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

Péter Balázs
Lecture Notes in Computer Science  
This paper collects several statistics 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.  ... 
doi:10.1007/978-3-540-78275-9_10 dblp:conf/iwcia/Balazs08 fatcat:dpy3tvryyracvbhhtk2scnnbb4

A benchmark set for the reconstruction of hv-convex discrete sets

Péter Balázs
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] .  ... 
doi:10.1016/j.dam.2009.02.019 fatcat:455iya3j2vaozjnootgdxgl3qm

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

Emese Balogh
2001 Acta Cybernetica  
This algorithm is based 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).  ... 
dblp:journals/actaC/Balogh01 fatcat:y4e6l6mjfveyzoxorape6twlhi

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

Péter Balázs
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.  ... 
doi:10.1007/978-3-642-10210-3_22 fatcat:hmlougjxszeljnle3krnbdosvu

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

Péter Balázs
2008 Theoretical Computer Science  
Especially, 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.  ... 
doi:10.1016/j.tcs.2008.06.010 fatcat:t6nhxoxbbbawrmrmgy7uerxjhu

On the Ambiguity of Reconstructing hv-Convex Binary Matrices with Decomposable Configurations

Péter Balázs
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.  ... 
dblp:journals/actaC/Balazs08 fatcat:me7rom4kzzhjteff4dvpspyjpi

Comparison of algorithms for reconstructing hv-convex discrete sets

Emese Balogh, Attila Kuba, Csaba Dévényi, Alberto Del Lungo
2001 Linear Algebra and its Applications  
All these algorithms have two versions: 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.  ... 
doi:10.1016/s0024-3795(01)00430-x fatcat:jahmfmiad5ayxk7ekxba3aft6a

X-rays characterizing some classes of discrete sets

Elena Barcucci, Alberto Del Lungo, Maurice Nivat, Renzo Pinzani
2001 Linear Algebra and its Applications  
In this paper, we study 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.  ... 
doi:10.1016/s0024-3795(01)00431-1 fatcat:sagmusyixbaxjnw5ch42ryamj4

An Empirical Study of Reconstructing hv-Convex Binary Matrices from Horizontal and Vertical Projections

Zoltán Ozsvár, Péter Balázs
2013 Acta Cybernetica  
Using a large 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.  ... 
doi:10.14232/actacyb.21.1.2013.11 fatcat:jbguksfcgbb47moc2rvlbj4mq4

Reconstruction in Different Classes of 2D Discrete Sets [chapter]

Attila Kuba
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.  ... 
doi:10.1007/3-540-49126-0_12 fatcat:ahjo6tqblfd33kjgyfrh6v3iai

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

Jobanpreet Kaur, Shiv Kumar Verma, Anupriya Sharma
2016 Indian Journal of Science and Technology  
This paper is related to reconstruct 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.  ... 
doi:10.17485/ijst/2016/v9i45/104103 fatcat:libtmcy5indczgirkpnut4mjcy

Detection of the Discrete Convexity of Polyominoes [chapter]

Isabelle Debled-Rennesson, Rémy Jean-Luc, Jocelyne Rouyer-Degli
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.  ... 
doi:10.1007/3-540-44438-6_40 fatcat:eria52ncyzh27j74wjvgoafdxi

Combinatorial approach to image analysis

Valentin E. Brimkov, Reneta P. Barneva
2009 Discrete Applied Mathematics  
Using 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.  ... 
doi:10.1016/j.dam.2009.06.030 fatcat:skntxcwdybdvjgohod32jxvixi

A Fast Algorithm for Reconstructing hv-Convex 8-Connected but Not 4-Connected Discrete Sets [chapter]

Péter Balázs, Emese Balogh, Attila Kuba
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.  ... 
doi:10.1007/978-3-540-39966-7_37 fatcat:ms5swcvzbra5jhoyyvlb2h3azm

Reconstruction of convex 2D discrete sets in polynomial time

Attila Kuba, Emese Balogh
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  ... 
doi:10.1016/s0304-3975(01)00080-9 fatcat:f2af2eku6nhttha3kkwhyxemvm
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