Abstract
In this paper, fractional quaternion cosine transforms (FrQCT) is proposed to generalize the conventional fractional cosine transforms (FrCT) to quaternion signal processing in a holistic manner. Firstly, the new transform FrQCT is defined and the proof of its inverse transform is presented. An efficient discrete implementation method of FrQCT is then proposed, in which the relationship between FrQCT and FrCT of four components is used for a quaternion signal. Finally, a new color image copy-move forgery detection algorithm based on FrQCT and modified PatchMatch matching algorithm is proposed to evaluate the performance of the proposed FrQCT. Experimental results on two public datasets (FAU dataset and GRIP dataset) demonstrate that: (a) the proposed efficient implementation method takes only half the computational time of the direct method; (b) the proposed FrQCT-based forgery detection algorithm can achieve a better performance than some state-of-the-art algorithms, especially in the additional operation case.
Similar content being viewed by others
References
Amer YA, Mandy AMS, Youssef ESM (2018) Solving fractional integro-differential equations by using sumudu transform method and Hermite spectral collocation method. Computers Materials & Continua 54(2):161–180
Amerini I, Ballan L, Caldelli R, Bimbo AD, Tongo LD, Serra G (2013) Copy-move forgery detection and localization by means of robust clustering with J-linkage. Signal Process Image Commun 28(6):659–669
Barnes C, Shechtman E, Finkelstein A, Goldman DB (2009) PatchMatch: a randomized correspondence algorithm for structural image editing. ACM Trans Graph 28(3):24
Bashar M, Noda K, Ohnishi N, Mori K (2010) Exploring duplicated regions in natural images. IEEE Trans Image Process. https://doi.org/10.1109/TIP.2010.2046599
Bayram S, Sencar H, Memon N (2009) An efficient and robust method for detecting copy-move forgery. In: Proc. IEEE Int. Conf. Acoustics, Speech, and Signal Processing, pp. 1053-1056
Bi X, Pun CM (2017) Fast reflective offset-guided searching method for copy-move forgery detection. Inf Sci 418:531–545
Bi X, Pun CM, Yuan XC (2016) Adaptive polar based filtering method for image copy-move forgery detection. In: Proc. 2016 IEEE Trustcom-BigDataSE-ISPA, pp. 952-956
Bravo-Solorio S, Nandi AK (2011) Exposing duplicated regions affected by reflection, rotation and scaling. in: Proc. Int. Conf. Acoustics, Speech and Signal Processing, pp. 1880-1883
Cao Y, Zhou Z, Sun X, Cao C (2018) Coverless information hiding based on the molecular structure images of material. Computers, Materials & Continua 54(2):197–207
Chen BJ, Coatrieux G, Chen G, Sun XM, Coatrieux JL, Shu HZ (2014) Full 4-D quaternion discrete Fourier transform based watermarking for color images. Digit Signal Process 28(5):106–119
Chen BJ, Coatrieux G, Wu JS, Dong ZF, Coatrieux JL, Shu HZ (2015) Fast computation of sliding discrete Tchebichef moments and its application in duplicated regions detection. IEEE Trans Signal Process 63(20):5424–5436
Chen BJ, Qi XM, Sun XM, Shi YQ (2017) Quaternion pseudo-Zernike moments combining both of RGB information and depth information for color image splicing detection. J Vis Commun Image R 49:283–290
Chen BJ, Shu HZ, Coatrieux G, Chen G, Sun XM, Coatrieux JL (2015) Color image analysis by quaternion-type moments. J Math Imaging Vis 51(1):124–144
Chen BJ, Zhou CF, Jeon B, Zheng YH, Wang JW (2018) Quaternion discrete fractional random transform for color image adaptive watermarking. Multimed Tools Appl 77(16): 20809–20837
Choi JY, Ro YM, Plataniotis KN (2009) Color face recognition for degraded face images. IEEE Trans Syst Man Cybern B Cybern 39(5):1217–1230
Christlein V, Riess C, Jordan J, Riess C, Angelopoulou E (2012) An evaluation of popular copy-move forgery detection approaches. IEEE Trans Inf Foren Sec 7(6):1841–1854
Cozzolino D, Poggi G, Verdoliva L (2014) Copy-move forgery detection based on patchmatch. In: Proc. 2014 IEEE Int. Conf. Image Processing (ICIP), pp. 5312-5316
Cozzolino D, Poggi G, Verdoliva L (2015) Efficient dense-field copy–move forgery detection. IEEE Trans Inf Foren Sec 10(11):2284–2297
Ell TA, Sangwine SJ (2007) Hypercomplex fourier transforms of color images. IEEE Trans Image Process 16(1):22–35
Feng W, Hu B (2008) Quaternion discrete cosine transform and its application in color template matching. In: Proc. 1st Int. Cong. Image and Signal Processing (CISP 2008), no. 2, pp. 252-256
