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Reconstruction of Connected Sets from Two Projections

  • Alberto Del Lungo
  • Maurice Nivat
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Abstract

The problem of reconstructing a two-dimensional discrete set from its projections has been studied in discrete mathematics and applied in several areas. It has some interesting applications in image processing, electron microscopy, statistical data security, biplane angiography and graph theory. This chapter presents the computational complexity results of the problem of reconstructing a set from its horizontal and vertical projections with respect to some classes of sets on which some connectivity constrzints are imposed. We show that this reconstruction problem can be solved in polynomial time in a class of discrete sets, and is NP-complete otherwise.

Keywords

Reconstruction Problem Vertical Projection Disjoint Cycle Median Column Filling Operation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Alberto Del Lungo
    • 1
  • Maurice Nivat
    • 2
  1. 1.Dipartimento di Sistemi e Informatica (DSI)Università di FirenzeFirenzeItaly
  2. 2.Laboratoire d’Informatique, Algorithmique, Fondements et Applications (LIAFA)Université Denis DiderotParisFrance

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