Monotonic tree

Yuqing Song; Aidong Zhang

doi:10.1007/3-540-45986-3_10

Monotonic tree

Yuqing Song
, Aidong Zhang

Department of Computer Science and Engineering

SUNY Buffalo

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

10 Scopus citations

Abstract

Contour trees have been used in geographic information systems (GIS) and medical imaging to display scalar data. Contours are only defined for continuous functions. For an image represented by discrete data, a continuous function is first defined as an interpolation of the data. Then the contour tree is defined on this continuous function. In this paper, we introduce a new concept termed monotonic line, which is directly defined on discrete data. All monotonic lines in an image form a tree, called monotonic tree. As compared with contour trees, monotonic trees avoid the step of interpolation, thus can be computed more efficiently. Monotonic tree can also be used as a hierarchical representation of image structures in computer imagery.

Original language	English
Title of host publication	Discrete Geometry for Computer Imagery - 10th International Conference, DGCI 2002, Proceedings
Editors	Achille Braquelaire, Jacques-Olivier Lachaud, Anne Vialard
Publisher	Springer Verlag
Pages	114-123
Number of pages	10
ISBN (Print)	3540433805, 9783540433804
DOIs	https://doi.org/10.1007/3-540-45986-3_10
State	Published - 2002
Event	10th International Conference on Discrete Geometry for Computer Imagery, DGCI 2002 - Bordeaux, France Duration: Apr 3 2002 → Apr 5 2002

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	2301
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	10th International Conference on Discrete Geometry for Computer Imagery, DGCI 2002
Country/Territory	France
City	Bordeaux
Period	04/3/02 → 04/5/02

Access to Document

10.1007/3-540-45986-3_10

Cite this

Song, Y., & Zhang, A. (2002). Monotonic tree. In A. Braquelaire, J.-O. Lachaud, & A. Vialard (Eds.), Discrete Geometry for Computer Imagery - 10th International Conference, DGCI 2002, Proceedings (pp. 114-123). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2301). Springer Verlag. https://doi.org/10.1007/3-540-45986-3_10

Song, Yuqing ; Zhang, Aidong. / Monotonic tree. Discrete Geometry for Computer Imagery - 10th International Conference, DGCI 2002, Proceedings. editor / Achille Braquelaire ; Jacques-Olivier Lachaud ; Anne Vialard. Springer Verlag, 2002. pp. 114-123 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "Contour trees have been used in geographic information systems (GIS) and medical imaging to display scalar data. Contours are only defined for continuous functions. For an image represented by discrete data, a continuous function is first defined as an interpolation of the data. Then the contour tree is defined on this continuous function. In this paper, we introduce a new concept termed monotonic line, which is directly defined on discrete data. All monotonic lines in an image form a tree, called monotonic tree. As compared with contour trees, monotonic trees avoid the step of interpolation, thus can be computed more efficiently. Monotonic tree can also be used as a hierarchical representation of image structures in computer imagery.",

author = "Yuqing Song and Aidong Zhang",

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Song, Y & Zhang, A 2002, Monotonic tree. in A Braquelaire, J-O Lachaud & A Vialard (eds), Discrete Geometry for Computer Imagery - 10th International Conference, DGCI 2002, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2301, Springer Verlag, pp. 114-123, 10th International Conference on Discrete Geometry for Computer Imagery, DGCI 2002, Bordeaux, France, 04/3/02. https://doi.org/10.1007/3-540-45986-3_10

Monotonic tree. / Song, Yuqing; Zhang, Aidong.
Discrete Geometry for Computer Imagery - 10th International Conference, DGCI 2002, Proceedings. ed. / Achille Braquelaire; Jacques-Olivier Lachaud; Anne Vialard. Springer Verlag, 2002. p. 114-123 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2301).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - Contour trees have been used in geographic information systems (GIS) and medical imaging to display scalar data. Contours are only defined for continuous functions. For an image represented by discrete data, a continuous function is first defined as an interpolation of the data. Then the contour tree is defined on this continuous function. In this paper, we introduce a new concept termed monotonic line, which is directly defined on discrete data. All monotonic lines in an image form a tree, called monotonic tree. As compared with contour trees, monotonic trees avoid the step of interpolation, thus can be computed more efficiently. Monotonic tree can also be used as a hierarchical representation of image structures in computer imagery.

AB - Contour trees have been used in geographic information systems (GIS) and medical imaging to display scalar data. Contours are only defined for continuous functions. For an image represented by discrete data, a continuous function is first defined as an interpolation of the data. Then the contour tree is defined on this continuous function. In this paper, we introduce a new concept termed monotonic line, which is directly defined on discrete data. All monotonic lines in an image form a tree, called monotonic tree. As compared with contour trees, monotonic trees avoid the step of interpolation, thus can be computed more efficiently. Monotonic tree can also be used as a hierarchical representation of image structures in computer imagery.

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SN - 9783540433804

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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Song Y, Zhang A. Monotonic tree. In Braquelaire A, Lachaud JO, Vialard A, editors, Discrete Geometry for Computer Imagery - 10th International Conference, DGCI 2002, Proceedings. Springer Verlag. 2002. p. 114-123. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-45986-3_10

Monotonic tree

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