Sauber et al.: Multifield-Graphs Multifield-Graphs: An Approach to Visualizing Correlations in...

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


Motivation Definition:

– Multifield = n (scalar) fields

Occurrence of Multifield-Data– Physical simulations– Medical imaging– Usually between 5 and 100 fields

Pressure

Up wind

IceSnow


Scalar field Visualization

Iso surface:

Direct volume

rendering:

Orthogonal

slices:

Standard approaches for single scalar field visualisation:


Single Field visualization techniques are not sufficient for showing and detecting– Relations – Global and local differences– Redundancies

Multifield Visualization


Single field visualization technique:– Side-by-side

-> Problem: no subtle differences visible



Single field visualization technique:– Sequential-in-time

-> Problem: only pairwise



Previous work Visualization approach

– Correlation fields– Multifield-Graph

Application– ABC-Flow features– Hurricane Simulation

Overview


Dimension brushing [Doleisch 05] Brush values in 2D scatterplot:

Previous work


Dimension brushing [Doleisch 05] Brush values in 2D scatterplot:

Visualize brushed values in 3D:

Many degrees of freedom

Previous work


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





Overview


Our Approach– n Scalar Fields:




– Correlation fields: Contain local correlation

between fields




– Correlation fields: Contain local correlation

between fields

– Multifield-Graph: Overviews correlation fields




– Correlation fields: contain local correlation

between fields

– Multifield-Graph: overview correlation fields

– Select and visualize certaincorrelation fields






Overview


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 S0, S

1, and S

2

Correlation fields


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


Desired properties:– Similarity of gradient magnitude:

Normalized fields

– Similarity of gradient direction:

Gradient similarity measure

equal similar(no influence of orientation)

maximal dissimilar


Similarity of pair vectors:

Directions similarity:

Magnitude similarity:

Range: [0;1]



Similarity measure for |N| vectors out of contained pairs:

Using the angle between least similar gradients:


similar dissimilar


Scalar fields:

Correlationfield:






Overview


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


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


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


Multifield-Graph

Multifield-Graph of n=6 fields

– Subset relationships(dark backgroundand edges)

Focus on correlation fields with

high correlation:– High percentage of correlating

values

– High average correlation


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


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





Overview


Analyze ABC-Flow:– An ABC-Flow is a steady solution of the force free

Euler equation

Application


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


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


Application

6: Average particle velocity along a pathline

7: Length of a pathline


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


Application

1: Flow magnitude

0: Vorticity


Correlation field of two flow characteristics

– 0: vorticity– 1: magnitude

Application

Correlation field of vorticity and flow magnitude


Application


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


6 fields of a hurricane simulation:

Application


Multifield-Graph of the 6 hurricane fields

Application


Local Multifield-Graphs of 2 layers of the dataset

Application


Visualization of 2 layers of correlation field C{45}

– 4: Vapor– 5: Temperature

Application


Application


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


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


Multifield-Graphs: An Approach to Visualizing Correlations in Multifield Scalar Data

Natascha Sauber, Holger Theisel, Hans-Peter Seidel

MPI Informatik


Thanks for your attention!


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


Gradient similarity measure Example:

Fields:

CorrelationFields:


Direct Volume Rendering [kniss02] Multi-dimensional Transfer-Function Additional dimension: gradient

Previous work



ScalarFields:

CorrelationField:


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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