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Extraction of Dominant Extremal Structures in Volumetric Data using Separatrix Persistence Corresponding Publication
Logo Extremal lines and surfaces are features of a 3D scalar field where the scalar function becomes minimal or maximal with respect to a local neighborhood. These features are important in many applications, e.g., computer tomography, fluid dynamics, cell biology. We present a novel topological method to extract these features using discrete Morse theory. In particular, we extend the notion of Separatrix Persistence from 2D to 3D, which gives us a robust estimation of the feature strength for extremal lines and surfaces. Not only does it allow us to determine the most important (parts of) extremal lines and surfaces, it also serves as a robust filtering measure of noise-induced structures. Our purely combinatorial method does not require derivatives or any other numerical computations. D. Günther, H.-P. Seidel, T. Weinkauf
Extraction of Dominant Extremal Structures in Volumetric Data using Separatrix Persistence
Computer Graphics Forum 31(8), December 2012
[slideshow]
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aneurism_lines_zoomIn
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aneurism_surface
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aneurism_surface_zoomIn
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artificial_initial
artificial_persistenceAndData
artificial_persistenceAndData
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attractingSurface
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BonsaiSepAll
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BonsaiSepFilteredSmooth
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bonsai_ridges_allLines_cropped
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bonsai_ridges_angleFilter_cropped
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bonsai_ridges_thresholdFilter_cropped
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cellComplex
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cellGraph_v2
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cellMembrane_gaussData_ridgeSurface
cellMembrane_gaussData_sepSurface
cellMembrane_gaussData_sepSurface
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cellMembrane_origData_ridgeSurface
cellMembrane_origData_sepSurface
cellMembrane_origData_sepSurface
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discreteSurface
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extremalStructures
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Persistence1D
Persistence1D
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repellingSurface
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ridgeLines
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sepLineImportance
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vortexstreet_cuttedQ
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vortexStreet_v2
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