Visibility within the Framework of Matroids

                               Roland Glantz

                       Vienna University of Technology

The theory of matroids is about dependence. It covers dependence of
points in a projective space, dependence of edges in a graph and
dependence of representatives for families of subsets. The concept of
visibility closure with respect to two cameras, as proposed by Pajdla,
is related to dependence as defined in the framework of matroids. The
plan of the talk is as follows:

1) Matroids are introduced and examples are given. In particular,
   matroids are constructed from lattices of visibility closures.

2) A graph G is defined, the vertices and edges of which represent the
   rays and the intersections of rays from different cameras,
   respectively.

3) The graph G is contracted into a graph M, whose vertices represent
   the visibility closures. The receptive fields of the vertices in M
   induce subgraphs of G.

4) The induced subgraphs in G are used to characterize several types
   of visibility closures.

5) Extensions to more than two cameras are discussed.