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dc.contributor.advisorNatarajan, Vijay
dc.contributor.authorThomas, Dilip Mathew
dc.date.accessioned2018-01-09T02:12:22Z
dc.date.accessioned2018-07-31T04:38:46Z
dc.date.available2018-01-09T02:12:22Z
dc.date.available2018-07-31T04:38:46Z
dc.date.issued2018-01-09
dc.date.submitted2014
dc.identifier.urihttp://etd.iisc.ac.in/handle/2005/2989
dc.identifier.abstracthttp://etd.iisc.ac.in/static/etd/abstracts/3852/G26732-Abs.pdfen_US
dc.description.abstractScalar fields are used to represent physical quantities measured over a domain of interest. Study of symmetric or repeating patterns in scalar fields is important in scientific data analysis because it gives deep insights into the properties of the underlying phenomenon. This thesis proposes three methods to detect symmetry in scalar fields. The first method models symmetry detection as a subtree matching problem in the contour tree, which is a topological graph abstraction of the scalar field. The contour tree induces a hierarchical segmentation of features at different scales and hence this method can detect symmetry at different scales. The second method identifies symmetry by comparing distances between extrema from each symmetric region. The distance is computed robustly using a topological abstraction called the extremum graph. Hence, this method can detect symmetry even in the presence of significant noise. The above methods compare pairs of regions to identify symmetry instead of grouping the entire set of symmetric regions as a cluster. This motivates the third method which uses a clustering analysis for symmetry detection. In this method, the contours of a scalar field are mapped to points in a high-dimensional descriptor space such that points corresponding to similar contours lie in close proximity to each other. Symmetry is identified by clustering the points in the descriptor space. We show through experiments on real world data sets that these methods are robust in the presence of noise and can detect symmetry under different types of transformations. Extraction of symmetry information helps users in visualization and data analysis. We design novel applications that use symmetry information to enhance visualization of scalar field data and to facilitate their exploration.en_US
dc.language.isoen_USen_US
dc.relation.ispartofseriesG26732en_US
dc.subjectScalar Fieldsen_US
dc.subjectSymmetry in Scalar Fielden_US
dc.subjectScientific Data Analysisen_US
dc.subjectScalar Field Symmetry Detectionen_US
dc.subjectScalar Field Data Analysisen_US
dc.subjectScalar Field Visualizationen_US
dc.subjectContour Treesen_US
dc.subjectExtremum Graphsen_US
dc.subjectComputational Geometryen_US
dc.subjectSymmetry Detectionen_US
dc.subjectContour Clusteringen_US
dc.subjectMultiscale Symmetry Detectionen_US
dc.subjectClustering Contoursen_US
dc.subjectSymmetric Structuresen_US
dc.subject.classificationComputer Scienceen_US
dc.titleSymmetry in Scalar Fieldsen_US
dc.typeThesisen_US
dc.degree.namePhDen_US
dc.degree.levelDoctoralen_US
dc.degree.disciplineFaculty of Engineeringen_US


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