It is shown that the polynomials based image registration, which is widely used in remote sensing field, does not have a sound mathematical basis. In fact, there seems no theoretical basis for the polynomials based transform to outperform the affine transformation, a much simpler one,in image registration. If the transformation functions are polynomials of order n, the corresponding scene is shown to be in general the intersection of two curved surfaces of order n + 1, in other words,a space curve. In some special cases, the scene is approaching to a plane. To our knowledge, such results did not appear in the literature previously.
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