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dc.contributor.advisorNatarajan, Vijay
dc.contributor.authorHarish, D
dc.date.accessioned2018-02-22T21:48:30Z
dc.date.accessioned2018-07-31T04:38:55Z
dc.date.available2018-02-22T21:48:30Z
dc.date.available2018-07-31T04:38:55Z
dc.date.issued2018-02-23
dc.date.submitted2012
dc.identifier.urihttp://etd.iisc.ac.in/handle/2005/3173
dc.identifier.abstracthttp://etd.iisc.ac.in/static/etd/abstracts/4033/G25656-Abs.pdfen_US
dc.description.abstractLevel sets are extensively used for the visualization of scalar fields. The Reeb graph of a scalar function tracks the evolution of the topology of its level sets. It is obtained by mapping each connected component of a level set to a point. The Reeb graph and its loop-free version called the contour tree serve as an effective user interface for selecting meaningful level sets and for designing transfer functions for volume rendering. It also finds several other applications in the field of scientific visualization. In this thesis, we focus on designing algorithms for efficiently computing the Reeb graph of scalar functions and using the Reeb graph for effective visualization of scientific data. We have developed three algorithms to compute the Reeb graph of PL functions defined over manifolds and non-manifolds in any dimension. The first algorithm efficiently tracks the connected components of the level set and has the best known theoretical bound on the running time. The second algorithm, utilizes an alternate definition of Reeb graphs using cylinder maps, is simple to implement and efficient in practice. The third algorithm aggressively employs the efficient contour tree algorithm and is efficient both theoretically, in terms of the worst case running time, and practically, in terms of performance on real-world data. This algorithm has the best performance among existing methods and computes the Reeb graph at least an order of magnitude faster than other generic algorithms. We describe a scheme for controlled simplification of the Reeb graph and two different graph layout schemes that help in the effective presentation of Reeb graphs for visual analysis of scalar fields. We also employ the Reeb graph in four different applications – surface segmentation, spatially-aware transfer function design, visualization of interval volumes, and interactive exploration of time-varying data. Finally, we introduce the notion of topological saliency that captures the relative importance of a topological feature with respect to other features in its local neighborhood. We integrate topological saliency with Reeb graph based methods and demonstrate its application to visual analysis of features.en_US
dc.language.isoen_USen_US
dc.relation.ispartofseriesG25656en_US
dc.subjectComputer Graphics - Algorithmsen_US
dc.subjectReeb Graphsen_US
dc.subjectReeb Graphs - Visualizationen_US
dc.subjectReeb Graphs - Applicationsen_US
dc.subjectReeb Graphs - Computationen_US
dc.subjectScalar Functionsen_US
dc.subjectReeb Graphs - Algorithmsen_US
dc.subjectTopological Saliencyen_US
dc.subjectSweep Algorithmen_US
dc.subjectCylinder Map Algorithmen_US
dc.subjectRecon Algorithmen_US
dc.subject.classificationComputer Scienceen_US
dc.titleReeb Graphs : Computation, Visualization and Applicationsen_US
dc.typeThesisen_US
dc.degree.namePhDen_US
dc.degree.levelDoctoralen_US
dc.degree.disciplineFaculty of Engineeringen_US


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