Invariant standard positions of ordered sets of points
The determination of invariant characteristics is an important problem in pattern recognition. Many invariants are known, which have been obtained either by normalization [Ar90, As94, Si94, Ro94, Vo95] or by other methods [Mu92, Re93, Fl93, We93]. This paper uses the method of normalization to derive invariants for ordered sets of points. Special attention is payed to obtain a standard position of the set of points considered. Projective invariants are calculated which, however, are not starting point independent; that means at least one pair of reference points has to be known. For ordered sets of points, no invariants independent of the choice of a starting point are known from the literature. For the affine case, this paper provides a solution by using the discrete Fourier coefficients; affinely invariant and starting point independent features and their standard positions are derived for ordered sets of points.
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