with the distribution of DCT coefficients in the decoding process. The coding block size of the gradation area is easily expanded by simple operations using the hierarchy of SLT. In accordance with our experimental analysis, the proposed scheme has been performed to clarify the improvement of quality in gradation areas.

No-Reference Quality Assessment of H.264/AVC Encoded Video

This paper proposes a no-reference quality assessment metric for digital video subject to H.264/advanced video coding encoding. The proposed metric comprises two main steps: coding error estimation and perceptual weighting of this error. Error estimates are computed in the transform domain, assuming that discrete cosine transform (DCT) coefficients are corrupted by quantization noise. The DCT coefficient distributions are modeled using Cauchy or Laplace probability density functions, whose parameterization is performed using the quantized coefficient data and quantization steps. Parameter estimation is based on a maximum-likelihood estimation method combined with linear prediction. The linear prediction scheme takes advantage of the correlation between parameter values at neighbor DCT spatial frequencies. As for the perceptual weighting module, it is based on a spatiotemporal contrast sensitivity function applied to the DCT domain that compensates image plane movement by considering the movements of the human eye, namely smooth pursuit, natural drift, and saccadic movements. The video related inputs for the perceptual model are the motion vectors and the frame rate, which are also extracted from the encoded video. Subjective video quality assessment tests have been carried out in order to validate the results of the metric. A set of 11 video sequences, spanning a wide range of content, have been encoded at different bitrates and the outcome was subject to quality evaluation. Results show that the quality scores computed by the proposed algorithm are well correlated with the mean opinion scores associated to the subjective assessment.

GG DCT COEFFICIENT MODELS

It has been known that the distribution of the discrete cosine transform (DCT) coefficients of most natural images follow a Laplace distribution. However, recent work has shown that the Laplace distribution may not be a good fit for certain types of images and that the Gaussian distribution will be a realistic model in such cases. A model that contains both Laplace and Gaussian distributions as particular cases is the generalized Gaussian (GG) distribution. Assuming this generalized model, we derive a comprehensive collection of formulas for the distribution of the actual DCT coefficients. The corresponding estimation procedures are derived by the method of moments and the method of maximum likelihood. Finally, the superior performance of the derived distributions over the standard Gaussian and Laplace models is illustrated. It is expected that this work could serve as a useful reference and lead to improved modeling with respect to image analysis and image coding.

H.264/AVC에서 DCT계수 분포를 이용한 고속 인트라 모드 결정 방법

he rate-distortion optimization (RDO) method in the H.264/AVC encoder is a technology that improves the coding efficiency, but increases the computational complexity. In this paper, a fast Intra mode decision algorithm using DCT (Discrete Cosine Transform) coefficients distribution is proposed to reduce the H.264 encoder complexity. The proposed method reduces the encoder complexity on average 68.40%, while the coding efficiency is slightly decreased compared with the H.264/AVC encoder.

Fast Intra Mode Decision Using DCT Coefficient Distribution in H.264/AVC

The rate-distortion optimization (RDO) method in the H.264/AVC encoder is an informative technology that improves the coding efficiency, but increases the computational complexity. In this letter, a fast Intra mode decision algorithm using DCT (Discrete Cosine Transform) coefficients distribution is proposed to reduce the H.264 encoder complexity. The proposed method reduces the encoder complexity on average 63.44%, while the coding efficiency is slightly decreased compared with the H.264/AVC encoder.

Generalised Gaussian distribution to early detect zero quantised discrete cosine transform coefficients in H.264/AVC video encoding

In H.264/AVC video encoding, zero quantised discrete cosine transform (DCT) coefficients blocks, called ZQBs, are quite common in low bit-rate video applications. The computations of DCT and quantisation can be remarkably reduced if ZQBs are detected prior to DCT and quantisation. A mathematical model is established based on analysing DCT coefficient distribution and applying the generalised Gaussian distribution theorem. Using this model, four conditions corresponding to four kinds of transform and quantisation methods are proposed. As compared with other methods in the literature, the proposed method is able to detect more ZQBs and hence reduce more computations. Experimental results show our method is superior to other methods in terms of the total number of reduced computations and usability.

Modeling the distribution of DCT coefficients for JPEG reconstruction

In the paper, the one moment (OM) method for the estimation of the shape parameter of generalized Gaussian distribution (GGD) is derived from the two moments method in the case when the moments converge in the limits to the same value. The one moment method reduces to the maximum likelihood (ML) method in the special case when the moment equals the shape parameter. The proposed method exhibits smaller complexity of calculations over ML keeping the same error. Assuming Laplacian distribution, there exists a method for optimally biasing the reconstruction levels for the quantized AC discrete cosine transform (DCT) coefficients using only the quantized ones available at the JPEG decoder [J.R. Price, M. Rabbani, Biased reconstruction for JPEG decoding, IEEE Signal Process. Lett. 6 (12) (1999) 297–299; R. Krupiński, J. Purczyński, First absolute moment and variance estimators used in JPEG reconstruction, IEEE Signal Process. Lett. 11 (8) (2004) 674–677]. Many researchers stated that the subset of images can be modeled with GGD with the shape parameter lower than 1. By assuming a source signal with GGD with the exponent 0.5, equations in a closed form for the centroid reconstruction can be obtained as it cannot be done for a GGD model. The ML method of discrete GGD 0.5 is derived, which requires the estimation of only one parameter. For selected images, the values of PSNR coefficients are compared for both distributions.

A General Method for Detecting All-Zero Blocks Prior to DCT and Quantization

This paper presents an innovative algorithm for detecting all-zero discrete cosine transform (DCT) coefficient blocks prior to DCT and quantization for all block-based video coding standards. A mathematic model is established based on analyzing DCT coefficient distribution and applying Paseval energy conservation theorem. The algorithm is applied to H.264 video coding and experimental results show up to 32% higher detection ratio without degrading video quality, compared with results of the existing methods. Furthermore, up to 47% higher detection ratio is achieved by changing the threshold based on DCT coefficient distribution. For motion estimation, much less search points needed by using the proposed method as early termination criterion than that by using the existing methods