Abstract
A new blind watermarking scheme for three-dimensional point-cloud models is proposed based on vertex curvature to achieve an appropriate trade-off between transparency and robustness. The root mean square curvature of local set of every vertex is first calculated for the three-dimensional point-cloud model and then the vertices with larger root mean square curvature are used to carry the watermarking information; the vertices with smaller root mean square curvature are exploited to establish the synchronization relation between the watermark embedding and extraction. The three-dimensional point-cloud model is divided into ball rings, and the watermarking information is inserted by modifying the radial radii of vertices within ball rings. Those vertices taking part in establishing the synchronization relation do not carry the watermarking information; therefore, the synchronization relation is not affected by the embedded watermark. Experimental results show the proposed method outperforms other well-known three-dimensional point-cloud model watermarking methods in terms of imperceptibility and robustness, especially for against geometric attack.
Highlights
Over the past few years, three-dimensional (3D) models are more and more important to business objectives
1 Stage 1: distinguish the vertices of the 3D model 2 for each vertex Vido 3 Calculate root mean square curvature (RMSC) (Krmsc(Vi)) value of its local set using equation (4). 4 if Krmsc(Vi) is not less than Kh, vertex Vi is a vertex of the candidate set Sf else vertex Vi is assigned to the reference set Sr. 5 end 6 7 Stage 2: establish the synchronization relation 8 Build a new coordinate space using the steps outlined in section ‘‘Establishing the synchronization information.’’ 9 Cartesian coordinate of the model is converted to spherical coordinate
We present a blind and robust watermarking method for 3D point-cloud models
Summary
Over the past few years, three-dimensional (3D) models are more and more important to business objectives. In order to be still able to locate the watermarked vertices in the case of the disorder of vertices of 3D point-cloud model, the synchronization relation is first established; the model is separated into ball rings in terms of radial radius and the watermark bit is repeatedly inserted into vertices of each ball ring. 4 if Krmsc(Vi) is not less than Kh, vertex Vi is a vertex of the candidate set Sf else vertex Vi is assigned to the reference set Sr. 5 end 6 7 Stage 2: establish the synchronization relation 8 Build a new coordinate space using the steps outlined in section ‘‘Establishing the synchronization information.’’ 9 Cartesian coordinate of the model is converted to spherical coordinate. The main steps of watermark extraction were summarized as below
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