NDLI: Geometry-preserving topological landscapes

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Geometry-preserving topological landscapes

Content Provider	ACM Digital Library
Author	Hamann, Bernd Beketayev, Kenes Morozov, Dmitriy Weber, Gunther H. Abzhanov, Aidos
Abstract	We propose a novel technique for building geometry-preserving topological landscapes. Our technique creates a direct correlation between a scalar function and its topological landscape. This correlation is accomplished by introducing the notion of geometric proximity into the topological landscapes, reflecting the distance of topological features within the function domain. Furthermore, this technique enables direct comparative analysis between scalar functions, as long as they are defined on the same domain. We describe a construction technique that consists of three stages: contour tree computation, contour tree layout, and landscape construction. We provide a detailed description for the latter two steps. For the contour tree layout stage, we discuss dimension reduction and edge routing techniques that produce a drawing of the contour tree on the plane that preserves the geometric proximity. For the landscape construction stage, we develop a contour construction algorithm that takes the contour tree layout as an input, adds contours at heights that correspond to saddles of the contour tree, and produces a contour map. After an additional triangulation step, this construction method results in the landscape that has the same contour tree as the original function.
Starting Page	155
Ending Page	160
Page Count	6
File Format	PDF
ISBN	9781450318358
DOI	10.1145/2425296.2425324
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2012-11-26
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Scalar field topology Topological landscapes Multidimensional scaling Visual metaphor
Content Type	Text
Resource Type	Article

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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