Cryptography Reference
In-Depth Information
Mesh-Spectral Domain Schemes
Although the application of 2D vector maps and 3D models are very different,
there are still many similarities between the two data types. They are both
vector data and composed of many vertices. It is possible to apply some 3D
model watermarking methods to 2D vector maps. Ohbuchi et al. proposed a
2D vector map watermarking scheme [14] in mesh-spectral domain. This was
originally used on 3D models [15]. In the algorithm, some techniques in 3D
world can be adapted to process 2D vector data. Firstly, all vertices in the
original map are connected to establish a 2D mesh using
Delaunay Triangula-
tion
. The whole map is adaptively divided into many blocks using the rule
k-d
tree. For each block, a mesh-spectral analysis is performed on the 2D mesh
within the block. The mesh-spectral coe
cients are obtained and have the
same size as the original coordinate sequence in the block. The spectral coef-
ficient sequence is then considered as the cover data for watermarking. The
method of data embedding is similar to the work [7] described in Section 6.2.1.
And the scheme is also a non-blind scheme. Owing to the use of the original
data, the scheme is robust to many attacks such as map rotating, translating,
rotating, map interpolation, simplification, additive noise, and cropping.
6.2.3 Shape-Preserving Method
The algorithms mentioned above are the typical methods for robustly water-
marking 2D vector maps in the spatial or transform domain. By analyzing
the shortcoming of the former works, a statistic based scheme will be further
presented in the remaining part of this section.
Motivation
Considering the main defects of the former works, the proposed scheme will
focus on the following two aspects.
1. Shape Distortion and Cover Data Selection.
A principle used in most former works is to enhance the robustness. This is
done by strictly controlling the distortion of every vertex under the precision
tolerance τ for the sake of keeping the fidelity of the watermarked map. All
former works take the 2D coordinates or their frequency coe
cients as the
cover data to control the distortions of vertices. This criteria is not enough
to meet the requirements of the vector map watermarking. This is because
the detail shape of the map objects is apt to be modified even if the fidelity
of map data is well preserved. An experiment can be done to illustrate the
problem. Figure 6.6(a) is an enlarged part of the original map. Fig. 6.6(b) is
its corresponding watermarked part. Here the raw coordinates were selected
as the cover data and the embedding procedure didnt take account of the
map shape. Although the induced distortion of every vertex in Fig. 6.6(b) is
