The main disadvantage of TPSs is that, to represent a warping transformation accurately, they should be constrained at all extreme points of the warping function. This is not a problem in smoothly varying transformations, such as the change of coordinate systems (if the exact transformation functions are not known). However, when using TPSs to georegister a photograph in rough terrain, it may be necessary to acquire hundreds of GCPs, since there should be a point at every extreme of terrain (peak or valley bottom), and along breaklines. The derivation of TPS transformation parameters involves solving an equation system with a square (N+3) by (N+3) matrix, where N is the number of GCPs. For a very large N it is a time consuming task. Moreover, the evaluation of TPS functions at every image pixel requires calculation of N values of natural logarithms, and for large N this calculation may be prohibitively slow: on a Sun SPARCstation LX the evaluation rate is 1440 pixels per second for a model with 83 GCPs.
The other disadvantage of TPSs is that they reproduce exactly (within numerical computation errors) the values at all GCPs. Therefore the method does not provide direct means of detecting and correcting errors in GCP coordinates. To verify the derived transformation, an independent set of Check Points has to be acquired, and their number should be large enough to ensure a thorough verification (say, half the number of GCPs). This obviously increases the total cost of the approach, or may compromise the quality of the final product if the number of check points is low.
To summarize, Thin Plate Spline warping is recommended for distortions which can be accurately represented by up to several tens of ground control points. It is not recommended for removal of terrain distortion, for which an analytical approach should be used. The analytical approach is based on photogrammetric model of the viewing geometry, and uses terrain elevations from a Digital Elevation Model of the area.