VIEWPOINT INVARIANT CHARACTERISTICS OF ARTICULATED OBJECTS

The aim of this paper is to investigate whether it is possible to cons truct invariants for articulated objects-these are objects that are co mposed of different rigid parts which are allowed to perform a restric ted motion with respect to each other-which use only partial informati on from each component. To this end, the transformation group describi ng the deformations of the image of an articulated object due to relat ive motions of the components, and/or changes in the position of the c amera, is identified. It turns out that for a planar articulated objec t with two rigid components that are allowed to move within the object plane, this transformation group is (anti-isomorphic to) the semi-dir ect product of the group one would obtain if the object was rigid, and its smallest normal subgroup containing the transformations due to th e relative motions of the components. Depending on the projection mode l, different answers to the question above evoke. For instance, when u sing perspective projection no other invariants exist than those obtai ned by considering each part separately as a rigid object, whereas in the pseudo-orthographic case simpler invariants (using only partial in formation from each component) do exist. Examples of such invariants a re given.