Completion of visible contours

Maurizio Paolini, Giovanni Bellettini, Valentina Beorchia

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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 to prove our result are a Morse description of K and the Huffman labelling for apparent contours.
Original languageEnglish
Pages (from-to)777-833
Number of pages57
JournalSIAM Journal on Imaging Sciences
Publication statusPublished - 2009


  • apparent contours
  • artificial vision
  • image segmentation


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