  We introduce a method for modeling a configuration of objects in 2D or 3D
images using a mathematical "skeletal linking structure" which will
simultaneously capture the individual shape features of the objects and their
positional information relative to one another. The objects may either have
smooth boundaries and be disjoint from the others or share common portions of
their boundaries with other objects in a piecewise smooth manner. These
structures include a special class of "Blum medial linking structures," which
are intrinsically associated to the configuration and build upon the Blum
medial axes of the individual objects. We give a classification of the
properties of Blum linking structures for generic configurations. The skeletal
linking structures add increased flexibility for modeling configurations of
objects by relaxing the Blum conditions and they extend in a minimal way the
individual "skeletal structures" which have been previously used for modeling
individual objects and capturing their geometric properties. This allows for
the mathematical methods introduced for single objects to be significantly
extended to the entire configuration of objects. These methods not only capture
the internal shape structures of the individual objects but also the external
structure of the neighboring regions of the objects.
