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the orthophotos in the sense of a further subdivision; i.e. the bor-
ders defined by the vector data are not changed, only additional
39: CC
borders introduced. For the parameters “scale”, “shape”, “com-
pactness" the values 100, 0.2, and 0.9 were selected.
3-2 Interpolation of the Hyperspectral Channels on the Finer
Grid by Inverse Distance Interpolation
For the interpolation on the finer grid we have chosen the In-
verse Distance Method. This method on the one hand requires
less computational effort than e.g. Minimum Curvature Interpo-
lation, on the other hand avoids undesired oscillations as might
appear with Kriging or Linear Prediction. The pixel centers of
the hyperspectral image are considered as data points, whereas
the pixel centers of the panchromatic grid (finer resolution) are
considered as interpolation points. The workflow of the interpo-
lation is as follows:
We run through all the segments and determine for each segment
S a list of pixels of the finer grid which are contained in 5; the
centers of these pixels define the interpolation points. In addition,
we select all the pixels of the coarser grid which are completely
contained in S - they will give us the data points. The Inverse
Distance Interpolation for any interpolation point and channel is
performed according to the formula
K
m Yk Wik = 2 5
v= > ~~ where wir = AT TR) (6 CR) +O
= SC 2 ( 2 ) ( )
Here y denotes the observation vector, ie. the grey values of
the data pixels for the respective channel, o is a regularizing
parameter, K is the number of data points within the segment.
Ti, Tk, Ci, Ck are the row and column indices of the interpolation
or data point with respect to the finer grid.
Higher powers of the distance are common for Inverse Distance
Interpolation. As our data are somewhat noisy, we appreciate the
smoothing effect within the segments due to the low power 1 of
the distance.
For many small segments no pixel in the low resolution was en-
countered, which was located completely inside the segment. For
such cases all grey values in the pansharpened image were set to
the corresponding values of the original hyperspectral image.
4 TEST DATA
For the evaluation of the pansharpening methods we use hyper-
spectral data of Ludwigsburg, Germany. The data was recorded
on August, 20 2010 with the HyMap sensor within the annual
HyEurope-campaign of the German center of aviation and space
flight (DLR); it comprises 125 channels in the range of 0.45 —
2.49 um. The ground resolution is 4 m. The test area consists in
6 strips with an overall extension of 9.6 x 9.0 km?. The panchro-
matic image was derived from an RGB-orthophoto which was
registered in the spring of 2010. The ground resolution of this
orthophoto amounted originally to 25 cm; it was degraded to 1m
in order to keep the pansharpening factor moderate.
5 EVALUATION OF THE PANSHARPENING
METHODS
5-1 General Visual Impression
The most obvious criterion for the quality of a pansharpening re-
sult is the visual impression. This criterion might be misleading
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
389
in some cases, hoewever, human vision is quite perceptive for im-
age sharpness and color differences. Figures 2 — 6 show the RGB
orthophoto, RGB-channels of the original HyMap data and the
pansharpened data, achieved with three different methods, for a
small region in the downtown in Ludwigsburg. In the lower left
corner the station and some railway tracks are visible. As the re-
sults of the PCA Fusion and the Gram-Schmidt Fusion can hardly
be distinguished with bare eyes, only one of them is reproduced.
Figure 2: Original RGB-orthophoto
Figure 3: RGB channels of the original hyperspectral image
At first glance, unambiguously the result of the Gram-Schmidt
Fusion looks best. The Wavelet Fusion shows some undesired
“ghost-” or “staircase-” artefacts. This phenomenon is also re-
ported by (Hirschmugl et al. 2005); it might be due to the com-
bination of different spatial wavelength ranges from different im-
ages. A sharp edge in the space domain corresponds to strong
short-wave components in the frequency domain with well-defined
ratios between amplitudes of different wavelengths. If long- and
short-wave components are assembled from different data sources,
these ratios might be distorted, which results at best in unsharp
edges, at worst in "staircase-" or even oscillation effects, so that
the edge appears to be “echoed”. The segmentation-based pan-
sharpening on the other hand features a pronounced terrace- or
“sycamore-bark”-like pattern; the edges clearly reflect the seg-
mentation borders. Whereas the visual impression might be un-
satisfactory, this “sharpening” of edges turns out to be beneficial
when it comes to classification.
