better than the global approach, and the radial basis function
methods generally improve the results slightly further.
According to Table 1, we can also state that a pure multi-
quadric approach without either simultaneous or prior affine
or polynomial transformation terms does not better than the
global transformation. Global transformation terms are rather
crucial, with the radial basis function terms modeling only the
distortions of higher spatial frequencies.
The best result is achieved by elastic registration using the
thin-plate spline function U(r) = r?Inr, however, the differ-
ence between the various radial basis functions is not signifi-
cant when compared with respect to the standard deviations
through the spectral bands.
6. CONCLUSION
We have compared five different locally adaptive image reg-
istration techniques with conventional global second degree
polynomial registration. The methods were compared by ap-
plication to experimental image data recorded by an airborne
multispectral line scanner. The performance of the various
methods was evaluated by the reduction of the amount of
erroneous ‘change’, where the latter was measured as the
variance of the second principal component in the regression
of the multitemporal reflectance values in each spectral band.
The best results were achieved with elastic registration using
the thin-plate spline function U(r) = r?Inr which reduced
‘change’ by ca. 9%. Although, no significant difference in
performance can be observed between various radial basis
functions. The comparison shows that also local AKIMA reg-
istration improves the result significantly (ca. 796) over global
polynomial registration, with elastic registration techniques
being slightly better still.
We conclude that elastic registration is a preferable tool for
the geocoding of airborner scanner imagery. Local AKIMA
quintic polynomials may be used for cases of high ground
control point numbers, where the computation time is signi-
ficantly less than for elastic registration.
ACKNOWLEDGEMENT
One of the authors (RW) was supported by the Volkswagen-
Stiftung. We would like to thank Johann Bienlein, Leonie
Dreschler-Fischer, Christian Drewniok and Hartwig Spitzer
for inspiring discussions. Moreover, we wish to thank Mar-
tin Kollewe and Thomas Kollewe for the organization of the
image flights. The image data was recorded in collabora-
tion with DLR, Oberpfaffenhofen, particularly with the help
of Volker Amann, Peter Hausknecht and Rudolf Richter.
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