Image Processing Reference
In-Depth Information
Successive
approximations
of the original
image
Difference of information
between two successive
approximations
Original image
Fig. 11.1
Representation of the successive approximations of an image based on a multi-resolu-
tion algorithm
wavelet coefficient image is obtained by subtracting the
approximation to the original image in a pixel-by-pixel
basis. This algorithm provides at each step one context and
one non-directional wavelet coefficient image. To perform
a dilation of the scale function, one adds zero between
each coefficient of the filter. Hence, no sub-sampling of
the image is performed and all images will have the same
size. The reconstruction is done by summation of the last
context and the wavelet coefficient images computed.
These two mathematical tools: the wavelet transform
and the multi-resolution analysis enable an image to be decomposed into the struc-
tures of different sizes that participate to its information content. Some examples of
using these tools in remote sensing applications can be found in Ranchin (
1997
).
multi-resolution
analysis offers a
hierarchical
modeling,
also called a
scale-by-scale
representation of
signals and images
11.3
Encrustation of Higher Spatial Resolution Quickbird
Image in Low Resolution Image
This section discusses with an example the problem of merg-
ing partially overlapping images (including raster maps)
with different spatial resolutions. Specifically we discuss the
problem of the encrustation of a higher spatial resolution
“imagette” (image of small size) into an image of lower
resolution with the attenuation of the discontinuities created
at the edges of the imagette by the difference in resolutions.
It is assumed that both the image and imagette offer the
same level of “radiometric” accuracy, i.e. none of these
images is superior to the other with respect to radiometry.
In that case, the encrustation of the higher resolution imagette into the wider, lower
resolution image is the best way to merge the data and obtain a final image offering
encrustation is a
means to benefit
from images with
high spatial
resolution in a
localized area
within an image of
lower resolution
