Cryptography Reference
In-Depth Information
elements. That is points, polylines and polygons. These geometrical elements
are composed by organized vertices, and the spatial data is the coordinates
of these vertices based on a particular geographical coordinate system. At-
tribution data describes the properties of map objects such as their names,
categorizations and some other information. It is obvious that the informa-
tion recorded by attribution data is very important and normally cannot be
modified arbitrarily, as does the other additional data mentioned above. Un-
til now, all proposed watermarking schemes embedded the watermark into
the spatial data of the cover map, namely the coordinates of vertices. Every
vector map has a precision tolerance which are denoted as τ . This gives the
maximum amplitude of the permissible distortions for the coordinates. Any
coordinate distortions definitely below τ will not degrade the validity of the
map. The precision tolerance of a cover map plays a similar role as the
visual
cover model
in digital image watermarking. It provides a little redundancy for
hiding extra information. The basic principle of vector map watermarking is
that the coordinate distortions induced by data hiding should not exceed the
tolerance τ .
Fidelity of Vector Map Data
A common principle followed by all watermarking schemes is that the embed-
ding of a hidden message should not degrade the validity of the cover data.
The term fidelity is often used as a measure of the datas validity in the wa-
termarking world. According to the different data types and their respective
usages, the term fidelity could have different meanings. For digital images,
videos, audio and other general multimedia data sets, direct use of the data
is by the use of human sense organ. In that sense, human eyes can be used
to measure the fidelity of images. If the human eyes cannot distinguish be-
tween two images, those two images then can be considered as having the
same use value. That is, having the same fidelity. Some quantified parameters
are defined in order to measure the difference between two data sets such as
PSNR, MSE, for example. With respect to evaluating the fidelity of vector
map data, neither human perception nor PSNR can provide an appropriate
measure. Firstly, the direct user of vector maps are no longer human sense
organs but are computers. In a typical scale, even two digital maps are quite
similar when judged by the eye. It is still possible that coordinate differences
between two maps could exceed the precision tolerance τ . Secondly, the term
PSNR mainly reflects the energy of the errors. It is much more appropriate to
evaluate images but not vector maps. That is because even a high PSNR of
a vector map can not ensure that all vertex errors are within the maps pre-
cision tolerance. When we evaluate the fidelity of a vector map, some other
factors must be taken into account. That is the shape and the topology of the
map objects which cannot be directly reflected by PSNR. In other words, a
low fidelity map with obviously distorted shapes or topologies could also have
a high PSNR. Due to these factors, it is di
cult to perfectly watermark a
