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## Filters

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On the Number of hv-Convex Discrete Sets
[chapter]

*
Lecture Notes in Computer Science
*

This paper collects several statistics

doi:10.1007/978-3-540-78275-9_10
dblp:conf/iwcia/Balazs08
fatcat:dpy3tvryyracvbhhtk2scnnbb4
*on**hv*-*convex**discrete**sets*, which are*of*great importance in*the*analysis*of*algorithms for reconstructing such kind*of**discrete**sets*. ...*One**of**the*basic problems in*discrete*tomography is*the*reconstruction*of**discrete**sets*from few projections. ... Enumeration*of**hv*-*Convex**Discrete**Sets**The*class*of**hv*-*convex**discrete**sets*is*one**of**the*most important classes in*discrete*tomography. ...##
###
A benchmark set for the reconstruction of hv-convex discrete sets

2009
*
Discrete Applied Mathematics
*

*of*

*hv*-

*convex*

*discrete*

*sets*and its subclasses. ... By using this benchmark

*set*

*the*paper also collects several statistics

*on*

*hv*-

*convex*

*discrete*

*sets*, which are

*of*great importance in

*the*analysis

*of*algorithms for reconstructing such kinds

*of*

*discrete*... Preliminary version

*of*

*the*paper was presented at

*the*12th International Workshop

*on*Combinatorial Image Analysis, Buffalo, NY, USA, April 2008 [1] . ...

##
###
Generation and Reconstruction of hv-convex 8-connected Discrete Sets

2001
*
Acta Cybernetica
*

This algorithm is based

dblp:journals/actaC/Balogh01
fatcat:y4e6l6mjfveyzoxorape6twlhi
*on*an extension*of*a theory previously used for a more special class*of**hv*-*convex**discrete**sets*. ...*The*second part*of**the*paper deals with*the*reconstruction*of**hv*-*convex*8-connected*discrete**sets*.*The*main idea*of*this algorithm is to rewrite*the*whole reconstruction problem as a 2SAT problem. ... This work was supported by FKFP 0908/1997 Grant*of**the*Hungarian Ministry*of*Education, OTKA T032241, and by joint project MTA-NSF 123 "Aspects*of**Discrete*Tomography" (NSF DMS9612077). ...##
###
Reconstruction of Canonical hv-Convex Discrete Sets from Horizontal and Vertical Projections
[chapter]

2009
*
Lecture Notes in Computer Science
*

*The*problem

*of*reconstructing some special

*hv*-

*convex*

*discrete*

*sets*from their two orthogonal projections is considered. ... 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 ... Conclusion We introduced an intermediate subclass

*of*

*hv*-

*convex*

*discrete*

*sets*that lies in between

*the*class

*of*

*hv*-

*convex*8-connected

*sets*and

*the*class

*of*general

*hv*-

*convex*

*discrete*

*sets*. ...

##
###
A framework for generating some discrete sets with disjoint components by using uniform distributions

2008
*
Theoretical Computer Science
*

Especially,

doi:10.1016/j.tcs.2008.06.010
fatcat:t6nhxoxbbbawrmrmgy7uerxjhu
*the*uniform random generation*of**hv*-*convex**discrete**sets*and Q-*convex**discrete**sets*according to*the*size*of**the*minimal bounding rectangle are discussed. ... Assuming that*the**set*to be reconstructed belongs to a certain class*of**discrete**sets*with some geometrical properties is a commonly used technique to reduce*the**number**of*possibly many different solutions ... Random generation*of**hv*-*convex**discrete**sets**The*class*of**hv*-*convex**discrete**sets*is*one**of**the*most important classes in*discrete*tomography. ...##
###
On the Ambiguity of Reconstructing hv-Convex Binary Matrices with Decomposable Configurations

2008
*
Acta Cybernetica
*

*The*goal

*of*this paper is to study

*the*class

*of*

*hv*-

*convex*matrices which have decomposable configurations from

*the*viewpoint

*of*ambiguity. ...

*One*

*of*

*the*main difficulties in this task is that in certain cases

*the*projections do not uniquely determine

*the*binary matrix. ... Acknowledgments

*The*author

*of*this paper would like to thank

*the*anonymous reviewer for his suggestions which considerably improved

*the*quality

*of*

*the*paper. ...

##
###
Comparison of algorithms for reconstructing hv-convex discrete sets

2001
*
Linear Algebra and its Applications
*

All these algorithms have two versions:

doi:10.1016/s0024-3795(01)00430-x
fatcat:jahmfmiad5ayxk7ekxba3aft6a
*one*for reconstructing*hv*-*convex*polyominoes and another*one*for reconstructing*hv*-*convex*8-connected*discrete**sets*. ... Three reconstruction algorithms to be used for reconstructing*hv*-*convex**discrete**sets*from their row and column sums are compared. ... We thank*the*anonymous reviewer for asking*the*question about*the*execution times when there is no guarantee that there is a solution in*the*studied class*of**discrete**sets*. ...##
###
X-rays characterizing some classes of discrete sets

