Journal of mathematical imaging and vision vol:6 issue:1 pages:37-57
The aim of this paper is to investigate whether it is possible to construct invariants for articulated objects-these are objects that are composed of different rigid parts which are allowed to perform a restricted motion with respect to each other-which use only partial information from each component. To this end, the transformation group describing the deformations of the image of an articulated object due to relative motions of the components, and/or changes in the position of the camera, is identified. It turns out that for a planar articulated object with two rigid components that are allowed to move within the object plane, this transformation group is (anti-isomorphic to) the semi-direct product of the group one would obtain if the object was rigid, and its smallest normal subgroup containing the transformations due to the relative motions of the components. Depending on the projection model, different answers to the question above evoke. For instance, when using perspective projection no other invariants exist than those obtained by considering each part separately as a rigid object, whereas in the pseudo-orthographic case simpler invariants (using only partial information from each component) do exist. Examples of such invariants are given.