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Sauber et al.: Multifield-Graphs Multifield-Graphs: An Approach to Visualizing Correlations in Multifield Scalar Data Natascha Sauber, Holger Theisel, Hans-Peter Seidel MPI Informatik

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Sauber et al.: Multifield-Graphs Motivation Definition: –Multifield = n (scalar) fields Occurrence of Multifield-Data –Physical simulations –Medical imaging –Usually between 5 and 100 fields Pressure Up wind Ice Snow

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Sauber et al.: Multifield-Graphs Scalar field Visualization Iso surface: Direct volume rendering : Orthogonal slices: Standard approaches for single scalar field visualisation:

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Sauber et al.: Multifield-Graphs Single Field visualization techniques are not sufficient for showing and detecting –Relations –Global and local differences –Redundancies Multifield Visualization

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Sauber et al.: Multifield-Graphs Single field visualization technique: –Side-by-side -> Problem: no subtle differences visible Multifield Visualization

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Sauber et al.: Multifield-Graphs Single field visualization technique: –Sequential-in-time -> Problem: only pairwise Multifield Visualization

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Sauber et al.: Multifield-Graphs Single field visualization technique: –Sequential-in-time -> Problem: only pairwise Multifield Visualization

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Sauber et al.: Multifield-Graphs Previous work Visualization approach –Correlation fields –Multifield-Graph Application –ABC-Flow features –Hurricane Simulation Overview

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Sauber et al.: Multifield-Graphs Dimension brushing [Doleisch 05] Brush values in 2D scatterplot: Previous work

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Sauber et al.: Multifield-Graphs Dimension brushing [Doleisch 05] Brush values in 2D scatterplot: Visualize brushed values in 3D: Many degrees of freedom Previous work

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Sauber et al.: Multifield-Graphs Local and Global Comparison of continuous functions [Edelsbrunner 04] –Comparison of the gradients –Global comparison: –Local comparison: –Problem: restricted to k <= d fields (d = # dimensions) Previous work

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Sauber et al.: Multifield-Graphs Previous work Visualization approach –Correlation fields –Multifield-Graph Application –ABC-Flow features –Hurricane Simulation Overview

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Sauber et al.: Multifield-Graphs Our Approach –n Scalar Fields: Multifield Visualization

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Sauber et al.: Multifield-Graphs Our Approach –n Scalar Fields: –Correlation fields: Contain local correlation between fields Multifield Visualization

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Sauber et al.: Multifield-Graphs Our Approach –n Scalar Fields: –Correlation fields: Contain local correlation between fields –Multifield-Graph: Overviews correlation fields Multifield Visualization

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Sauber et al.: Multifield-Graphs Our Approach –n Scalar Fields: –Correlation fields: contain local correlation between fields –Multifield-Graph: overview correlation fields –Select and visualize certain correlation fields Multifield Visualization

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Sauber et al.: Multifield-Graphs Previous work Visualization approach –Correlation fields –Multifield-Graph Application –ABC-Flow features –Hurricane Simulation Overview

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Sauber et al.: Multifield-Graphs Definitions: –A correlation field C N with N {1... n} is a scalar field which contains the local correlation of the fields in N –Local correlation := similar local changes –Example: C {012} contains local correlation between the fields S 0, S 1, and S 2 Correlation fields

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Sauber et al.: Multifield-Graphs Computation of local correlation with an arbitrary local correlation measure –Region based –Point based We used a measure based on gradients –Local –Important feature –Independent of scalar values Correlation fields

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Sauber et al.: Multifield-Graphs Desired properties: – Similarity of gradient magnitude: Normalized fields – Similarity of gradient direction: Gradient similarity measure equal similar (no influence of orientation) maximal dissimilar

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Sauber et al.: Multifield-Graphs Similarity of pair vectors: Directions similarity: Magnitude similarity: Range: [0;1] Gradient similarity measure

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Sauber et al.: Multifield-Graphs Similarity measure for |N| vectors out of contained pairs: Using the angle between least similar gradients: Gradient similarity measure similar dissimilar

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Sauber et al.: Multifield-Graphs Scalar fields: Correlation field: Gradient similarity measure

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Sauber et al.: Multifield-Graphs Previous work Visualization approach –Correlation fields –Multifield-Graph Application –ABC-Flow features –Hurricane Simulation Overview

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Sauber et al.: Multifield-Graphs It is not possible to examine all correlation fields, because of their exponential number => get overview with Multifield-Graph Goal show the core information of many correlation Fields –Reduce information of every correlation field to an Icon Multifield-Graph

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Sauber et al.: Multifield-Graphs Icons show: –Disc Size: volume percentage of high correlation (correlation value above a threshold θ) Color: average value of these highly correlated values –Label: Identities of corresponding scalar Fields Color coding –Average correlation values Multifield-Graph Threshold θ

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Sauber et al.: Multifield-Graphs The Multifield-Graph G = (V,E) consists of: –Nodes V = Icons represent correlation fields of sets of fields –Edges E: visualize subset relationships of correlation fields Multifield-Graph

