N-dimensional data-dependent reconstruction using topological changes

Zsolt Toth; Ivan Viola; Andrej Ferko; Eduard Groeller

doi:10.1007/978-3-540-70823-0_13

N-dimensional data-dependent reconstruction using topological changes

Zsolt Toth^*, Ivan Viola, Andrej Ferko, Eduard Groeller

^*Corresponding author for this work

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

Abstract

We introduce a new concept for a geometrically based feature preserving reconstruction technique of n-dimensional scattered data. Our goal is to generate an n-dimensional triangulation, which preserves the high frequency regions via local topology changes. It is the generalization of a 2D reconstruction approach based on data-dependent triangulation and Lawson's optimization procedure. The definition of the mathematic optimum of the reconstruction is given. We discuss an original cost function and a generalization of known functions for the n-dimensional case.

Original language	English
Title of host publication	TOPOLOGY-BASED METHODS IN VISUALIZATION
Editors	H Hauser, H Hagen, H Theisel
Publisher	Springer-Verlag Berlin Heidelberg
Pages	183-+
Number of pages	5
ISBN (Print)	978-3-540-70822-3
DOIs	https://doi.org/10.1007/978-3-540-70823-0_13
State	Published - 2007
Externally published	Yes
Event	Workshop on Topology-Based Methods in Visualization - Budmerice, Slovakia Duration: Sep 29 2005 → Sep 30 2005

Publication series

Name	Mathematics and Visualization
Publisher	SPRINGER-VERLAG BERLIN
ISSN (Print)	1612-3786

Conference

Conference	Workshop on Topology-Based Methods in Visualization
Country/Territory	Slovakia
City	Budmerice
Period	09/29/05 → 09/30/05

Keywords

SCATTERED DATA
INTERPOLATION
TRIANGULATION

Access to Document

10.1007/978-3-540-70823-0_13

Cite this

@inproceedings{8c82bab796d64fc5a878c32867da7505,

title = "N-dimensional data-dependent reconstruction using topological changes",

abstract = "We introduce a new concept for a geometrically based feature preserving reconstruction technique of n-dimensional scattered data. Our goal is to generate an n-dimensional triangulation, which preserves the high frequency regions via local topology changes. It is the generalization of a 2D reconstruction approach based on data-dependent triangulation and Lawson's optimization procedure. The definition of the mathematic optimum of the reconstruction is given. We discuss an original cost function and a generalization of known functions for the n-dimensional case.",

keywords = "SCATTERED DATA, INTERPOLATION, TRIANGULATION",

author = "Zsolt Toth and Ivan Viola and Andrej Ferko and Eduard Groeller",

year = "2007",

doi = "10.1007/978-3-540-70823-0_13",

language = "English",

isbn = "978-3-540-70822-3",

series = "Mathematics and Visualization",

publisher = "Springer-Verlag Berlin Heidelberg",

pages = "183--+",

editor = "H Hauser and H Hagen and H Theisel",

booktitle = "TOPOLOGY-BASED METHODS IN VISUALIZATION",

note = "Workshop on Topology-Based Methods in Visualization ; Conference date: 29-09-2005 Through 30-09-2005",

}

Toth, Z, Viola, I, Ferko, A & Groeller, E 2007, N-dimensional data-dependent reconstruction using topological changes. in H Hauser, H Hagen & H Theisel (eds), TOPOLOGY-BASED METHODS IN VISUALIZATION. Mathematics and Visualization, Springer-Verlag Berlin Heidelberg, pp. 183-+, Workshop on Topology-Based Methods in Visualization, Budmerice, Slovakia, 09/29/05. https://doi.org/10.1007/978-3-540-70823-0_13

N-dimensional data-dependent reconstruction using topological changes. / Toth, Zsolt; Viola, Ivan; Ferko, Andrej et al.
TOPOLOGY-BASED METHODS IN VISUALIZATION. ed. / H Hauser; H Hagen; H Theisel. Springer-Verlag Berlin Heidelberg, 2007. p. 183-+ (Mathematics and Visualization).

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

TY - GEN

T1 - N-dimensional data-dependent reconstruction using topological changes

AU - Toth, Zsolt

AU - Viola, Ivan

AU - Ferko, Andrej

AU - Groeller, Eduard

PY - 2007

Y1 - 2007

N2 - We introduce a new concept for a geometrically based feature preserving reconstruction technique of n-dimensional scattered data. Our goal is to generate an n-dimensional triangulation, which preserves the high frequency regions via local topology changes. It is the generalization of a 2D reconstruction approach based on data-dependent triangulation and Lawson's optimization procedure. The definition of the mathematic optimum of the reconstruction is given. We discuss an original cost function and a generalization of known functions for the n-dimensional case.

AB - We introduce a new concept for a geometrically based feature preserving reconstruction technique of n-dimensional scattered data. Our goal is to generate an n-dimensional triangulation, which preserves the high frequency regions via local topology changes. It is the generalization of a 2D reconstruction approach based on data-dependent triangulation and Lawson's optimization procedure. The definition of the mathematic optimum of the reconstruction is given. We discuss an original cost function and a generalization of known functions for the n-dimensional case.

KW - SCATTERED DATA

KW - INTERPOLATION

KW - TRIANGULATION

U2 - 10.1007/978-3-540-70823-0_13

DO - 10.1007/978-3-540-70823-0_13

M3 - Conference contribution

SN - 978-3-540-70822-3

T3 - Mathematics and Visualization

SP - 183-+

BT - TOPOLOGY-BASED METHODS IN VISUALIZATION

A2 - Hauser, H

A2 - Hagen, H

A2 - Theisel, H

PB - Springer-Verlag Berlin Heidelberg

T2 - Workshop on Topology-Based Methods in Visualization

Y2 - 29 September 2005 through 30 September 2005

ER -

N-dimensional data-dependent reconstruction using topological changes

Abstract

Publication series

Conference

Keywords

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