respect to their covariance as metric, exactly in the vein of the
classical Gram-Schmidt-orthogonalization:
Q
G; = (Gi — mi) — “= Gx
k.k
i
Q
1
Here G; denotes the greyvalue of an individual pixel in the orig-
inal channel i, G; the greyvalue of the same pixel in the (trans-
formed) Gram-Schmidt channel k. y; is the mean greyvalue of
channel ? taken over all pixels. The covariance C;,; between two
original channels 7, j is empirically determined by
2 (Gi - Hi)(G; — 6j)
Ci; = Pixels %
where NN denotes the total number of pixels. Due to construction,
the Gram-Schmidt channels are all uncorrelated.
The histogram of the high-resolving panchromatic image is matched
to the histogram of the artificial, low-resolving panchromatic im-
age. In this way at least the global (if not the local) grey value
distribution of the panchromatic image is adjusted to the intensity
distribution of the hyperspectral data. Then, the low-resolution
panchromatic is replaced by the high resolution panchromatic,
the remaining hyperspectral channels are upsampled and adopted.
Finally, the Gram-Schmidt transform is inverted.
2-2 PCA Fusion
This method resembles very much the Gram-Schmidt Fusion. In
contrast to the latter, the “artificial” low resolution panchromatic
channel is constructed as that linear combination of all bands,
which corresponds to the maximal eigenvalue of the principal
component analysis. The eigenvectors of the PCA are by con-
struction orthogonal; the corresponding combination bands are
uncorrelated. The further processing is the same as with the
Gram-Schmidt Fusion.
Obviously, PCA Fusion is based on the assumption that the pan-
chromatic image corresponds best with the linear combination of
bands which features the highest variance. As in the case of the
Gram-Schmidt Fusion, a global histogram matching is employed.
2-3 Wavelet Fusion
Wavelet Fusion is based on the concept of image pyramids, see
e.g. (Ranchin and Wald 2000). Given a high resolution im-
age, the base of the pyramid is just the image itself, whereas
the higher levels of the pyramid consist in successive approxima-
tions, i.e. each level consists in an approximation of the previous
level. In a second pyramid the difference images between con-
secutive approximations are represented. For the purpose of pan-
sharpening, the high resolution panchromatic image is approxi-
mated successively until the resolution of the hyperspectral data
is reached. Then for each individual channel, the approximation
of the panchromatic image is replaced by the respective hyper-
spectral data. High resolution images are constructed by succes-
sively adding the difference images of the panchromatic image to
each individual channel.
Whereas many approximation methods are imaginable for this
process, the Discrete Wavelet Transform constitutes a particu-
larly elegant and — in view of the famous Mallat algorithm — also
efficient possibility, see e.g. (Mallat 2009). The workflow of
the wavelet fusion reminds to the workflow of PCA Fusion. For
the former method, however, the transformations (forward and in-
verse wavelet transform) act on the panchromatic image, whereas
for the latter the transformations (forward and inverse PCA) work
on the hyperspectral data.
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B7, 2012
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia
Hyperspectral
Color Channel
Histogram
matching Replace
m LELLELLELI IE
chrom. |— =» = — | sharp.
Image channel
Inverse wavelet
transform
wavelet transform
Figure 1: Workflow of Wavelet Fusion according to (Hirschmugl
et. al 2005)
Different from PCA and Gram-Schmidt Fusion, only /ocal varia-
tions of the panchromatic image affect the pansharpening result.
This is due to the fact that only the wavelet coefficients (i.e. the
difference images) of the panchromatic image remain, whereas
the approximation coefficients of the low resolution level are re-
placed by the corresponding coefficients of the respective hyper-
spectral channel.
3 ASEGMENTATION-BASED PANSHARPENING
METHOD
In a common RGB image the absolute grey and color values may
differ noticeable from exposure to exposure. Hyperspectral data
in contrast are usually calibrated in such a way, that the grey val-
ues represent the absolute reflectivity of the respective surface
materials for the respective wavelength, i.e. the ratio between
reflected and incident radiation. The reflectivity is a property of
the surface material alone; it is of particular value for the distinc-
tion of surface materials. Therefore we aim at a pansharpening
method which respects as much as possible the original hyper-
spectral data. In a first step, we perform a segmentation of the
high resolution panchromatic image. The segments are assumed
to be homogeneous, ideally each segment should feature one ma-
terial only. In a second step, the hyperspectral data are interpo-
lated by means of an inverse distance method on the finer grid.
Hereby only such pixels of the original hyperspectral image are
used, which are located completely in the same segment as the
interpolation position.
3-1 Segmentation of the Panchromatic Image (RGB-image)
The segmentation of the panchromatic image was performed by
the well-known eCognition software, see (eCognition User Guide).
This software enables the simultaneous processing of multiple
channels in a hierarchical way. eCognition successively aggre-
gates pixels with similar grey values to segments. Criteria for the
aggregation of adjacent objects are on the one hand the hetero-
geneity of the grey values of the combined object, on the other
hand its geometric form. These criteria can be balanced by three
parameters: “scale”, “color” and “shape”. Adequate parameters
have to be selected by trial and error. Focused on application
in urban areas, in most cases a one-to-one relation between seg-
ments and building regions will be optimal, though roofs also
may consist of different materials.
As for our test area RGB orthophotos and in addition ALK vec-
tor data (parcels, buildings) were available, the segmentation was
performed hierarchically. The borders as given by the vector data
already imply a segmentation. This segmentation was refined by
