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John Bosco Kyalo Kiema
segmentation is then applied. Fusing the valid object segments for the class Buildings results in Fig. 2. In general, the
delaunay triangulation results compare very well with similar results obtained using the first segmentation approach and
can therefore be used in the automatic verification of GIS databases.
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Figure 2: Selection and fusion of valid building segments
3 WAVELET COMPRESSION
Applications of wavelet analysis in remote sensing are rapidly increasing. The main areas of this include: the fusion of
satellite sensor imagery using multi-resolution analysis ((Garguetduport et. al, 1996); (Ranchin and Wald, 1997); (Wald
et. al, 1998)), image compression (Werness et. al, 1994), speckle noise reduction in SAR data (Horgan, 1998) etc. The
basic difference between wavelet compression and the Joint Photographic Experts Group (JPEG) compression standard
is in the transformation of the image from a spatial to a frequency domain. Whereas this is realised in JPEG through the
use of the Discrete Cosine Transform (DCT), the same is achieved in wavelet compression through the Discrete
Wavelet Transform (DWT). In general, wavelet compression results in a better image quality than the JPEG method,
especially in applications where high compression rates are required (Shiewe, 1998). Moreover, the undesirable blocky
artifacts that often result from the use of the 8x8 pixel blocks in the JPEG method are avoided. The wavelet method is
also significantly faster than fractal image compression at similar compression rates.
The mathematical framework behind wavelets is beyond the scope of the work presented here. A more comprehensive
discussion of this is given in ((Daubechies, 1992); (Chui, 1996); (Louis et.al, 1997)) etc. In general, wavelets are
defined as mathematical functions that partition data into different frequency components and then facilitate the analysis
of each component with a resolution matched to its scale. This takes into account the fact that the level of detail in an
image may not be constant. In contrast to Fourier methods, wavelets allow the partition of the input signal not only with
respect to its spectral, but also spatial properties. Therefore, whereas Fourier methods are ideal for ,,continuous tone”
(homogeneous) data, wavelet methods on the other hand, are suited for input signal that is characterised by
discontinuities and sharp spikes. Hence, remotely sensed data that depict a high concentration of heterogeneous objects
(e.g., urban environments) are best compressed using wavelet compression schemes.
high-frequency information in the horizontal,
H H vertical and diagonal orientations respectively,
YX YY while the fourth contains low-frequency
information. The three high-frequency information
quadrants are subsequently eliminated. The
transformation is then repeated once again on the
low-frequency image quadrant. Ideally, this is
iterated until the last low-pass image contains only a
single pixel. Fig. 3 shows a schematic description of this procedure up to the second level of wavelet decomposition.
In principle, the DWT method operates by splitting
the image into four new image quadrants within the
wavelet domain. Three of these new images contain
Figure 3. Schematic image decomposition using wavelets
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 491
