Tierny, J and Carr, HA (2017) Jacobi Fiber Surfaces for Bivariate Reeb Space Computation. IEEE Transactions on Visualization and Computer Graphics, 23 (1). pp. 960-969. ISSN 1077-2626
Abstract
This paper presents an efficient algorithm for the computation of the Reeb space of an input bivariate piecewise linear scalar function f defined on a tetrahedral mesh. By extending and generalizing algorithmic concepts from the univariate case to the bivariate one, we report the first practical, output-sensitive algorithm for the exact computation of such a Reeb space. The algorithm starts by identifying the Jacobi set of f , the bivariate analogs of critical points in the univariate case. Next, the Reeb space is computed by segmenting the input mesh along the new notion of Jacobi Fiber Surfaces, the bivariate analog of critical contours in the univariate case. We additionally present a simplification heuristic that enables the progressive coarsening of the Reeb space. Our algorithm is simple to implement and most of its computations can be trivially parallelized. We report performance numbers demonstrating orders of magnitude speedups over previous approaches, enabling for the first time the tractable computation of bivariate Reeb spaces in practice. Moreover, unlike range-based quantization approaches (such as the Joint Contour Net), our algorithm is parameter-free. We demonstrate the utility of our approach by using the Reeb space as a semi-automatic segmentation tool for bivariate data. In particular, we introduce continuous scatterplot peeling, a technique which enables the reduction of the cluttering in the continuous scatterplot, by interactively selecting the features of the Reeb space to project. We provide a VTK-based C++ implementation of our algorithm that can be used for reproduction purposes or for the development of new Reeb space based visualization techniques.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works. |
Keywords: | Topological data analysis, multivariate data, data segmentation |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) |
Funding Information: | Funder Grant number EPSRC EP/J013072/1 |
Depositing User: | Symplectic Publications |
Date Deposited: | 11 Aug 2016 15:10 |
Last Modified: | 15 Jun 2018 08:58 |
Published Version: | https://dx.doi.org/10.1109/TVCG.2016.2599017 |
Status: | Published |
Publisher: | Institute of Electrical and Electronics Engineers (IEEE) |
Identification Number: | 10.1109/TVCG.2016.2599017 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:103600 |