Image Processing Reference
It may be seen as the inference of the information that is missing in the images B kl
for the construction of the synthesized images B* kh .
The ARSIS concept is based on the assumption that the missing information is
linked to the high frequencies of the representations A and B . It searches for a rela-
tionship between the high frequencies in B and A and models this relationship.
A method belonging to the ARSIS concept performs typically the following opera-
tions: (i) the extraction of a set of information from A , (ii) the inference of the infor-
mation that is missing in the images B kl using information extracted from A, and (iii)
the construction of the synthesized images B* kh . Current methods perform a scale-by-
scale description of the information content of both images. High frequency informa-
tion that is missing is synthesized so that low spatial resolution images are transformed
into high spatial resolution, high spectral content images. Ranchin and Wald ( 2000 b)
show that many schemes can be accommodated within the ARSIS concept.
The images A and B do not need to be commensurate. Some studies have been
published where images acquired in thermal infrared bands have been synthe-
sized with images acquired in the visible range to create an image of satisfactory
quality and better spatial resolution (Kishore Das et al. 2001 ; Liu and Moore
1998 ; Nishii et al. 1996 ; Wald and Baleynaud 1999 ).
It is difficult to sketch the general scheme for the application of the ARSIS con-
cept. In the HPF and other methods (Liu and Moore 1998 ; Cornet et al. 2001 ;
Diemer and Hill 2000 ; Pradines 1986 ; Price 1999 ), the modeling of the missing
information from the image A to the image B is performed on moving windows of
these images themselves. It is possible to focus more on the modeling of the missing
high frequencies, expressed by Fourier coefficients, wavelet coefficients or other
appropriate spatial transformations (Wald 2002 ).
Figure 11.5 presents the general scheme that applies in the case of a multi-scale
model (Ranchin and Wald 2000b ), which is used the following section to describe
the ARSIS concept. Input to the fusion process includes the images A at high spatial
resolution ( A h , resolution n°1) and the spectral images B at low spatial resolution
( B kl , resolution n°2).
Three models appear in this scheme. A Multi-scale Model (MSM) performs a
hierarchical description of the information content relative to spatial structures of an
image. An example of such a model is the combination of the wavelet transform
and multiresolution analysis (Ranchin 1997 ). Ranchin and Wald ( 2000b ) provide
practical details for the implementation of the algorithm of Mallat combined with
a Daubechies wavelet. When applied to an image, the MSM provides one or more
images at higher frequencies (detail images), and one image of approximation at
lower frequencies. For instance, imagine an Ikonos image with 1 m resolution. The
first iteration of the MSM gives one image of the structures comprised between, say,
1 and 2 m (details image) and one image of the structures larger than 2 m (approxima-
tion image). The spatial variability within an image can thus be modeled and the
model can be inverted (MSM −1 ) to perform a synthesis of the high-frequency infor-
mation to retrieve the original image at 1 m.
The Inter-Band Structure Model (IBSM) deals with the transformation of spatial
structures with changes in spectral bands. It models the relationships between the