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CN 34-1054/N

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Open AccessOpen Access JUSTC Original Paper

A fast algorithm of image moments in copy-move forgery detection

  • 1.

    School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007, China

  • 2.

    Fujian Provincial University Engineering Research Center of Big Data Analysis and Application, Fujian Normal University, Fuzhou 350007, China

Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2016.09.005
  • Received Date: 01 March 2016
  • Accepted Date: 17 September 2016
  • Rev Recd Date: 17 September 2016
  • Publish Date: 30 September 2016
    Abstract

  • Abstract

    In copy-move forgery detection, feature extraction is an important step. The image moments (e.g., Zernike moments, radial harmonic Fourier moments, Exponential Fourier moments) are common feature vectors. In view of the excessive length of running time of most existing feature extraction algorithms, a fast algorithm of image moments in copy-move forgery detection was proposed. Integral expression should be discretized and turn integration turned into sum. In the final discretization expression, we can divide it into two parts. One is the fixed section, the other is the grey level of the image. In the classical computing algorithm of image moments, the two parts should be calanlated Num times to get their product if Num image moments are to be obtoined. A fast computing method was put forward to calculate the two parts independently. The fixed parts are calculated just once and the grey level Num times before the product was obtained. This reduced the running time because of the decline of the computing times. If the resolution ratios of the images are invariant and the numbers of the image moments sufficiently large, the fast algorithm of image moments can greatly reduce the running time compared with the classical method.

