Cryptography Reference
In-Depth Information
6.5.2 Fidelity: Error, Shape, Topology, etc.
The most important principle, which must be strictly followed by vector map
watermarking schemes, is that distortions induced by data hiding must be
strictly controlled in order to ensure the quality of the marked map. With
respect to vector maps, the term distortion has many meanings. One is that
distortions may mean the coordinate errors of vertices. Almost all existing al-
gorithms have taken this factor into account. It is a well known rule that the
errors of vertices induced by watermarking should not exceed the cover maps
precision tolerance τ . For the schemes in the spatial domain, data embedding
directly modifies coordinates, and it is convenient to control the errors. In the
case of transform domains, the situation is different. Those Transform Do-
main Based Schemes directly modify the transform coe
cients instead of the
coordinates. It is not convenient to control the introduced errors. In addition
to vertex errors, distortions also mean the errors of many other features such
as the shape or topology of map objects. This kind of distortion is of great im-
portance to map quality. They have been ignored by almost all former works.
Even slight distortions of vertices can also induce unacceptable changes in
shape or topology information. For example by destroying the smoothness of
map objects, or making the originally separated objects overlapped. It is one
of the future work needed to control distortions in vector map watermarking
schemes.
6.5.3 Fidelity Evaluation
Although kinds of algorithms for watermarking vector maps have been pro-
posed, there is still no appropriate measure for evaluating the fidelity of water-
marked maps. Such a measure could be important for a watermarking scheme
in order to evaluate the extent of the distortion introduced by the embedding
procedure. An ideal measure of the map fidelity should take into account not
only the errors of coordinates, but also the distortions of the map shapes. We
have described that both human perception and PSNR are not appropriate
candidates. A method to rationally evaluate vector maps fidelity remains a
topic for a future work.
6.5.4 Reversible and Fragile Schemes
Until now, few works in current world literatures have considered the topic
of designing reversible watermarking schemes for vector maps. Since the most
important restriction of vector map watermarking is the precision of the cover
data, reversible schemes provide the best solution to this requirement. In ad-
dition, most former works focused on designing robust schemes, but few have
considered the fragile schemes. Map data authentication is still a crucial issue
for many special applications, especially for the military applications. Design-
ing fragile schemes for the purpose of map data authentication is another
important future work.
