Thin Plate Spline is a simple math model in which all the collected ground control points (GCPs) are used simultaneously to compute a transformation. The warping is distributed throughout the image with minimum curvature among the GCPs becoming almost linear with distance.
Thin Plate Spline fits the GCPs exactly; therefore, a GCP can be added in an area where the transformation is unsatisfactory. However, this means that the math model does not provide direct means of detecting and correcting errors in GCP coordinates. To verify the derived transformation, acquire a number of check points (CP) that are large enough to ensure a thorough verification; for example, an amount equal to half the number of GCPs.
Unlike standard two-dimensional polynomials that approximate (and smooth), Thin Plate Spline interpolates. Provided GCPs are collected at local extremes of the distortions, the algorithm models images with distortions changing frequently and rapidly in space. A typical example is an image orthorectified without a digital elevation model (DEM) or with a DEM more coarse than the image. If 2-D GCPs are collected at local extrema of the distortions, such as mountain peaks and valley bottoms, Thin Plate Spline will properly represent the required spatial corrections to the image.
To compute a warping transformation accurately, collect GCPs at the extremes of the terrain and along break lines. When using Thin Plate Spline with an image in rough terrain, you may need to acquire many (hundreds) of GCPs. Therefore, use Thin Plate Spline only for distortions that can be represented accurately from a few dozen GCPs. To remove terrain distortions, or with images of rough terrain, a rigorous model, such as Optical Satellite Modeling or Aerial Photography, may produce better results.
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