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A robust 3D point cloud watermarking method based on the graph Fourier transform

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Abstract

Many modern applications make use of 3D modeling and / or reconstruction of complex objects, such as historical monuments and entire urban centers. One of the most common representations of these 3D models is by point clouds, which are a dense set of points irregularly organized in a 3D coordinate system. Usually, the acquisition methods are highly expensive due to the necessary equipment and size of these models. This factor motivates the proposal of watermarking techniques to guarantee the copyright protection as well as to detect illegal copies. This paper presents a non-blind watermarking method for 3D point clouds. The method is based on the graph Fourier transform, a recently introduced signal processing tool which has been applied to signals lying over arbitrarily irregular domains. Unlike other published works regarding point cloud watermarking, instead of inserting the bit sequence in the models’ spatial coordinates, in this work the bits are embedded in the color information attributed in each point of a cloud. Simulation results show high imperceptibility and robustness against several attacks, such as affine transformations, reordering, noise addition and cropping.

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Notes

  1. Such β values have been empirically chosen, aiming at maintaining a reasonable degradation of the watermarked point clouds and an acceptable robustness level against specific attacks; details are given in the next sections.

  2. From this point forward, we will refer to the noise added in an attack by specifying a percentage value of noise amplitude; such a value actually corresponds to a × 100%, where a is the amplitude used to produce the noisy signal as in (23).

References

  1. Agarwal P, Prabhakaran B (2009) Robust blind watermarking of point-sampled geometry. IEEE Trans Inform Forensics Secur 4(1):36

    Article  Google Scholar 

  2. Alface PR, Macq B (2007) From 3D mesh data hiding to 3D shape blind and robust watermarking: a survey. In: Transactions on data hiding and multimedia security II. Springer, pp 91–115

  3. Asikuzzaman M, Alam MJ, Lambert AJ, Pickering MR (2016) Robust DT CWT-based DIBR 3D video watermarking using chrominance embedding. IEEE Trans Multimed 18(9):1733

    Article  Google Scholar 

  4. Asikuzzaman M, Pickering MR (2018) An overview of digital video watermarking. IEEE Trans Circuits Syst Video Technol 28(9):2131

    Article  Google Scholar 

  5. Bhowmik D, Oakes M, Abhayaratne C (2016) Visual attention-based image watermarking. IEEE Access 4:8002

    Article  Google Scholar 

  6. Bors AG, Luo M (2013) Optimized 3D watermarking for minimal surface distortion. IEEE Trans Image Process 22(5):1822

    Article  Google Scholar 

  7. Cai Z, Chin TJ, Bustos AP, Schindler K (2019) Practical optimal registration of terrestrial LiDAR scan pairs. ISPRS J Photogramm Remote Sens 147:118

    Article  Google Scholar 

  8. Chan HT, Hwang WJ, Cheng CJ (2015) Digital hologram authentication using a hadamard-based reversible fragile watermarking algorithm. J Disp Technol 11 (2):193

    Article  Google Scholar 

  9. Chen B, Wornell GW (2001) Quantization index modulation: a class of provably good methods for digital watermarking and information embedding. IEEE Trans Inf Theory 47(4):1423

    Article  MathSciNet  Google Scholar 

  10. Chen S, Varma R, et al. (2015) Discrete signal processing on graphs: sampling theory. IEEE Trans Signal Process 63(24):6510

    Article  MathSciNet  Google Scholar 

  11. Cheng CJ, Hwang WJ, Zeng HY, Lin YC (2014) A fragile watermarking algorithm for hologram authentication. J Disp Technol 10(4):263

    Article  Google Scholar 

  12. Cotting D, Weyrich T, Pauly M, Gross M (2004) Robust watermarking of point-sampled geometry. In: Shape modeling applications, 2004. Proceedings. IEEE, pp 233–242

  13. Cox I, Miller M, Bloom J, Fridrich J, Kalker T (2007) Digital watermarking and steganography. Morgan Kaufmann, San Mateo

    Google Scholar 

  14. Fedorenko R, Gabdullin A, Fedorenko A (2018) Global UGV path planning on point cloud maps created by UAV. In: 2018 3rd IEEE international conference on intelligent transportation engineering (ICITE). IEEE, pp 253–258

  15. Garg H, Agrawal S, Varshneya G (2013) A non-blind image based watermarking for 3-D polygonal mesh using its geometrical properties. In: 2013 Sixth international conference on contemporary computing (IC3). IEEE, pp 313–318

