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Topology-based Smoothing of 2D Scalar Fields with C1-Continuity Corresponding Publication
Logo Data sets coming from simulations or sampling of real-world phenomena often contain noise that hinders their processing and analysis. Automatic filtering and denoising can be challenging: when the nature of the noise is unknown, it is difficult to distinguish between noise and actual data features; in addition, the filtering process itself may introduce artificial features into the data set that were not originally present. In this paper, we propose a smoothing method for 2D scalar fields that gives the user explicit control over the data features. We define features as critical points of the given scalar function, and the topological structure they induce (i.e., the Morse-Smale complex). Feature significance is rated according to topological persistence. Our method allows filtering out spurious features that arise due to noise by means of topological simplification, providing the user with a simple interface that defines the significance threshold, coupled with immediate visual feedback of the remaining data features. In contrast to previous work, our smoothing method guarantees a C1-continuous output scalar field with the exact specified features and topological structures. T. Weinkauf, Y. Gingold, O. Sorkine
Topology-based Smoothing of 2D Scalar Fields with C1-Continuity
Computer Graphics Forum (Proc. EuroVis) 29(3), June 2010
[slideshow]
BenzeneOrig
BenzeneOrig
BenzeneReconstructed
BenzeneReconstructed
DiscreteEmbedding
DiscreteEmbedding
HarmonicVersusC1_Harmonic
HarmonicVersusC1_Harmonic
HarmonicVersusC1_Optimized
HarmonicVersusC1_Optimized
HarmonicVersusC1_Orig
HarmonicVersusC1_Orig
MergingMorseCellsAfter
MergingMorseCellsAfter
MergingMorseCellsBefore
MergingMorseCellsBefore
MonotonicityGraph
MonotonicityGraph
MorseCell
MorseCell
MorseSmaleCells3a
MorseSmaleCells3a
MorseSmaleCells3b
MorseSmaleCells3b
MorseSmaleCells4
MorseSmaleCells4
OverlayHistogram
OverlayHistogram
Overlay_ABCDCombinedHF
Overlay_ABCDCombinedHF
Overlay_ABCDCombinedHFTopo
Overlay_ABCDCombinedHFTopo
Overlay_ABCDSimplified
Overlay_ABCDSimplified
Overlay_Noise2D
Overlay_Noise2D
Overlay_NoiseOrigTopo
Overlay_NoiseOrigTopo
Overlay_NoiseOrigTopoHF
Overlay_NoiseOrigTopoHF
Overlay_NoiseSimplified
Overlay_NoiseSimplified
Overlay_Orig
Overlay_Orig
Overlay_OrigTopo
Overlay_OrigTopo
Persistence1D
Persistence1D
PIVB9_Height_Orig
PIVB9_Height_Orig
PIVB9_Height_P18
PIVB9_Height_P18
PIVB9_Height_P5
PIVB9_Height_P5
PIVB9_Histo
PIVB9_Histo
PIVB9_PSNR
PIVB9_PSNR
PIVB9_Slice_Orig
PIVB9_Slice_Orig
PIVB9_Slice_P18
PIVB9_Slice_P18
PIVB9_Slice_P5
PIVB9_Slice_P5
PressureHistogram
PressureHistogram
Pressure_Orig
Pressure_Orig
Pressure_OrigTopo
Pressure_OrigTopo
Pressure_Simplified
Pressure_Simplified
Pressure_SimplifiedTopo
Pressure_SimplifiedTopo
SeparatrixFairingAfter
SeparatrixFairingAfter
SeparatrixFairingBefore
SeparatrixFairingBefore
SimpleReconstruction_CP
SimpleReconstruction_CP
SimpleReconstruction_Harmonic
SimpleReconstruction_Harmonic
SimpleReconstruction_HarmonicTop
SimpleReconstruction_HarmonicTop
SimpleReconstruction_OrigSep
SimpleReconstruction_OrigSep
SimpleReconstruction_ReSep
SimpleReconstruction_ReSep
Smooth1DOrigTopo
Smooth1DOrigTopo
Smooth1DSimpleReconstruction
Smooth1DSimpleReconstruction
Smooth1DSmoothReconstruction
Smooth1DSmoothReconstruction
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