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