Using graphs for some discrete tomography problems

Given a rectangular array where entries represent the pixels of a digitalized image, we consider the problem of reconstructing an image from the number of occurrences of each color in every column and in every row. The complexity of this problem is still open when there are just three colors in the image. We study some special cases where the number of occurences of each color is limited to small values. Formulations in terms of edge coloring in graphs and as timetabling problems are used; complexity results are derived from the model. Keywords : discrete tomography, complete bipartite graphs, perfect matchings, edge coloring, timetabling

• Type: Journal
• Year: 2006
• Where: DAM
• Authors: Marie-Christine Costa, Dominique de Werra, Christophe Picouleau
• Keywords: DAM 2006, Digitalized Image, Image, Rectangular Array