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Sauber et al.: Multifield-Graphs Multifield-Graph Multifield-Graph of n=6 fields –Subset relationships (dark background and edges) Focus on correlation fields with high correlation: –High percentage of correlating values –High average correlation

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Sauber et al.: Multifield-Graphs Computation of the Multifield-Graph: –Choose a similarity threshold θ –For each correlation field: Count the number points above θ Compute average value of these points Multifield-Graph

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Sauber et al.: Multifield-Graphs Computation time depends on –The Number of input fields –Size of fields –Correlation measure Optimization –Similarity measure = minimum of pair similarities => compute and store only pair correlation fields –Perform sub-sampling Example: –Multifield-Graph computation of 6 fields 250x250x50: 1 minute Multifield-Graph

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Sauber et al.: Multifield-Graphs Previous work Visualization approach –Correlation fields –Multifield-Graph Application –ABC-Flow features –Hurricane Simulation Overview

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Sauber et al.: Multifield-Graphs Analyze ABC-Flow: –An ABC-Flow is a steady solution of the force free Euler equation Application

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Sauber et al.: Multifield-Graphs Compute 8 scalar characteristics of the ABC- Flow: –0: Vorticity –1: Flow magnitude –2: Stableness –3,4,5: x,y,z-component of the average flow direction of a pathline –6: Average particle velocity along a pathline –7: Length of a pathline Application

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Sauber et al.: Multifield-Graphs Multifield-Graph of ABC-Flow characteristics: –Focused on correlation fields with more than 11 % of the volume having a correlation above θ = 0.8 Application

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Sauber et al.: Multifield-Graphs Application 6: Average particle velocity along a pathline 7: Length of a pathline

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Sauber et al.: Multifield-Graphs Correlation field of two flow characteristics: –6: Average particle velocity along a pathline –7: Length of a pathline Application Correlation field of field 6 and 7 Close-up view

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Sauber et al.: Multifield-Graphs Application 1: Flow magnitude 0: Vorticity

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Sauber et al.: Multifield-Graphs Correlation field of two flow characteristics –0: vorticity –1: magnitude Application Correlation field of vorticity and flow magnitude

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Sauber et al.: Multifield-Graphs Application

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Sauber et al.: Multifield-Graphs Correlation field C {1267} of characteristics: –Correlation field between: 1: magnitude 2: stableness 6: average particle velocity along a pathline 7: length of a pathline Application

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Sauber et al.: Multifield-Graphs 6 fields of a hurricane simulation: Application

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Sauber et al.: Multifield-Graphs Multifield-Graph of the 6 hurricane fields Application

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Sauber et al.: Multifield-Graphs Multifield-Graph of the 6 hurricane fields Application

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Sauber et al.: Multifield-Graphs Local Multifield-Graphs of 2 layers of the dataset Application

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Sauber et al.: Multifield-Graphs Visualization of 2 layers of correlation field C {45} –4: Vapor –5: Temperature Application

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Sauber et al.: Multifield-Graphs Application

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Sauber et al.: Multifield-Graphs Visualization approach –Correlation fields: local correlations –Multifield-Graph: overview Adaptable to –Other correlation measures –Other interpretation aims Results –Useful for detecting similar fields and expressing the differences and redundancies between them Conclusion

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Sauber et al.: Multifield-Graphs Involve user guided interpretation aims Search for other similarity measures –Which can inherently compare more than two input fields –Which can detect more general relations –Which can better express differences between fields Extend the method to vector and tensor fields Future work

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Sauber et al.: Multifield-Graphs Multifield-Graphs: An Approach to Visualizing Correlations in Multifield Scalar Data Natascha Sauber, Holger Theisel, Hans-Peter Seidel MPI Informatik

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Sauber et al.: Multifield-Graphs

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Thanks for your attention!

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Sauber et al.: Multifield-Graphs References [doleisch 05] H. Doleisch, M. Mayer, M. Hauser: Interactive Feature Specification for Simulation Data on Time-Varying Grids. Simvis 2005 [kniss 02] J. Kniss, G. Kindlmann, C. Hansen: Multidimensional Transfer Functions for Interactive Volume Rendering. IEEE Transactions on Visualization and Computer Graphics 2002 [telea 99] A. Telea, J. J. van Wijk: Simplified representation of vector fields. IEEE Visualisation 1999 [edelsbrunner 04] H. Edelsbrunner, J. Harer, V. Natarajan and V. Pascucci: Local and global comparison of continuous functions. IEEE Visualization 2004

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Sauber et al.: Multifield-Graphs

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Gradient similarity measure Example: Fields: Correlation Fields:

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Sauber et al.: Multifield-Graphs Direct Volume Rendering [kniss02] Multi-dimensional Transfer-Function Additional dimension: gradient Previous work

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Sauber et al.: Multifield-Graphs Gradient similarity measure Scalar Fields: Correlation Field:

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Sauber et al.: Multifield-Graphs Gradient similarity measure Similarity of a pair of vectors: Direction similarity: Magnitude similarity: Isolines of vectors equal similar to the red reference vector:

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