2011 Third International Conference on Multimedia Information Networking and Security
Detecting Copy-move Forgery using Non-Negative Matrix Factorization Heng Yao1, Tong Qiao1, Zhenjun Tang2, Yan Zhao1, Hualing Mao1 1
2
School of Communication and Information Engineering Shanghai University Shanghai, China
[email protected]
this photo. Lately, the author of this photo admitted that he added a pigeon on this photo using Photoshop software.
Abstract—Copy-move is a common manipulation of digital image tampering. Block matching after feature extraction is mostly applied method to detect this kind of forgery. In this paper, we propose an efficient copy-move detecting scheme with the capacity of some post-processing resistances. The image is divided into fixed-size overlapped blocks, and then non-negative matrix factorization (NMF) coefficients are extracted from list of all blocks. It is worth noting that all the coefficients are quantized before matching, in other words, we could use relatively few data to interpret a sub-image. Besides, we apply lexicographical sorting method to reduce the probability of invalid matching. Lastly we measure the hamming distance of each block pair in the matching procedure, if the distance is shorter than a threshold, we localize them as the tampering areas. Experimental results show the efficacy of our scheme.
Figure 1. An example of copy-move forgeries. Author of this photo copied the pigeon from the top right corner of his photo and pasted it to the top left corner.
The simplest approach to detect this kind of forgery is dividing the image into blocks and exhaustively searching the differences between each block pair according to their pixel values. When the differences are below a threshold, we could identify they are copy-move forgery pairs. This method could match precisely when the images do not undergo any post processing. However, to make convincing forgeries, the duplicated regions are often retouched with illumination and sharpness adjustments. To improve the robustness of matching accuracy and reduce computational complexity, many researches have been done to use block matching methods. Fridrich et al. [7] firstly propose a method to detect copy-move forgery. They sorted the discrete cosine transform coefficients of divided blocks lexicographically and then detect the forgeries by comparing the similarity of each coefficients block pair. Similarly, Popescu et al. [8] search the similar blocks in one image by means of principal component analysis (PCA) features. Li et al.[9] measure the difference between each block pairs via discrete wavelet transform and singular vector decomposition. Luo et al. [10] detect copy-move forgery using comprehensive block characteristics. Mahdian et al. [11] detect the blurred copy-move forgery using blur invariant moments. Recently some researches consider detecting copy-move forgery using image rotation and scaling invariant features such as Zernike moments, scale invariant feature transform, Fourier-Mellin transform and log-polar Fourier transform [12, 13]. These approaches could only resist some limited scaling and almost all these methods have high computational costs. In this paper, we propose a novel copy-move detecting scheme based on non-negative matrix factorization (NMF). We could use relative few data
Keywords-digtal forensics; non-negative matrix factorization; copy-move forgery detection
I.
INTRODUCTION
Digital images have been widely used in our daily life. Relative to text, it is images that enable us to believe and understand vividly. With the development of digital camera sensors, many manufactures have released miscellaneous digital cameras unceasingly. We could shoot and share our photos everywhere even if we are not the professional photographers. At the same time, we could use some piece of sophisticated photo editing software such as Photoshop to decorate our photos. Such convenience of optimization was unimaginable before the digital age. However not every photo modification is performed for good looking, some vicious tampering has misled the public about the truth. Meantime digital forensic techniques are springing up to discover increasing lies. These techniques are designed to detect the traces from image acquisition or modifications. In [1], Farid roughly classified digital images forensics approaches into five categories: 1) pixel-based techniques [2]; 2) format-based techniques [3]; 3) camera-based techniques [4]; 4) physical-based techniques [5]; 5) geometric-based techniques [6]. One kind of common pixel-based manipulation is called copy-move forgery. The forgers duplicate some part of an image and move to another place in the same image. An example of a copy-move forgery is shown in Figure 1. It was an award-winning photograph of China International Press Photo Contest, which is one of world’s most high-level press photo contests. Many people queried the authentication of 978-0-7695-4559-2/11 $26.00 © 2011 IEEE DOI 10.1109/MINES.2011.104
Department of Computer Science Guangxi Normal University Guilin, China
592 591
to interpret an image. Experimental results show the efficacy of our proposed method, even minor variations occurred in the image due to noise or compression. This Paper is organized as follows, in section 2, we briefly describe the fundamental theory of non-negative matrix factorization. Our proposed method is presented in Section3. Section 4 presents extensive experimental results to demonstrate the efficacy of our algorithm. Finally paper is concluded in Section 5.
composed of following four steps: 1) image pre-processing, 2) image block-dividing, 3) Non-negative factorization and coefficients quantization and 4) Block matching. First, we normalize the original image. When the largest side of an image is larger than 512, we re-size it to 512. The main consideration of this process is to save the matching running time. Since the luminance plane contains most of the geometric and visually significant information, for a color image we only consider the luminance component of the YCbCr space in our algorithm. Then the converted image is underwent a low-pass filtering, the purpose of above filtering is to alleviate the influences of smooth image modification and improve the robustness of our method. We denote the normalized image as U of N×M pixels. In the second step, we divide the pre-processed suspicious image U into overlapped sub-blocks of B×B pixels in dimension. Assuming that the forgery area is larger than any block, we slide the window, one by one, from the top-left corner to the bottom-right corner in a raster-scan order. Denote C(i) as i-th block in the scan process. Totally we could get L blocks, where:
II. NON-NEGATIVE MATRIX FACTORIZATION Non-negative matrix factorization (NMF) is an effective mathematic tool for finding representations of non-negative data. Given a non-negative matrix V of size N×M, NMF seeks two non-negative matrices W and H such that V≈WH, where the sizes of W and H are N×R and R×M respectively. We define W as the base matrix and H as the coefficient matrix. Equivalently, for any column of V, NMF approximates it by a linear combination of R “basis” columns in W. Minimizing the difference between V and WH is the common approach to find W and H. In our work, we employ the multiplicative update algorithm proposed in [14] to calculate the coefficient matrix H. It is simple to implement and often yields good results. At each iteration of this method, the elements of W and H are multiplied by certain factors. As the zero elements are not updated, all the components of W and H are strictly positive for all iterations. The iteration rules could be described as follows:
L=(N-B+1)×(M-B+1)
Next, we apply non-negative matrix factorization to each sub-block C(i) using the iteration method as defined in (1) and (2) to obtain the corresponding coefficient matrix H(i). This process could be described as follows: [W(i), H(i)]=Nmf (C(i), R, P)
M
m1 H r ,m Vn,m WH n,m Wn,r Wn,r M m1 H r ,m
where n=1,2…,N; m=1,2,…,M; r=1,2,...,R. Aforementioned rules correspond to the following cost function which is known as the generalized Kullback-Leibler (KL) divergence: Vm, n N M F n 1 m 1 Vm, n log Vm, n WH m, n (3) WH m, n If R
