Characterization algorithms of binary pictures

Given a vector A of m row projections and a vector B of n column projections, efficient reconstruction algorithms of a binary picture Z from A and B have been developed by Chang. 1 The set of projections Se(A,B) is empty, unique or multiple if it determines no binary picture, exactly one binary picture or more than one binary picture respectively. Two binary pictures are similar if they are determined by the same set of projections. A binary picture Z is ambiguous if it has at least another similar binary picture, otherwise it is unambiguous. A complete characterization of binary pictures with respect to their projection sets is summarized in two questions. Given a binary picture Z, is it unambiguous? Given a set of projections Se(A,B), is it empty, unique or multiple? Two algorithms base upon the idea of Ryser are presented. 2 The first algorithm answers the first question and the second algorithm answers the second question.