A Robust Embedding Scheme and an Efficient Evaluation Protocol for 3D Meshes Watermarking

A Robust Embedding Scheme and an Efficient Evaluation Protocol for 3D Meshes Watermarking

Saoussen Ben Jabra (RIADI Laboratory, Team of Research SIIVA, High Institute of Computer Science, University of Tunis El Manar, Tunisia) and Ezzeddine Zagrouba (RIADI Laboratory, Team of Research SIIVA, High Institute of Computer Science, University of Tunis El Manar, Tunisia)
Copyright: © 2011 |Pages: 17
DOI: 10.4018/ijcvip.2011040102
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Abstract

This paper proposes two main contributions. In the first one, a 3D mesh watermarking using Maximally Stable Meshes detection and multi-signatures embedding is presented. The originality of this scheme is to detect the attack type applied on marked mesh. In plus, it is robust against numerous attacks, blind and invisible. The proposed scheme uses the Maximally Stable meshes (MSMs) to insert signature. After MSMs detection using an extension of Maximally Stable Efficient Regions, three MSMs are selected to be marked. Then, three different signatures are embedded using three different watermarking schemes. This embedding allows knowing the type of the applied attack by detecting which of the signatures resisted. In more, it maximizes robustness by profiting from advantages of every scheme. The second contribution is a new evaluation protocol for 3D watermarking which allows generating a performance score for 3D mesh watermarking schemes. This protocol is based on six criteria having different weights in performance score computing. Finally, this protocol is used to evaluate the proposed watermarking scheme and to compare it with other algorithms. The obtained results verified the good performances of the proposed algorithm which presents the highest score.
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Mesh Watermarking Overview

Recently, 3D meshes have been widely used in virtual reality, medical imaging, video games and computer aided design. A 3D mesh is a collection of polygonal facets targeting to constitute an appropriate approximation of a real 3D object. It possesses three different combinatorial elements: vertices, edges and facets. From another viewpoint, a mesh can also be completely described by two kinds of information. The geometry information gives the positions (coordinates) of all its vertices, while the connectivity information provides the adjacency relations between the different combinatorial elements. Although there are many other 3D representations, such as cloud of points, parametrized surface, implicit surface and voxels, 3D mesh has been a standard of numerical representation of 3D objects thanks to its simplicity and usability. Furthermore, it is quite easy to convert other representations to 3D mesh, which is considered as an effective model. This fact partially explains why much of the work in the area of 3D watermarking deals with 3D triangle meshes. Although some schemes have been proposed to watermark NURBS (Lee, 2002) and point-sampled surfaces (Cotting et al., 2004).

Existing techniques concerning 3D meshes can be classified in two main categories, depending on whether the watermark is embedded in the spatial domain (by modifying the geometry or the connectivity) or in the frequency domain (by modifying some kind of mesh transformation like spectral decomposition or wavelet transformation).

Spatial Schemes

They can be classified in two main categories: geometric schemes which modify vertices coordinates and topologic schemes which modify vertices connectivity.

Geometric Schemes

Harte et al. (2002) have proposed a blind watermarking scheme to embed a watermark in the point positions. One bit is assigned to each point: 1 if the point is outside a bounding volume defined by its point neighborhood and 0 otherwise. This bounding volume may be either defined by a set of bounding planes or by a bounding ellipsoid. The Vertex Flood Algorithm (VFA) (Benedenes, 1999) embeds also information in point positions. Given a point p in the mesh, all points are clustered in subsets Sk accordingly with their distance to p. Each non-empty subset is subdivided in m + 2 intervals in order to encode m bits. The distance of each point in a subset is modified so that it is placed on the middle of one of the m+2 intervals.

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