A New Watermarking Algorithm for Point Model Using Angle Quantization Index Modulation. Feng Xiaoqing

Transcription

1 4th National Conference on Electrical, Electronics and Computer Engineering (NCEECE 015) A Ne Watermarking Algorithm for Point Model Using Angle Quantization Index Modulation Feng Xiaoqing Institute of Computer Application echniques, Zhejiang University of Finance & Economics, China zllinda13@sohu.com Keyords: point cloud; Angle Quantization Index Modulation; PCA Abstract. Point cloud models are idely used in industry. It is also faced ith increasingly serious copyright protection issues. A ne atermarking algorithm of 3D point cloud model using angle quantization index modulation is proposed. At first, a point cloud model is segmented into many patches according to the length of atermark information. hen, for each patch, 1 bit atermark is embedded into by modulating the angle of feature signal. Experiments sho that the algorithm is certain robustness against affine transformation, reorder and lo intensity of noise. Introduction Digital atermarking by inserting some invisible information is an effective method to protect copyright of digital media. People mainly focused on images [1] and videos []. And fe orks have been done on point model. Hoever, point cloud model can express a complicated object only by point information. his character makes point cloud used idely in fields of computer graphic. It is becoming urgent to research a practical atermark algorithm for point clouds. So far, several point cloud atermark schemes have been developed. A fast hierarchical clustering algorithm is applied to partition patches by Cott [3]. hen, Laplacian eigen-functions of each patch are achieved to insert atermark. It is robust against attacks, including affine transformations, cropping, noising and resampling. Ohbuchi et al. extend a mesh atermarking algorithm to point models [4]. So, it need generates a non-manifold mesh for each cluster of the points. hen, avelet-based spectral analysis technique proposed by Zachi Karni[5] is applied to insert into atermark. o atermark algorithms in above are non-blind atermark because original point model is need provided during extraction. Zhu proposed an improved AQIM algorithm [6], and prove the effectiveness of the scheme on images. In this paper, e extend this image AQIM algorithm to 3D point cloud models. Because there is not inherent order to sho point cloud like image from left to right, a point cloud model should be sorted in a certain order. Furthermore, for decreasing the distortion causing by embedding atermark into model, a point model need to divided into many groups according to the numbers of atermark bit. For each group, 1 bit atermark are embedded into by an angle quantization index modulation scheme. he remainder of this paper is organized as follos. In Section, related ork is described. An improved AQIM atermarking is described in detail in Section 3. he performance of algorithm is shon in section 4. Finally the future ork is looked forard in Section 5. elated orks Watermarking algorithms based on QIM he QIM scheme proposed by Chen et al. [7] modulate the host signal to its closest code ords according to the atermark bit, as shon in figure 1. Dither modulation (DM) is a kind of basic implementation of QIM. his algorithm can keep a better balance beteen imperceptible, atermark capacity and robustness. So, QIM algorithm is idely used in image atermarking scheme he authors - Published by Atlantis Press 963

2 1-1 1 x Δ Figure 1 Principle of QIM Hoever, the QIM atermarking method does not resist against some attacks, for example, compensation and scaling. For improving the performance of atermarking, a lot of efforts have been done in terms of choosing a suitable quantization feature. hus, many improved methods based on QIM have been proposed, such as the spread-transform dither modulation (SDM) [8], the logarithmic QIM (LQIM) [9], and the angle QIM (AQIM) method [10]. SDM is as an extension of DM in [7], projection feature is quantized along a random direction, hich makes SDM has significant advantages. Logarithmic transform and non-uniform quantization step are used in LQIM, hich makes it can resist against scaling attack. AQIM first introduced in [10] is an extension of the QIM to angle. he different ith traditional QIM method, the angle is quantized instead of quantizing the amplitude values. he angle of vector is changed to the most closed codeline according to embedded atermark bit as shon in Figure.. AQIM algorithm can be simplified described as folloing: 1) he angle of the host vector is quantized according to quantizers Q(). θ + m Q( θ ) = + m ) Change the angle of the vector to closest code ords to obtain the atermarked vector. Figure AQIM algorithm Figure.3 he relationship beteen x, y, z and r,θ,φ Although the types of a carrier signal are not any restricted in QIM, they are not directly applied to 3D model. Darazi [11] developed a sparse QIM for 3D mesh models. he scheme of quantization the distance of vertex in the spherical coordinate system makes the algorithm robust to affine transformation. In our QIM of 3D point model, e adopt Darazi s scheme to against affine transformation. he atermarking algorithm We are inspired by papers [6,10]. And e try to apply this algorithm [6] to 3D point cloud model. In this section, a novel atermarking algorithm for point cloud model based on AQIM ill be descried in detail. he block diagram of this method is shon in Figure

3 Figure 4 he block diagram of the atermark algorithm A ne coordinate system of a point cloud model is constructed by PCA, and then, the Cartesian coordinates vi = ( xi, yi, zi) is converted into the spherical coordinates qi = ( ri, qi, ϕi), as shon in figure 3. A distance set D= { ri r1, r,... rn, ri < r i + 1} is divided into some bins according to the length of atermark. For each group, e calculate the angle 1 r1 r... r j... n = =..., j = n r r... r m p+ 1 q n, q = n n. θ = arccos m mu u. Here, In our algorithm, atermarking is embedded by modulating the angle ofθ m. o quantizers QQ 0 ( ) and QQ 1 ( ) are constructed, (, ) d Q Ζ Ζ 1 d 1 0 Ζ = + d and Q1 ( Ζ, ) = d + +. he signal of θ m is quantized by choosing one of quantizers, θ = Q( θm, ), { 1,1}. If θ [ 1,1], θ = θ ± In our embedding, the step size Δ=0.00, hich is an empirical value. Futhermore, atermarked angle signal A is required to satisfy a condition of θa = θ, here θ A has the same definition as θ. he embedding region is the surface of a circular cone ith the axis u and the angle θ A. For getting the minimize distortion causing by embedding, the embedding function is considered as θ project on the cone. Paper [6] descirbe the geometric interpretation of atermark embedding function. Aaccording to [6], = d d and d = λ d + µ Xd can be achieved. Moreover, the value of d satisfies the conditions = 1 and X = cos( θ ). According to these analysis in above, d d d d m 965

