We show that the completion problem of reconstructing the hidden arcs of the contours of an image, given only the visible ones, has a solution. More precisely we prove that, given an oriented plane graph $K$ having as vertices only $T$-junctions and nonexterior terminal points, there exists an apparent contour $G$ such that $K$ is the visible part of $G$. This result is sharp, since the converse statement is easily seen to be satisfied. As a consequence, from $K$ we can reconstruct a solid shape $E$ in three-dimensional space such that $K$ coincides with the visible part of the apparent contour of $E$. The main tools used to prove our result are a Morse description of $K$ and the Huffman labelling for apparent contours.