2001
*
Linear Algebra and its Applications
*

In this paper, we study

doi:10.1016/s0024-3795(01)00431-1
fatcat:sagmusyixbaxjnw5ch42ryamj4
*the*problem*of*determining*discrete**sets*by means*of*their X-rays. An X-ray*of*a*discrete**set*F in a direction u counts*the**number**of*points in F*on*each line parallel to u. ... A class F*of**discrete**sets*is characterized by*the**set*U*of*directions if each element in F is determined by its X-rays in*the*directions*of*U. ... Introduction A*discrete**set*is a finite subset*of**the*integer lattice Z 2 . An X-ray*of*a*discrete**set*in a direction u is a function giving*the**number**of*its points*on*each line parallel to u. ...##
###
An Empirical Study of Reconstructing hv-Convex Binary Matrices from Horizontal and Vertical Projections

2013
*
Acta Cybernetica
*

Using a large

doi:10.14232/actacyb.21.1.2013.11
fatcat:jbguksfcgbb47moc2rvlbj4mq4
*set**of*test images*of*different sizes and with varying*number**of*components, we show that*the*reconstruction quality can depend not only*on**the*size*of**the*image, but*on**the**number*and location ... In this paper we study*the*reconstruction*of**hv*-*convex*binary images from*the*horizontal and vertical projections, from an experimental point*of*view. ...*The**discrete**set*is called*hv*-*convex*if it is both h-and v-*convex*. ...##
###
Reconstruction in Different Classes of 2D Discrete Sets
[chapter]

1999
*
Lecture Notes in Computer Science
*

*The*reconstruction algorithms and complexity results are summarized in

*the*case

*of*

*hv*-

*convex*

*sets*,

*hv*-

*convex*polyominoes,

*hv*-

*convex*8-connected

*sets*, and directed h-

*convex*

*sets*. ...

*The*problem

*of*reconstruction

*of*two-dimensional

*discrete*

*sets*from their two projections is considered in different classes. ... Acknowledgments This work was supported by FKFP 0908/1997 Grant

*of*

*the*Hungarian Ministry

*of*Education. ...

##
###
Reconstruction of hv-Convex Binary Images with Diagonal and Anti-Diagonal Projections using Genetic Algorithm

2016
*
Indian Journal of Science and Technology
*

This paper is related to reconstruct

doi:10.17485/ijst/2016/v9i45/104103
fatcat:libtmcy5indczgirkpnut4mjcy
*the*binary images from small*number**of*projections. Objectives: To enhance*the*unambiguousness*of*image reconstructed. ... Then Genetic Algorithm is applied*on*image reconstructed after Chang's algorithm. ... To decrease*the**number**of*solution, geometrical properties*of**set*can be used. They applied connectivity restraint to attain polynomial-time recreation*of**hv**convex**discrete**sets*. ...##
###
Detection of the Discrete Convexity of Polyominoes
[chapter]

2000
*
Lecture Notes in Computer Science
*

*The*

*convexity*

*of*a

*discrete*region is a property used in numerous domains

*of*computational imagery. We study its detection in

*the*particular case

*of*polyominoes. ... Correlatively, we obtain a characterisation

*of*lower and upper

*convex*hulls

*of*a

*discrete*line segment. Finally, we evoke some applications

*of*these results to

*the*problem

*of*

*discrete*tomography. ... Acknowledgements We thank

*the*members

*of*

*the*PolKA research group

*of*LORIA for their review and constructive remarks. ...

##
###
Combinatorial approach to image analysis

2009
*
Discrete Applied Mathematics
*

Using

doi:10.1016/j.dam.2009.06.030
fatcat:skntxcwdybdvjgohod32jxvixi
*the*benchmark*set*,*the*author obtains several statistics*on**hv*-*convex**discrete**sets*, which can be used in*the*analysis*of*reconstruction algorithms. ... In*the*next paper, Péter Balázs considers*the*problem*of*reconstruction*of*an*hv*-*convex**discrete**set*. ...##
###
A Fast Algorithm for Reconstructing hv-Convex 8-Connected but Not 4-Connected Discrete Sets
[chapter]

2003
*
Lecture Notes in Computer Science
*

*One*important class

*of*

*discrete*

*sets*where

*the*reconstruction from two given projections can be solved in polynomial time is

*the*class

*of*

*hv*-

*convex*8-connected

*sets*. ... However, as it is shown, in

*the*case

*of*8-connected but not 4-connected

*sets*we can give an algorithm with worst case complexity

*of*O(mn · min{m, n}) by identifying

*the*so-called S4-components

*of*

*the*

*discrete*... In [2] an algorithm is also given to generate

*hv*-

*convex*8-connected

*discrete*

*sets*having fixed row and column

*numbers*with uniform distribution. ...

##
###
Reconstruction of convex 2D discrete sets in polynomial time

2002
*
Theoretical Computer Science
*

*The*reconstruction algorithms and complexity results are summarized in

*the*case

*of*

*hv*-

*convex*

*sets*,

*hv*-

*convex*8-connected

*sets*,

*hv*-

*convex*polyominoes, and directed h-

*convex*

*sets*. ... As new results some properties

*of*

*the*feet and spines

*of*

*the*

*hv*-

*convex*8-connected

*sets*are proven and it is shown that

*the*spine

*of*such a

*set*can be determined from

*the*projections in linear time. ... Acknowledgements This work was supported by FKFP 0908=1997 Grant

*of*

*the*Hungarian Ministry

*of*Education, OTKA Grant T032241, and by

*the*joint project MTA-NSF 123 "Aspects

*of*

*Discrete*Tomography" (NSF DMS9612077 ...

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