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30 December 1994 High-precision geometric correction of airborne remote sensing revisited: the multiquadric interpolation
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For a geographic analysis of multispectral scanner data from aircraft and their integration in spatial databases and geographic integration systems (GIS), geometric registration/rectification of the scanner imagery is required as a first step. Usually, one has to rely on global mapping functions such as polynomial equations as provided by most commercial image processing systems. These techniques have been proven to be very effective and accurate for satellite images. However, there are a umber of shortcomings when this method is applied to aircraft data. We see the multiquadric interpolation method as a promising alternative. The multiquadric function was first developed for the interpolation of irregular surfaces. It could be modified, however, to be used for image correction of remotely sensed data. In this form, it is particularly suited for the rectification of remote sensing images of large scale and locally varying geometric distortions. The multiquadric interpolation method yields a perfect fit at the used control points (CPs). With this, it is necessary to withhold independent test points that can be used for accuracy assessment. Within the registration/rectification process, all CPs contribute to the geometric warping of any given pixel in the image. Their effects, however, are weighted inversely to the distances between CPs and the current pixel location. The paper presents the multiquadric interpolation techniques and demonstrates successful application with airborne scanner data.
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Manfred Ehlers and David N. Fogel "High-precision geometric correction of airborne remote sensing revisited: the multiquadric interpolation", Proc. SPIE 2315, Image and Signal Processing for Remote Sensing, (30 December 1994);

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