Journal ArticleDOI
Characterization of Binary Patterns and Their Projections
TLDR
Algorithms for reconstruction of a two-dimensional binary pattern Z from its row- projection vector A and column-projection vector B have been developed by Chang and characterization questions of binary patterns and their projections are posed.Abstract:
Algorithms for reconstruction of a two-dimensional binary pattern Z from its row-projection vector A and column-projection vector B have been developed by Chang. The projection set (A,B) is said to be unique, nonunique, or inconsistent if it determines one binary pattern, more than one binary pattern, or no binary pattern. A binary patern Z is said to be ambiguous if there exists another pattern with the same projections, otherwise it is unambiguous. Two characterization questions of binary patterns and their projections are posed. First, given Z what is the necessary and sufficient condition for Z to be ambiguous, or unambiguous? Second, given (A,B), what is the necessary and sufficient condition for (A,B) to be unique, nonunique, or inconsistent? These two combinational questions are discussed and efficient algorithms to answer them are derived from some ideas of Ryser.read more
Citations
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Book ChapterDOI
Efficient CNF encoding of Boolean cardinality constraints
Olivier Bailleux,Yacine Boufkhad +1 more
TL;DR: The proposed encoding into CNF clauses of Boolean cardinality constraints that arise in many practical applications is efficient with respect to unit propagation, which is implemented in almost all complete CNF satisfiability solvers.
Journal ArticleDOI
Reconstructing convex polyominoes from horizontal and vertical projections
TL;DR: Some operations for recontructing convex polyominoes by means of vectors H's and V's partial sums allows a new algorithm to be defined whose complexity is less than O(n2m2).
Journal ArticleDOI
The reconstruction of two-directionally connected binary patterns from their two orthogonal projections
TL;DR: It is proved that after a finite number of iterative steps this algorithm produces all thex- andy-directionally connected binary patterns belonging to the given two projections.
Book ChapterDOI
Discrete Tomography: A Historical Overview
Attila Kuba,Gabor T. Herman +1 more
TL;DR: This chapter gives the details of the classical special case (namely, two-dimensional discrete sets — i.e.,binary matrices — and two orthogonal projections) including a polynomial time reconstruction algorithm.
References
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Picture processing by computer
TL;DR: The field of picture processing by computer is reviewed from a technique-oriented standpoint and the processing of given pictures (as opposed to computer-synthesized pictures) is considered.
Journal ArticleDOI
Reconstruction of pictures from their projections
Richard Gordon,Gabor T. Herman +1 more
TL;DR: Three algorithms are described (all using Monte Carlo methods) which were designed to solve the problem of estimating gray levels of a digital picture at the individual points from the sums of the gray levels along straight lines (projections) at a few angles.
Journal ArticleDOI
The reconstruction of binary patterns from their projections
TL;DR: A characterization of patterns that are reconstructable from their projections is given and it is shown that an unambiguous pattern can be perfectly reconstructed in time and that a pattern similar to an ambiguous pattern can also be constructed in time.
Journal ArticleDOI
Recognition of Printed Chinese Characters
R. Casey,George Nagy +1 more
TL;DR: The problem of recognizing a large alphabet (1000 different characters) is approached using a two stage process where peephole templates are generated for each character in such a way as to guarantee discrimination against other characters in the same similarity class.