Graphics Reference
In-Depth Information
We have to find a polynomial that can approximate the surface satisfactorily,
and at the same time, preserve information that is psychovisually important.
That is exactly what we attempted to achieve with the proposed scheme.
Note that the order of the polynomial can be determined exactly in the
same way as we did in 2.4.3
4.2.2 Texture Coding
To encode the texture blocks we, first of all, Hilbert scan [134] each block. A
Hilbert scanned image or simply a Hilbert image corresponding to a graylevel
image is a 1-d image with its pixels identical to those in the graylevel image
through which the Hilbert curve passes. Hilbert drew a curve having the space
filling property in R 2 and he found a one-to-one mapping between segments
on the line and quadrants on the square. The merit of the curve is to pass
through all points on a quadrant and move to the neighboring quadrant.
Hilbert curves with different resolutions are shown in Figure 4.3 The eciency
Fig. 4.3. Hilbert curve with different resolutions.
of Hilbert scan has already been reported in 1-d image compression [86]. In our
texture compression scheme, Hilbert scan converts each texture block into its
corresponding 1-d Hilbert image. Line segments are then extracted from these
Hilbert images in a straightforward way because texture blocks are all labeled
by the threshold values. Also, since the blocks are textured in nature, we get
tiny line segments in large number. Repetition of line segments of identical
size and identical labels is very frequent. Huffman coding, therefore, provides
good compression for them. Since Hilbert scan is used for texture blocks, one
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