2015 · 35 citations · 28 references
ComputingComputer ScienceData StructuresFeature EngineeringTopologyDistance MeasurementGraph AnalyticsMetric GeometryMetric LearningScalar Field TopologyTopological Data ModelTopological Data StructuresTopological Features
Scientific phenomena are often studied through collections of related scalar fields generated from different observations of the same phenomenon. Exploration of such data requires a robust distance measure to compare scalar fields for tasks such as identifying key events and establishing correspondence between features in the data. Towards this goal, we propose a topological data structure called the complete extremum graph and define a distance measure on it for comparing scalar fields in a feature-aware manner. We design an algorithm for computing the distance and show its applications in analysing time varying data.
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Algorithm 457: finding all cliques of an undirected graph
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Topology matching for fully automatic similarity estimation of 3D shapes
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Topological Persistence and Simplification
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