International Archives of Photogrammetry and Remote Sensing, Vol. 32, Part 7-4-3 W6, Valladolid, Spain, 3-4 June, 1999
The Brovey Transform (Hallada and Cox, 1983), a special
combination of arithmetic combinations including ratio, is a
formula that normalises multispectral bands used for a RGB
display, and multiplies the result by any other desired higher
resolution image to add the intensity or brightness component to
the image. The algorithm is shown in Eq. 5 where DNfu Sed means
the DN of the resulting fused image produced from the input
data in ‘n’ multispectral bands b l5 b 2 , ... b n multiplied by the
high resolution image DNhighres.
DN bi * ^ xr (5)
DN fused ~ DN fel + DN b2 + ... + DN bn DN highres
3.4. Principal Component Analysis
PCA is a statistical technique that transforms a multivariate
dataset of correlated variables into a dataset of new uncorrelated
linear combinations of the original variables. The approach for
the computation of the principal components (PCs) comprises
the calculation of:
1. covariance (unstandardised PCA) or correlation
(standardised PCA) matrix
2. eigenvalues, eigenvectors
3. PCs
An inverse PCA transforms the combined data back to the
original image space. Replacing the first principal component
with a higher resolution intensity image, a multi-channel dataset
can be transformed into a spatial resolution image of higher
ground resolution. This is called Principal Component
Substitution - PCS (Shettigara, 1992). The idea of increasing
the spatial resolution of a multi-channel image by introducing
an image with a higher resolution. The channel, which will
replace PCI, is stretched to the variance and average of PCI.
The higher resolution image replaces PCI, since it contains the
information which is common to all bands while the spectral
information is unique for each band (Chavez et al., 1991). PCI
accounts for maximum variance, which can maximise the effect
of the high resolution data in the fused image (Shettigara,
1992) .
3.5. Wavelets
Wavelets, a mathematical tool developed originally in the field
of signal processing, can also be applied to fuse image data,
following the concept of the multi-resolution analysis (MRA).
The wavelet transform creates a summation of elementary
functions (= wavelets) from arbitrary functions of finite energy.
The weights assigned to the wavelets are the wavelet
coefficients, which play an important role in the determination
of structure characteristics at a certain scale in a certain
location. The interpretation of structures or image details
depends on the image scale, which is hierarchically compiled in
a pyramid produced during the MRA (Ranchin and Wald,
1993) . Once the wavelet coefficients are determined for the two
images of different spatial resolution, a transformation model
can be derived to determine the missing wavelet coefficients of
the lower resolution image. Using these, it is possible to create
a synthetic image from the lower resolution image at the higher
spatial resolution. This image contains the preserved spectral
information with the higher resolution, hence showing more
spatial detail. This method is called ARSIS, an abbreviation of
the French definition “amélioration de la résolution spatial par
injection de structures” (Ranchin et al., 1996).
3.6. Regression Variable Substitution
Multiple regression derives a variable, as a linear function of
multi-variable data that will have maximum correlation with
univariate data. In image fusion the regression procedure is used
to determine a linear combination (replacement vector) of image
channels that can replace an existing image channel. If the
channel to be replaced is one of the lower resolution input
bands, this procedure leads to an increase of spatial resolution.
To achieve the effect of fusion, the replacement vector should
account for a significant amount of variance or information in
the original multivariate dataset. The method can be applied to
spatially enhance data. In case of fusion of SPOT XS and PAN
channels, for each pixel location three new values are computed
to produce the 10 m multispectral pixels based on the known
relationship between PAN and XS. The linear regression is then
calculated for each channel combination, i.e. XS green band -
PAN, XS red band - PAN and IR band - PAN.
4. RESOLUTION MERGE CHALLENGES
The resolution merge is relatively straightforward, when using
data from the same satellite, e.g. SPOT PAN & XS, IRS-1C
PAN & LISS, etc. But it is also applicable to imagery
originating from different satellites carrying similar sensors, e.g.
SPOT XS & 1RS-1C PAN.
Some of the approaches are already implemented in
commercial-off-the-shelf (COTS) software packages, e.g. PCI
Geomatics and ERDAS IMAGINE. These include amongst
others multiplication techniques, PCA and Brovey transform.
Image providers already integrated resolution merged products
into their catalogue of standard products. Examples are SPOT
IMAGE (1999) and SSC Satellitbild (1999). However, very
often the user has to fine-tune individual parameters of the
fusion process. A good example is the use of arithmetic
combinations, which allow the user to put different weights on
the input images in order to enhance application relevant
features in the fused product.
The major difficulty is the co-registration of images with large
differences in spatial resolution. The identification of tie points
can cause problems in both datasets:
■ Multispectral data - difficulty of identifying corresponding
points due to the lower resolution;
■ Panchromatic data - shadow effect caused by buildings or
similar objects due to high level of detail.
Especially in the case of spatial resolution ratios of up to 1:10,
i.e. SPOT XS and Russian imagery, points or features have to
be selected with care, due to the additional large difference in
viewing geometry of the sensors involved. An integrated
approach is the use of sensor models, which provide a re
