Cryptography Reference
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with smooth shape feature. We also tested the algorithm on some other map
types such as river maps, and boundary maps for example. In most cases the
algorithm works well. However, the algorithm can not work on maps composed
of straight lines, rectangles representing streets and blocks because there are
usually few non-feature points in this type of maps. It should also be noticed
that the capacity of the proposed work is small. In the experiment, more than
two thousand of vertices are used to embed a watermark bit to achieve a
stable statistical feature.
6.3 Reversible Data Hiding
Reversible data hiding means that the embedding procedure is reversible.
That is the cover data could be recovered without loss after the hidden data
has been extracted completely. Due to the critical application environment
of vector maps, the modification of the map data is generally not expected.
Consequently, reversible schemes are more appropriate for hiding data in vec-
tor maps because the distortions could be removed after the extraction of the
hidden data. The main techniques of reversible data hiding have been studied
on some multimedia data types such as images and audio. The reversibility
of the scheme can be achieved by invertible modulo addition [17], lossless
compression [18], histogram shifting [19, 20], difference expansion [21], and
companding [22]. However, few works have concerned the topic of reversibly
hiding data in 2D vector maps. In this section two reversible data hiding
schemes for 2D vector maps based on the techniques of amplitude addition
and difference expansion respectively are discussed.
6.3.1 Amplitude Addition Scheme
Voigt et al. designed a reversible watermarking scheme [23] embedding wa-
termark bits in the integer Discrete Cosine Transform (DCT) domain. The
main idea of the scheme is to utilize an important feature of map data. That
is the high correlation of vertex coordinates. Generally, owing to the continu-
ous and smooth shape of the map objects, the coordinates of the consecutive
vertices within an object are always highly correlated. It is well known that
the Discrete Cosine Transform has the property of energy compaction for
highly correlated data. After the DCT, the energy of the transformed data
will be concentrated on DC and low frequency AC coe
cients. Taking ad-
vantage of the above characteristics, the proposed algorithm combines every
eight vertices into an unit and for each unit a single watermark bit will be
embedded into it by changing its eight points integer DCT coe
cients. The
basic embedding method is shown in Fig. 6.11.
The vertical axis in the figure represents the absolute values of the eight
DCT coe
cients of a unit. D is the DC coe
cient and A
1
to A
7
are AC
coe
cients. Due to the high correlation of the coordinates, the absolute value
