In this chapter we show how to solve the completion problem, namely we characterize those oriented plane graphs that are visible part of an apparent contour (Theorem 4.3.1). The proof is generalized to the case where the background is not reduced to the external region. In our presentation we need some elementary concepts of the theory of oriented graphs, and the Morse description of a graph, as outlined in Sect. 2.5.3 In Chap. 9 we describe a code that automates the construction of the proof of Theorem 4.3.1.
