Calculus of Variations and Geometric Measure Theory

G. Bellettini - V. Beorchia - M. Paolini

Completion of visible contours

created by belletti on 06 Sep 2008
modified on 09 Dec 2008


Submitted Paper

Inserted: 6 sep 2008
Last Updated: 9 dec 2008

Year: 2008


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.