Fig. 1. Components of an object recognition system.

Fig. 2. Some of the 8 possible relative positions of two regions and the corresponding descriptions using the formalism of region connection calculus. The other two can be obtained from (d) and (e) interchanging a with b. In the situation (a) a is disconnected from b, in (b) a is externally connected to b, in the situation (c) a is partially overlapped to b, in (d) a is tangential proper part of b, in (e) a is non-tangential proper part of b and, finally, in the situation (f) a and b coincide.

Fig. 3. Some of the possible positions of a convex region with respect to the convex hull of a non-convex one.

Fig. 4. With the formalism of region connection calculus the relation between these two disconnected non-convex regions, where a is partially inside the convex hull of b and vice versa, is denoted by P-INS_P-INSi_DC(a,b).

Fig. 5. A planar point configuration.

Fig. 6. In the triangle formed by p₁, p₂, and p₃ these points are counterclockwise ordered. This is recorded in the chirotope by χ(1,2,3)=+.

Fig. 7. Partition of the plane generated by the oriented ray from the point p₁ to p₄.

Fig. 8. Steps of encoding of the combinatorial properties of a view of an object into a chirotope.

Fig. 9. Three different views of the same scene which have the same representation using oriented matroids.

Fig. 10. Two views of two objects whose topological properties are indexed in Table 4.

Fig. 11. The three structural object recognition methods from a single view considered in the experiments. (a) Method based on adjacency graphs. (b) Method based on function described graphs. (c) Method presented in this paper. Whereas in (a) and (b) a distance measure is used, in (c) the selection of the m views of the test set most similar to a given view is based on counting the number of correspondences based on the type of connection between regions and on the set of cocircuits.

Fig. 12. Some of the views used for the experiments of object recognition, their segmented views and the adjacency graphs of the regions of the segmented views.

Vectors that corresponds to the points of the planar arrangement represented in Fig. 5

Chirotope of the planar arrangement of points represented in Fig. 5

Set of cocircuits of the planar arrangement of points represented in Fig. 5

Index of the topological properties of the two views v_1,1 and v_1,2 of the two objects represented in Fig. 10

Correctness of the three object recognition methods from a single view considered in the experiments