International Archives of Photogrammetry and Remote Sensing, Vol. 32, Part 7-4-3 W6, Valladolid, Spain, 3-4 June, 1999
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panchromatic band is used. Therefore, the original spectral
information of the multispectral channels is not or only
minimally affected. Such algorithms make use of classical filter
techniques in the spatial domain, as well as the more recently
introduced Wavelet Transform, which can be implemented in
the frequency domain. In view of the manifold possibilities
using wavelets for data fusion, we place only those wavelet
algorithms into this group, the intention of which is a
straightforward mixture of complementary frequencies,
analogous to filter techniques in spatial domain (e.g. Garguet-
Duport et al., 1996; Yocky, 1996). Other fusion procedures
using the wavelet domain make use of complex (local)
adjustments as described in chapter 2.3 (e.g. Iverson and
Lersch, 1994; Ranchin et al., 1994; Ranchin and Wald, 1996).
We would like to illustrate filter techniques in spatial domain
more detailed: to extract the panchromatic channel high
frequencies, a degraded or low-pass-filtered version of the
panchromatic channel has to be created. This low resolution
version should fit to the resolution level of the multispectral
image. Subsequently, the high frequency addition method
(HFA) extracts the high frequencies using a subtraction
procedure and adds them to the multispectral channels via
addition (Schowengerdt, 1980; Chavez, 1984; Chavez and
Bowell, 1988):
multi j Mgh = multi j tow + (pan 1 “ 8 * 1 - pan low ) (1)
where [multi / ow ] is the original low resolution multispectral
image, [pan low ] the degraded panchromatic band, [pan 1 “ 811 ] the
original (high resolution) panchromatic band, [multi j 1 “ 8 * 1 ] the
fusion result and [j] the channel index. The problem of the
addition operation is that the introduced texture will be of
different size relative to each multispectral channel, so a
channelwise scaling factor for the high frequencies is needed.
The alternative high frequency modulation method (HFM, or
Sparkle) extracts the high frequencies via division and adds
them to each multispectral channel via multiplication (Pradines,
1986; Filiberti et al., 1994; Vrabel, 1996):
multi j 111811 = multi j low * pan hlgh / pan low (2)
Because of the multiplication operation, every multispectral
channel is modulated by the same high frequencies. Thus, the
HFM technique allows a straightforward fusion of both datasets.
2.3. Fusion Procedures Using the Panchromatic Band
Indirectly
Fusion techniques described so far make use of the
panchromatic channel (high) frequencies with their strength and
polarity as they are. Certainly, the filter techniques do not or
only minimally distort the original spectral information of the
low resolution multispectral image, but the panchromatic high
frequencies are not necessarily suitable for the specific spectral
domain in which they are introduced. In particular, the (real)
local edges or boundaries of the NIR or SWIR channels often
exhibit an inverse polarity to that of the panchromatic band.
Such incompatibilities not only become visually apparent in
fusion results as undesired “ringing effect” (Schowengerdt,
1980), but may also corrupt further steps of image analysis.
To perform the radiometric fusion of a multi-resolution dataset
as accurately as possible, several authors do not use to the
original panchromatic information, but propose to use specific
derivatives adapted to each multispectral band. In this case, the
panchromatic band information just forms the basis for band
specific transformations or estimating procedures.
To adjust the panchromatic band information to the
uncorrelated NIR channel, Price (1987) performs a cross
tabulation between them. For each grey value of the degraded
panchromatic band, the corresponding values of the NIR
channel are found. The mean values of the latter are used to
build a new lookup-table (LUT), which is applied to the
degraded and original panchromatic bands, so that their grey
values fit better to those of the NIR band. These recoded
versions are then used together with the HFM algorithm.
Because of the usually wide value range of the NIR channel for
a given grey value of the panchromatic band (note that they are
not correlated), a significant spectral smoothing has to be
accepted using this adjustment method.
Moran (1990) tries to improve the value mapping or LUT
approach by using a small moving window as calculation unit.
In this case, all pixels of the high resolution image with same or
similar values as the central pixel are searched at the actual
window position. Subsequently, the mean or mode of the
geometrically corresponding values of the lower resolution
multispectral channel is calculated. The retrieved value replaces
the central pixel of the high resolution image. Zhukov et al.
(1995) and Zhukov and Oertel (1996) introduce a similar
“multi-sensor, multi-resolution technique” (MMT). Here, the
high resolution image can also be a classified multispectral
image instead of a panchromatic band. All authors using the
recoding method obtained fusion results of high radiometric
fidelity, while the sharpening effect appears only moderate (the
dynamic range of the fusion result does not exceed that of the
low resolution multispectral input).
Another approach, which makes use of the panchromatic
channel information indirectly, was introduced by Tom et al.
(1984), Tom and Carlotto (1985) and Tom (1986). They
propose an enhancement technique based on local correlation
properties not only in the context of data fusion but the
reduction of image noise. The local correlation modelling
technique was successfully adapted to the case of resolution
enhancement based on a single high resolution panchromatic
band (Tom, 1986; Hill et al., 1998).
3. IMAGE FUSION THROUGH LOCAL
CORRELATION MODELLING
The rationale for using a local modelling approach is based on
the fact that edges are manifestations of object or material
boundaries that occur wherever there is a change in material
type, illumination, or topography. Since most objects exhibit
