 
Summary: Distance geometric approach to recognize
a set of finitely many points
Ralph Schiller \Lambda
Technische Informatik I
Technische Universit¨at Hamburg Harburg
21071 Hamburg
Germany
1.8. 1994
Abstract
From classical differential geometry there are known for congru
ences, affine transformations and projective transformations invari
ant signatures which use terms like arclength and curvature. But
these terms are maybe too sophisticated, when for example exami
ning the weakly structured point sequences building the border of a
digitized image. Therefore it is worth paying attention to a couple of
theorems looking at invariant theory from a different point of view
due to the concept of 'the geometry of mild hypotheses' but which
were ignored from pattern recognition yet. As the congruences are
equivalent with the isometries in IR n , the isometries of finite point
sets are looked at and the affine equivalent point sets are normalized