  16. Golubski AJ, Westlund EE, et al. (2016) Ecological networks over the edge: hypergraph trait-mediated indirect interaction (TMII) structure. Trends in Ecology & Evolution 31(5):344

    Article  Google Scholar 

  17. Huang CC, Yang YW, Fan CM, Wang JT (2013) A spherical coordinate based fragile watermarking scheme for 3D models. In: International conference on industrial, engineering and other applications of applied intelligent systems. Springer, pp 566–571

  18. Itier V, Puech W (2017) High capacity data hiding for 3D point clouds based on static arithmetic coding. Multimed Tools Appl 76(24):26421

    Article  Google Scholar 

  19. Jain RK, Moura JMF, et al. (2014) Big data+ big cities: graph signals of urban air pollution. IEEE Signal Process Mag 31(5):130

    Article  Google Scholar 

  20. Karni Z, Gotsman C (2000) Spectral compression of mesh geometry. In: Proceedings of the 27th annual conference on computer graphics and interactive techniques. ACM Press/Addison-Wesley Publishing Co., pp 279–286

  21. Klyuzhin IS, Sossi V (2017) PET image reconstruction and deformable motion correction using unorganized point clouds. IEEE Trans Med Imaging 36(6):1263

    Article  Google Scholar 

  22. Koz A, Triantafyllidis GA, Alatan AA (2008) 3D watermarking: techniques and directions. In: Three-dimensional television. Springer, pp 427–470

  23. Lie WN, Lin GS, Cheng SL (2006) Dual protection of jpeg images based on informed embedding and two-stage watermark extraction techniques. IEEE Trans Inform Forensics Secur 1(3):330

    Article  Google Scholar 

  24. Liu J, Yang Y, Ma D, Wang Y, Pan Z (2018) A watermarking algorithm for 3D point cloud models using ring distribution. In: Transactions on Edutainment XIV. Springer, pp 56–68

  25. Liu Y, Prabhakaran B, Guo X (2012) Spectral watermarking for parameterized surfaces. IEEE Trans Inf Forensics Secur 7(5):1459

    Article  Google Scholar 

  26. Luo H, Lu ZM, Pan JS (2006) A reversible data hiding scheme for 3D point cloud model. In: 2006 IEEE international symposium on signal processing and information technology. IEEE, pp 863–867

  27. Luo M, Bors AG (2011) Surface-preserving robust watermarking of 3-D shapes. IEEE Trans Image Process 20(10):2813

    Article  MathSciNet  Google Scholar 

  28. Mei J, Moura JMF (2017) Signal processing on graphs: causal modeling of unstructured data. IEEE Trans Signal Process 65(8):2077

    Article  MathSciNet  Google Scholar 

  29. Mekarsari Y, Setiadi D, Sari C, Rachmawanto E (2018) Non-blind rgb image watermarking technique using 2-level discrete wavelet transform and singular value decomposition. In: International conference on information and communications technology (ICOIACT). IEEE, pp 623–627

  30. Menna F, Nocerino E, Remondino F, Dellepiane M, Callieri M, Scopigno R (2016) 3D digitization of an heritage masterpiece-a critical analysis on quality assessment. The international Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences 41:B5

    Google Scholar 

  31. Meyer M, Desbrun M, Schröder P, Barr AH (2003) Discrete differential-geometry operators for triangulated 2-manifolds. In: Visualization and mathematics III. Springer, pp 35–57

  32. Ohbuchi R, Mukaiyama A, Takahashi S (2004) Watermarking a 3D shape model defined as a point set. In: 2004 international conference on cyberworlds. IEEE, pp 392–399

  33. Ortega A, Frossard P, Kovacevic J, Moura JMF, Vandergheynst P (2018) Graph signal processing: overview, challenges, and applications. Proc IEEE 106(5):808

    Article  Google Scholar 

  34. Qi K, Dong-qing X, Da-fang Z (2010) A robust watermarking scheme for 3D point cloud models using self-similarity partition. In: 2010 IEEE international conference on wireless communications, networking and information security (WCNIS). IEEE, pp 287–291

  35. Ribeiro GB, Lima JB (2018) Graph signal processing in a nutshell. J Commun Inf Syst 33(1):1

    Google Scholar 

  36. Rolland-Neviere X, Doërr G, Alliez P (2014) Triangle surface mesh watermarking based on a constrained optimization framework. IEEE Trans Inform Forensics Secur 9(9):1491

