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Digital Image Processing
Structural Properties
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Closure Systems and their Structure
Closure Systems and their Structure,Robert E. Jamison,John L. Pfaltz
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Closure Systems and their Structure
(
Citations: 12
)
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Robert E. Jamison
,
John L. Pfaltz
this paper.In Section 1, we examine antimatroid closure spaces. In Section 2, we consider aclosure operator that has been widely used in
digital image processing
[25]. Thisoperator, which can be equally well defined on graphs, is not antimatroid; but it isshown in Section 3 that it retains many of the same structural properties, and isclosely related to the classic graphtheoretic theme of domination. Finally, in Section4, we relate these concepts to premise system[30].1 Antimatroid...
Conference:
Relational Methods in Computer Science  RelMiCS
, pp. 121132, 2000
Cumulative
Annual
Citation Context
(5)
...In terms of the structure of minimal generators for andclauses, an analog of Theorem 3, describing the minimal generators of a closed andclause as the minimal hitting sets of its differential lower shadow is already known [
9
]...
Lizhuang Zhao
,
et al.
BLOSOM: a framework for mining arbitrary boolean expressions
...A similar theorem was independently reported in [
6
]...
Mohammed Javeed Zaki
,
et al.
Reasoning about sets using redescription mining
...sets of its difierential lower shadow is already known [
16
]...
Lizhuang Zhao
,
et al.
BLOSOM: A Framework for Mining Arbitrary Boolean Expressions over Attr...
...In terms of the strucure of minimal generators for andclauses, an analog of Theorem 3, describing the minimal generators of a closed andclause as the minimal hitting sets of its differential lower shadow is already known [
9
]...
Lizhuang Zhao
,
et al.
BLOSOM: A Framework for Mining Boolean Expressions
...In terms of the structure of minimal generators for andclauses, an analog of Theorem 3, describing the minimal generators of a closed andclause as the minimal hitting sets of its differential lower shadow is already known [
9
]...
Lizhuang Zhao
,
et al.
A Framework for Mining Arbitrary Boolean Expressions
References
(9)
Evaluating the binary partition function when N=2 n
(
Citations: 6
)
John L. Pfaltz
Published in 1995.
Fundamentals of domination in graphs
(
Citations: 620
)
T. W. Haynes
,
S. T. Hedetniemi
,
P. J. Slater
Published in 1998.
Distance functions on digital pictures
(
Citations: 297
)
Azriel Rosenfeld
,
John L. Pfaltz
Journal:
Pattern Recognition  PR
, vol. 1, no. 1, pp. 3361, 1968
Partition Coefficients of Acyclic Graphs
(
Citations: 2
)
John L. Pfaltz
Conference:
Workshop on GraphTheoretic Concepts in Computer Science  WG
, pp. 318322, 1995
Sequential Operations in Digital Picture Processing
(
Citations: 561
)
Azriel Rosenfeld
,
John L. Pfaltz
Journal:
Journal of The ACM  JACM
, vol. 13, no. 4, pp. 471494, 1966
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Citations
(12)
Mining Frequent Boolean Expressions: Application to Gene Expression and Regulatory Modeling
Mohammed Javeed Zaki
,
Naren Ramakrishnan
,
Lizhuang Zhao
Journal:
International Journal of Knowledge Discovery in Bioinformatics
, vol. 1, no. 3, pp. 6896, 2010
Efficient Mining of Frequent Closures with Precedence Links and Associated Generators
(
Citations: 1
)
Laszlo Szathmary
,
Petko Valtchev
,
Amedeo Napoli
Published in 2008.
BLOSOM: a framework for mining arbitrary boolean expressions
(
Citations: 5
)
Lizhuang Zhao
,
Mohammed J. Zaki
,
Naren Ramakrishnan
Conference:
Knowledge Discovery and Data Mining  KDD
, pp. 827832, 2006
Reasoning about sets using redescription mining
(
Citations: 19
)
Mohammed Javeed Zaki
,
Naren Ramakrishnan
Conference:
Knowledge Discovery and Data Mining  KDD
, pp. 364373, 2005
Extracting semantics from data cubes using cube transversals and closures
(
Citations: 9
)
Alain Casali
,
Rosine Cicchetti
,
Lotfi Lakhal
Conference:
Knowledge Discovery and Data Mining  KDD
, pp. 6978, 2003