    Abstract

    In copy-move forgery detection, feature extraction is an important step. The image moments (e.g., Zernike moments, radial harmonic Fourier moments, Exponential Fourier moments) are common feature vectors. In view of the excessive length of running time of most existing feature extraction algorithms, a fast algorithm of image moments in copy-move forgery detection was proposed. Integral expression should be discretized and turn integration turned into sum. In the final discretization expression, we can divide it into two parts. One is the fixed section, the other is the grey level of the image. In the classical computing algorithm of image moments, the two parts should be calanlated Num times to get their product if Num image moments are to be obtoined. A fast computing method was put forward to calculate the two parts independently. The fixed parts are calculated just once and the grey level Num times before the product was obtained. This reduced the running time because of the decline of the computing times. If the resolution ratios of the images are invariant and the numbers of the image moments sufficiently large, the fast algorithm of image moments can greatly reduce the running time compared with the classical method.
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    • References(15)
  • [1]
    CHRISTLEIN V, RIESS C, JORDAN J, et al. An evaluation of popular copy-move forgery detection approaches[J]. IEEE Transactions on Information Forensics and Security, 2012, 7(6): 1841-1854.
    [2]
    RYU S J, LEE M J, LEE H K. Detection of copy-rotate-move forgery using Zernike moments[C]// Proceedings of the 12th International Conference on Information Hiding. Springer, 2010: 51-65.
    [3]
    RYU S J, KIRCHNER M, LEE M J, et al. Rotation invariant localization of duplicated image regions based on Zernike moments [J]. IEEE Transactions on Information Forensics and Security, 2013, 8(8): 1355-1370.
    [4]
    秦娟, 李峰, 向凌云, 等. 采用圆谐-傅里叶矩的图像区域复制粘贴篡改检测[J]. 中国图象图形学报, 2013, 18(8): 919-923.
    QIN Juan, LIFeng, XISNG Lingyun, et al. Detection of image region copy-move forgery using radial harmonic Fourier moments[J]. Journal of Image and Graphics, 2013, 8(8): 919-923.
    [5]
    赖玥聪, 黄添强, 蒋仁祥. 采用指数矩的图像区域复制粘贴篡改检测[J]. 中国图象图形学报, 2015, 20(9): 1212-1221.
    LAI Y C, HUANG T Q, JIANG R X. Image region copy-move forgery detection based on Exponential-Fourier moments[J]. Journal of Image and Graphics, 2015,20(9): 1212-1221.
    [6]
    LI Y N. Image copy-move forgery detection based on polar cosine transform and approximate nearest neighbor searching [J]. Forensic science international, 2013, 224(1): 59-67.
    [7]
    LI L D, LI S S, ZHU H C, et al. Detecting copy-move forgery under affine transforms for image forensics [J]. Computers & Electrical Engineering, 2014, 40(6): 1951-1962.
    [8]
    姜永静. 指数矩及其在模式识别中的应用[D]. 北京:北京邮电大学, 2011.
    [9]
    TEAGUE M R. Image analysis via the general theory of moments [J]. Journal of the Optical Society of America, 1980, 70(8): 920-930.
    [10]
    REN H P, PING Z L, BO W, et al. Multidistortion-invariant image recognition with radial harmonic Fourier moments[J]. Journal of the Optical Society of America, 2003, 20(4): 631-637.
    [11]
    孟敏, 平子良. 基于指数矩的图像分解和重建 [J]. 内蒙古师范大学学报, 2011, 40(3): 258-260.
    [12]
    YAP P T, JIANG X D, KOT A C. Two-dimensional polar harmonic transforms for invariant image representation [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2010, 32(7): 1259-1270.
    [13]
    MUKUNDAN R, RAMAKRISHNAN K R. Fast computation of Legendre and Zernike moments [J] .Pattern Recognition, 1995, 28(9): 1433-1442.
    [14]
    UCID. Uncompressed Colour Image Database [DB/OL]. http://homepages.lboro.ac.uk/~cogs/datasets/ucid/ucid.html.
    [15]
    GRIP. Image processing research group of Università degli Studi di Napoli, Federico II[DB/OL]. http://www.grip.unina.it/.)
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    [1]
    CHRISTLEIN V, RIESS C, JORDAN J, et al. An evaluation of popular copy-move forgery detection approaches[J]. IEEE Transactions on Information Forensics and Security, 2012, 7(6): 1841-1854.
    [2]
    RYU S J, LEE M J, LEE H K. Detection of copy-rotate-move forgery using Zernike moments[C]// Proceedings of the 12th International Conference on Information Hiding. Springer, 2010: 51-65.
    [3]
    RYU S J, KIRCHNER M, LEE M J, et al. Rotation invariant localization of duplicated image regions based on Zernike moments [J]. IEEE Transactions on Information Forensics and Security, 2013, 8(8): 1355-1370.
    [4]
    秦娟, 李峰, 向凌云, 等. 采用圆谐-傅里叶矩的图像区域复制粘贴篡改检测[J]. 中国图象图形学报, 2013, 18(8): 919-923.
    QIN Juan, LIFeng, XISNG Lingyun, et al. Detection of image region copy-move forgery using radial harmonic Fourier moments[J]. Journal of Image and Graphics, 2013, 8(8): 919-923.
    [5]
    赖玥聪, 黄添强, 蒋仁祥. 采用指数矩的图像区域复制粘贴篡改检测[J]. 中国图象图形学报, 2015, 20(9): 1212-1221.
    LAI Y C, HUANG T Q, JIANG R X. Image region copy-move forgery detection based on Exponential-Fourier moments[J]. Journal of Image and Graphics, 2015,20(9): 1212-1221.
    [6]
    LI Y N. Image copy-move forgery detection based on polar cosine transform and approximate nearest neighbor searching [J]. Forensic science international, 2013, 224(1): 59-67.
    [7]
    LI L D, LI S S, ZHU H C, et al. Detecting copy-move forgery under affine transforms for image forensics [J]. Computers & Electrical Engineering, 2014, 40(6): 1951-1962.
    [8]
    姜永静. 指数矩及其在模式识别中的应用[D]. 北京:北京邮电大学, 2011.
    [9]
    TEAGUE M R. Image analysis via the general theory of moments [J]. Journal of the Optical Society of America, 1980, 70(8): 920-930.
    [10]
    REN H P, PING Z L, BO W, et al. Multidistortion-invariant image recognition with radial harmonic Fourier moments[J]. Journal of the Optical Society of America, 2003, 20(4): 631-637.
    [11]
    孟敏, 平子良. 基于指数矩的图像分解和重建 [J]. 内蒙古师范大学学报, 2011, 40(3): 258-260.
    [12]
    YAP P T, JIANG X D, KOT A C. Two-dimensional polar harmonic transforms for invariant image representation [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2010, 32(7): 1259-1270.
    [13]
    MUKUNDAN R, RAMAKRISHNAN K R. Fast computation of Legendre and Zernike moments [J] .Pattern Recognition, 1995, 28(9): 1433-1442.
    [14]
    UCID. Uncompressed Colour Image Database [DB/OL]. http://homepages.lboro.ac.uk/~cogs/datasets/ucid/ucid.html.
    [15]
    GRIP. Image processing research group of Università degli Studi di Napoli, Federico II[DB/OL]. http://www.grip.unina.it/.)
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