    Article  Google Scholar 

  37. Sandryhaila A, Moura JMF (2014) Big data analysis with signal process. on graphs: representation and process. of massive data sets with irreg. IEEE Signal Process Mag 31(5):80

    Article  Google Scholar 

  38. Sandryhaila A, Moura JMF (2014) Discrete signal processing on graphs: frequency analysis. IEEE Trans Signal Process 62(12):3042

    Article  MathSciNet  Google Scholar 

  39. Shao J, Zhang W, Mellado N, Grussenmeyer P, Li R, Chen Y, Wan P, Zhang X, Cai S (2018) Automated markerless registration of point clouds from TLS and structured light scanner for heritage documentation. J Cultural Heritage

  40. Shuman DI, Narang SK, Frossard P, Ortega A, Vandergheynst P (2013) The emerging field of signal processing on graphs: extending high-dimensional data analysis to networks and other irregular domains. IEEE Signal Process Mag 30 (3):83

    Article  Google Scholar 

  41. Shuman DI, Ricaud B, Vandergheynst P (2012) A windowed graph Fourier transform. In: Statistical signal processing workshop (SSP), 2012 IEEE. IEEE, pp 133–136

  42. Su Q, Niu Y, Wang G, Jia S, Yue J (2014) Color image blind watermarking scheme based on qr decomposition. Signal Process 94:219

    Article  Google Scholar 

  43. Toschi I, Ramos M, Nocerino E, Menna F, Remondino F, Moe K, Poli D, Legat K, Fassi F, et al. (2017) Oblique photogrammetry supporting 3D urban reconstruction of complex scenarios. International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences 42:519

    Article  Google Scholar 

  44. Tsai YY (2016) An efficient 3D information hiding algorithm based on sampling concepts. Multimed Tools Appl 75(13):7891

    Article  Google Scholar 

  45. Wang C, Ni J, Huang J (2012) An informed watermarking scheme using hidden markov model in the wavelet domain. IEEE Trans Inform Forensics Secur 7 (3):853

    Article  Google Scholar 

  46. Wang CM, Wang PC (2005) Data hiding approach for point-sampled geometry. IEICE Trans Commun 88(1):190

    Article  Google Scholar 

  47. Wang H, Wang B, Liu B, Meng X, Yang G (2017) Pedestrian recognition and tracking using 3D LiDAR for autonomous vehicle. Robot Auton Syst 88:71

    Article  Google Scholar 

  48. Wang J, Wu Q, Remil O, Yi C, Guo Y, Wei M (2018) Modeling indoor scenes with repetitions from 3D raw point data. Comput Aided Des 94:1

    Article  Google Scholar 

  49. Xiaoqing F (2015) A watermarking for 3D point cloud model using distance normalization modulation. In: 2015 4th international conference on computer science and network technology (ICCSNT), vol 1. IEEE, pp 1449–1452

  50. Yang Y, Pintus R, Rushmeier H, Ivrissimtzis I (2017) A 3D steganalytic algorithm and steganalysis-resistant watermarking. IEEE Trans Visualization Comput Graphics 23(2):1002

    Article  Google Scholar 

  51. Zeng Y, Hu Y, Liu S, Ye J, Han Y, Li X, Sun N (2018) Rt3d: real-time 3-d vehicle detection in lidar point cloud for autonomous driving. IEEE Robotics Automation Lett 3(4):3434

    Article  Google Scholar 

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Acknowledgements

This work was supported in part by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) under Grants 309598/2017-6 and 409543/2018-7, and by Fundação de Amparo à Ciência e Tecnologia do Estado de Pernambuco (FACEPE) under Grant IBPG-1275-3.04/16.

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  1. Department of Electronics and Systems, Federal University of Pernambuco, Recife, PE, Brazil

    Felipe A. B. S. Ferreira & Juliano B. Lima

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  1. Felipe A. B. S. Ferreira
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  2. Juliano B. Lima
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Correspondence to Juliano B. Lima.

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Ferreira, F.A.B.S., Lima, J.B. A robust 3D point cloud watermarking method based on the graph Fourier transform. Multimed Tools Appl 79, 1921–1950 (2020). https://doi.org/10.1007/s11042-019-08296-4

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