4 λ = 1 cos ( θ ) 1 cos ( θ ) atermarked signal and µ = cos( θ ) λcos( θ ) can be calculated. At last, e ill get the, = r 1 r rn bit [... ]. Watermark extracted he process of extraction algorithm is alike to embed process. For achieving the sort order of the original model, resampling operation must be done. he angle of attacked signal f A is calculated. At last, a atermark is extracted by the minimal distance decoder, = arg min θ Q ( θ ). he bit error rate (BE) is used for judging hether there are m { 1,1} A m A atermark embedded in a point model. Simulation results Embedding atermark ill cause geometrical distortion of a point model. HausdorffDist is a common evaluating indicator. So, e use HausdorffDist [1] of r i beteen original and atermarked point model. able 1 provides information of tested point cloud models. In the simulations, a 64 bits of atermark is embedded into a point model. able 1 Point cloud models Original Model NeVenus (10558 points) fo1 (1083 points) miscdino (3984 points) Watermarked Model HausdorffDist ) Affine transformation Affine transformation includes translation, scaling and rotation, hich are a common operation rather than any of attacks. hus, robustness against these operations is very important for a reversible atermark scheme. he simulation experiments of similarity transformation are shon in able. ) eordering Distances beteen points and the center of model is sorted in ascending order, atermark can be integrality extracted after model is attacked by reordering. 3) Noising Binary random noise is added to each vertex of line entities ith different error rates on the model. he experiment results of noising attacks are shon in able 3 and figure

5 Conclusion In this ne atermarking scheme based on AQIM, a point model is divided into many patches according to the numbers of atermarking bit. hen, 1 bit atermark information is embedded into a patch. he experimental results sho that the introduced algorithm is certain robust against some attacks, such as affine transformation, reorder and lo intensity of noise. Hoever, e find that BEs ill become greater ith the increasing of noise intensity. able Experiment results Model ype attacks NeVenus fo1 miscdino similarity transformation re-order strength of noising 0.5% 1/ % 13/64 9/64 5/64 % 6/64 31/64 34/64 5% 8/64 8/64 39/64 Figure 5 Noising attack Acknoledgment his ork is supported by the National Natural Science Foundation of China (No ). eferences [1] E. Nezhadarya, Z. J. Wang,. K. Ward, "obust image atermarking based on multiscale gradient direction quantization". IEEE rans. Inf. Forensics Security, 6( 4), (011), [] H. Y. Chen, Y. S. Zhu,"A robust video atermarking algorithm based on singular value decomposition and slope-based embedding technique". Multimed ools App. DOI /s , 01 [3] D. Cotting,. Weyrich, M. Pauly, M. Gross, "obust Watermarking of Point Sampled Geometry". In: the Proceedings of the international Conference on Shape Modeling and Application, Italy, 004: 33-4 [4] Ohbuchi., Mukaiyama A., akahashi S. "Watermarking a 3D shape model defined as a point set". In: Proceedings of the International Conference on Cyber orlds (CW04), okyo, 004, [5] S. Kanai, H. Date,. Kishinami, "Digital atermarking for 3D polygons using multiresolution avelet decomposition". In: Proceedings of the 6th IFIP WG 5. International Workshop on Geometric Modeling, okyo, 1998, B. Chen and G. W. Wornell, "Quantization index 967

6 modulation: a class of provably good methods for digital atermarking and information embedding". IEEE rans. Inf. heory, 47(4), (001), [6] X. S. Zhu, S. L. Pen, "Novel Quantization Watermarking Based on andom Angle Modulation". In: 011 Seventh International Conference on Computational Intelligence and Security. 16(7), (011), , [7] B. Chen, and G. W. Wornell, "Preprocessed and post processed quantization index modulation methods for migital atermarking", Proc. of the SPIE International Conference on Security and Watermarking of Multimedia, (000), [8] B. Chen, and G. W. Wornell, "Quantization index modulation: a class of provably good methods for digital atermarking and information embedding", Information heory IEEE ransactions on, 47(4), (001), [9] N. K. Kalantari, and S. M. Ahadi, "A logarithmic quantization index modulation for perceptually better data hiding", IEEE transactions on image processing : a publication of the IEEE Signal Processing Society, 19(6), (010), [10] F. Our ıque, V. Licks,. Jordan, and F. P erez-gonz` alez, "Angle qim :a novel atermark embedding scheme robust against amplitude scaling distortions". In Proc. Int. Conf. Acoustics, Speech and Signal Processing, (005), [11]. Darazi,. Hu, and B. Macq, "Applying spread transform dither modulation for 3D-mesh atermarking by using perceptual models", In Proc. IEEE Int. Conf. Acoust., Speech, and Signal Processing (ICASSP'10), Mar. 19, (010), [1] 968