Cryptography Reference
In-Depth Information
Noise Distortion
There are mainly two sources which can introduce noise into vector maps. The
first one is by some kind of daily work. For example, there are several popular
file formats in the GIS world. The transformation among those formats could
slightly distort the data. The other is a malicious attack. Attackers attempt
to destroy the watermark by adding noise into data sets. Noise distortion is
a serious attack but it is generally not a good choice by an attacker because
the imposition of noise could possibly degrade the maps validity.
6.2 Robust Watermarking
According to the location where the watermark is embedded, the existing
robust methods for vector map watermarking can be categorized into two
classes. These are the algorithms in spatial domain and the algorithms in
transform domain. In this section, a representative schemes of each class is
introduced. After this a shape-preserving algorithm is presented to improve
the previous methods.
6.2.1 Spatial Domain Schemes
Watermarking a vector map in spatial domain is to embed a watermark by
directly modifying the coordinate values of the vertices. The hidden bits could
be represented by some spatial features of vertices. That is the locational
relationship between vertices, or the statistical property of coordinates, for
example.
Based on Locational Relationship between Vertices
The algorithm proposed by Sakamoto et al. [2] is a typical scheme based on
the concept of modifying the locational relationship between vertices. Kang [3]
enhanced its robustness to noise attacks. The basic idea of those two schemes
is to shift the vertices within a predefined mask and make their locational re-
lationship follow specific patterns representing 0 or 1. Taking the enhanced
scheme proposed by Kang [3] as an example, two vertex patterns and the
embedding procedure are shown in Fig. 6.1. Firstly, the original map is seg-
mented into blocks and a mask is defined for each of them. Next, the mask
is divided into an upper triangle and a lower triangle by its diagonal line
connected by the south-east and the north-west vertices. To embed a bit 1,
all vertices in lower triangle are shifted to their mirror positions in the upper
triangle with respect to the diagonal line, as shown in Fig. 6.1(a). To embed
a bit 0 is just an inverse process shown in Fig. 6.1(b). The hidden data can
be extracted by finding which triangle both with the most of the vertices in
a mask. The scheme is blind and robust to noise and simplification attacks.
