Reconstruction of Canonical hv-Convex Discrete Sets from Horizontal and Vertical Projections

@inproceedings{Balzs2009ReconstructionOC,
  title={Reconstruction of Canonical hv-Convex Discrete Sets from Horizontal and Vertical Projections},
  author={P{\'e}ter Bal{\'a}zs},
  booktitle={IWCIA},
  year={2009}
}
  • P. Balázs
  • Published in IWCIA 17 November 2009
  • Mathematics
The problem of reconstructing some special hv -convex discrete sets from their two orthogonal projections is considered. In general, the problem is known to be NP-hard, but it is solvable in polynomial time if the discrete set to be reconstructed is also 8-connected. In this paper, we define an intermediate class --- the class of hv -convex canonical discrete sets --- and give a constructive proof that the above problem remains computationally tractable for this class, too. We also discuss some… 
A Fast Algorithm for Reconstructing hv-Convex Binary Images from Their Horizontal Projection
TLDR
This paper provides a fast polynomial-time algorithm for reconstructing canonical hv-convex images with given number of 4-connected components and with minimal number of columns satisfying a prescribed horizontal projection and shows that the method gives a solution that is always 8-connected.
Probabilistic Reconstruction of hv-convex Polyominoes from Noisy Projection Data
TLDR
The well-known problem of reconstructing hv-convex polyominoes is considered from a set of noisy data, and a probabilistic evaluation in the reconstruction algorithm, where different pixels assume different probabilities to be part of the reconstructed image.
Reconstructing Convex Matrices by Integer Programming Approaches
TLDR
This work reformulate the problem of reconstructing two-dimensional convex binary matrices from their row and column sums with adjacent ones by using integer programming and develops approximate solutions based on linearization and convexification techniques.
Solving Multicolor Discrete Tomography Problems by Using Prior Knowledge
TLDR
This paper shows how several polynomial reconstruction algorithms can be defined by assuming some prior knowledge on the set to be rebuilt, and describes some efficient reconstruction algorithms and gives a sufficient condition for uniqueness.
Combining Genetic Algorithm and Simulated Annealing Methods for Reconstructing HV-Convex Binary Matrices
In this paper, we consider the discret tomography problem (DTP), namely reconstruction convex binary matrices from their row and column sums respectively H and V, RBM(H,V). This is reformulated as an
Largest Empty Axis-Parallel Rectangular Annulus
In Euclidean plane, a rectangular annulus is the region between parallel rectangles such that the smaller rectangle lies wholly inside the outer rectangle. Given a set P of n points in the two
Largest Empty Axis-Parallel Rectangular Annulus Priya
In Euclidean plane, a rectangular annulus is the region between parallel rectangles such that the smaller rectangle lies wholly inside the outer rectangle. Given a set P of n points in the two
Reconstruction, Enumeration, and Examination of Binary Images with Prior Information
A tomografia celja egy haromdimenzios objektum ketdimenzios szeleteit abrazolo kepeinek előallitasa a vetuletek ismereteben. A tomografia elsősorban orvostudomanyi problema, de előfordul fizikai,

References

SHOWING 1-10 OF 13 REFERENCES
Reconstruction in Different Classes of 2D Discrete Sets (Invited Paper)
TLDR
It is shown that the reconstruction algorithms used in the class of hv-convex 4-connected sets (polyominoes) can be used, with small modifications, for reconstructing hV- Convex 8- connected sets and the directed h-Convex sets are uniquely reconstructible with respect to the row and column sum vectors.
Advances in discrete tomography and its applications
ANHA Series Preface Preface List of Contributors Introduction / A. Kuba and G.T. Herman Part I. Foundations of Discrete Tomography An Introduction to Discrete Point X-Rays / P. Dulio, R.J. Gardner,
Polyominoes Defined by Two Vectors
  • A. Lungo
  • Mathematics
    Theor. Comput. Sci.
  • 1994
...
...