Fridrich J, Soukal D, Lukáš J (2003) Detection of copy-move forgery in digital images. In: Proc. Digital Forensic Research Workshop
Guo LQ, Dai M, Zhu M (2012) Multifocus color image fusion based on quaternion curvelet transform. Opt Express 20(17):18846–18860
Guo LQ, Zhu M (2011) Quaternion Fourier–Mellin moments for color image. Pattern Recogn 44(2):187–195
Lan RS, Zhou YC (2016) Quaternion-Michelson descriptor for color image classification. IEEE Trans Image Process 25(11):5281–5292
Li YN (2013) Quaternion polar harmonic transforms for color images. IEEE Signal Process Lett 20(8):803–806
Li J, Li XL, Yang B, Sun XM (2015) Segmentation-based image copy-move forgery detection scheme. IEEE Trans Inf Foren Sec 10(3):507–518
Li C, Ma Q, Xiao LM, Ying SH (2016) An image copy move forgery detection method using QDCT. In: Proc. ACM Int. Conf. Internet Multimedia Computing and Service, pp. 5-8
Li JZ, Yu CY, Gupta BB, Ren XC (2018) Color image watermarking scheme based on quaternion Hadamard transform and Schur decomposition. Multimed Tools Appl 77(4):4545–4561
Lin H, Wang C, Kao Y (2009) Fast copy-move forgery detection. WSEAS Trans Signal Process 5(5):188–197
Liu ZJ, Zhao HF, Liu ST (2005) A discrete fractional random transform. Opt Commun 255(4):357–365
Luo W, Huang J, Qiu G (2006) Robust detection of region-duplication forgery in digital images. Proc Int Conf Pattern Recognition 4:746–749
Ma YY, Luo XY, Li XL, Bao ZK, Zhang Y (2018) Selection of rich model steganalysis features based on decision rough set α-positive region reduction. IEEE Trans Circ Syst Vid. https://doi.org/10.1109/TCSVT.2018.2799243
Mendlovic D, Zalevsky Z, Mas D, Garcia J, Ferreira C (1997) Fractional wavelet transform. Appl Opt 36(20):4801–4806
Namias V (1980) The fractional order Fourier transform and its application to quantum mechanics. J Inst Math Applicat 25:241–265
Pei SC, Ding JJ (2002) Fractional cosine, sine, and Hartley transforms. IEEE Trans Signal Process 50(7):1661–1680
Pei SC, Yeh MH (2001) The discrete fractional cosine and sine transforms. IEEE Trans Signal Process 49(6):1198–1207
Ryu SJ, Kirchner M, Lee MJ, Lee HK (2013) Rotation invariant localization of duplicated image regions based on Zernike moments. IEEE Trans Inf Foren Sec 8(8):1355–1370
Subakan ON, Vemuri BC (2011) A quaternion framework for color image smoothing and segmentation. Int J Comput Vis 91(3):233–250
Wang JW, Li T, Shi YQ, Lian SG, Ye JY (2017) Forensics feature analysis in quaternion wavelet domain for distinguishing photographic images and computer graphics. Multimed Tools Appl 76(22):23721–23737
Wang J, Liu G, Li H, Dai Y, Wang Z (2009) Detection of image region duplication forgery using model with circle block. In: Proc. Int. Conf. Multimedia Information Networking and Security, pp. 25-29
Wang X, Liu Y, Xu H, Wang P, Yang H (2016) Robust copy–move forgery detection using quaternion exponent moments. Pattern Anal Applic 21(2):451–467
Wang YQ, Peng ZM (2016) The optimal fractional S transform of seismic signal based on the normalized second-order central moment. J Appl Geophys 129:8–16
Wei DY, Li YM (2013) Different forms of Plancherel theorem for fractional quaternion Fourier transform. Optik 124(24):6999–7002
Xiao B, Li L, Li Y, Li W, Wang G (2017) Image analysis by fractional-order orthogonal moments. Inf Sci 382:135–149
Xu GL, Wang XT, Xu XG (2008) Fractional quaternion Fourier transform, convolution and correlation. Signal Process 88(10):2511–2517
Yu CY, Li JZ, Li X, Ren XC, Gupta BB (2017) Four-image encryption scheme based on quaternion Fresnel transform, chaos and computer generated hologram. Multimed Tools Appl 77(4):4585–4608
Zandi M, Mahmoudi-Aznaveh A, Talebpour A (2016) Iterative copy-move forgery detection based on a new interest point detector. IEEE Trans Inf Foren Sec 11(11):2499–2512
Acknowledgements
This work was supported by the NSFC under Grants 61572258, 61772281, 61771231, 61602253, and 61672294, the Natural Science Foundation of Jiangsu Province of China under Grants BK20151530, and BK20150925, the PAPD fund, sponsored by Qing Lan Project.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Chen, B., Yu, M., Su, Q. et al. Fractional quaternion cosine transform and its application in color image copy-move forgery detection. Multimed Tools Appl 78, 8057–8073 (2019). https://doi.org/10.1007/s11042-018-6595-z
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11042-018-6595-z