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Abstract
Hilbert curve can travel through every point in a space in
a specific way. In a given space with different resolutions,
the curve contains one kind of inclusion relationship, that is
once we know how Hilbert curve travels in a lower resolution
(for example 2 by 2) space, we can generate this curve in
higher resolution case (2N by 2N) based on this relationship.
In other words, Hilbert curve has the property of describing a
space with multiresolution.
In the start of this thesis, we briefly introduce several
properties of Hilbert curve first. One of which that we show
great interest is the way it travels. The curve always moves
from one point to its adjacent one and preserves point
neighboring as much as!possible. Based on this principle,
we discuss two applications of Hilbert curve.
The first part is the applications on two-dimensional space.
Gray image compression and image data encryption are achieved
in this part.
The second part is the applications on three-dimensional space.
We discuss a color image display using 256 colors only. And
finally, we list several possible future works.
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