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In this paper, we study the statistical theory of shape for ordered finite point congurations, or otherwise stated, the uncertainty of geometric invariants. Such studies have been made for affine invariants in e.g. [5], [13], where in the former case a bound on errors are used instead of errors described by density functions, and in the latter case a first order approximation gives an ellipsis as uncertainty region. Here, a general approach for defining shape and finding its density, expressed...

Recognition of planar point configurations using the density of affine shape