@conference {939,
	title = {Topological Subdivision Graphs for Comparative and Multifield Visualization},
	booktitle = {Topological Methods in Data Analysis and Visualization V},
	year = {2020},
	publisher = {Springer International Publishing},
	organization = {Springer International Publishing},
	address = {Cham},
	abstract = {We propose that a topological model of a real-valued function can be employed to define a spatial subdivision of the function{\textquoteright}s domain. When multiple topologically-induced subdivisions for the same or different functions on the same domain are combined, a finer spatial subdivision arises: the topological subdivision complex. The topological subdivision graph then gives adjacency relations among the d-cells of the subdivision complex and can be used to describe similarities among topological models. We apply this idea to give new topological models for multiple real-valued functions (multifields), extending contour trees and Morse-Smale complexes to these problem settings, and we illustrate our idea for piecewise-linear functions. We also discuss how our work relates to joint contour nets.},
	isbn = {978-3-030-43036-8},
	author = {Heine, Christian and Garth, Christoph},
	editor = {Carr, Hamish and Fujishiro, Issei and Sadlo, Filip and Takahashi, Shigeo}
}
@article {schneider2013interactive,
	title = {Interactive comparison of multifield scalar data based on largest contours},
	journal = {Computer Aided Geometric Design},
	volume = {30},
	number = {6},
	year = {2013},
	pages = {521{\textendash}528},
	publisher = {Elsevier},
	author = {Schneider, D. and Heine, C. and Carr, Hamish and Gerik Scheuermann}
}
@article {CGF:CGF12121,
	title = {Towards Multifield Scalar Topology Based on Pareto Optimality},
	journal = {Computer Graphics Forum},
	volume = {32},
	number = {3pt3},
	year = {2013},
	pages = {341{\textendash}350},
	publisher = {Blackwell Publishing Ltd},
	keywords = {and systems, I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling{\textemdash}Geometric algorithms, languages},
	issn = {1467-8659},
	doi = {10.1111/cgf.12121},
	url = {http://dx.doi.org/10.1111/cgf.12121},
	author = {Huettenberger, L. and Heine, C. and Carr, Hamish and Gerik Scheuermann and Garth, C.}
}
@article { HSC*:2011,
	title = {Drawing Contour Trees in the Plane},
	journal = {IEEE Transactions on Visualization and Computer Graphics},
	volume = {17},
	number = {11},
	year = {2011},
	pages = {1599-1611},
	author = {Heine, C. and Schneider, D. and Carr, Hamish and Gerik Scheuermann}
}
@article { SWC*:2008,
	title = {Interactive Comparison of Scalar Fields Based on Largest Contours with Applications to Flow Visualization},
	journal = {IEEE Transaction on Visualization and Computer Graphics},
	volume = {14},
	number = {6},
	year = {2008},
	pages = {1475-1482},
	author = {Schneider, D. and Alexander Wiebel and Carr, Hamish and Mario Hlawitschka and Gerik Scheuermann}
}
