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### A Rough Guide to Data Visualization

### Scientific Visualization

VizNET 2007 Annual Event

Ken Brodlie

School of Computing

University of Leeds

Data Visualization

- Visualization now seen as key part of modern computing
- High performance computing generates vast quantities of data ...
- High resolution measurement technology likewise ...
- microscopes, scanners, satellites
- Information systems involve not only large data sets but also complex connections...
- ... we need to harness our visual senses to help us understand the data

Applications - Meteorology

Pressure at levels

in atmosphere

- illustrated by

contour lines in a

slice plane

Generated by

the Vis5D system

from University of

Wisconsin (now

Vis5d+)

Vis5d: http://www.ssec.wisc.edu/~billh/vis5d.html

Vis5d+ : http://vis5d.sourceforge.net

Applications - Medicine

From scanner data, we can

visualize 3D pictures

of human anatomy, using

volume rendering

Generated by Anatomy.TV

used by Leeds medical students

to learn anatomy

Interface between immiscible fluids

e.g. oil / water

Loops and fingers arise when mixing starts

Rayleigh-Taylor instability

Simulated on ASCII Blue Pacific (Cook & Dimotakis, 2001)

Interface visualized using a density isosurface

Applications – Computational Fluid DynamicsApplications – Hierarchical Information

Usenet news

groups

For history of

treemaps see:

www.cs.umd.edu/

hcil/treemap-history

Developed over many years by Ben Schneiderman and colleagues

Structure of Session

Part 1

- Introduction
- What is visualization and some examples
- The humble graph
- Much to learn
- Scientific visualization
- Understanding 2D and 3D data

Part 2

- Exploratory data visualization
- Finding relationships in tables of data
- Visualizing structures
- Information hierarchies
- Interacting with visualizations
- Focus and context

The First Visualization

This picture is taken from Brian Collins

‘Data Visualization - Has it all been seen before?’

in ‘Animation and Scientific Visualization’, Academic Press

Simple data tables are often presented as line graphs, bar graphs, pie charts, dot graphs, histograms…

Which should we use and when?

Simple Data PresentationFundamental technique of data presentation

Used to compare two continuous variables

X-axis is often the control variable

Y-axis is the response variable

Good at:

Predicting values where data not given

Often (dubiously) used for trends when control is a categorical variable

Students participating in sporting activities

?

Line GraphBar graph

Presents categorical variables

Height of bar indicates value

Double bar graph allows comparison

Note spacing between bars

Can be horizontal (when would you use this?)

Simple Representations – Bar GraphNumber of police officers

Internet use at a school

Pie chart summarises a set of categorical/nominal data

Shows proportions

But use with care…

… too many segments are harder to compare than in a bar chart

Pie ChartShould we have a long lecture?

Favourite movie genres

Histograms summarise discrete or continuous data that are measured on an interval scale

No gaps if variable is continuous

HistogramsDistribution of salaries

in a company

Used to present measurements of two variables

Effective if a relationship exists between the two variables

Example taken from

NIST Handbook –

Evidence of strong

positive correlation

Scatter PlotCar ownership by household income

Edward Tufte has written a series of books on the design of good visualizations

Visit:

http://www.edwardtufte.com/tufte/

Here are some of the things he teaches us….

A Visualization GuruTufte Design Principles

- “Give the viewer the greatest number of ideas in the shortest space of time using the least ink in the smallest space”
- Try to maximize the data-ink ratio
- Show data variation, not design variation
- Tell the truth about the data

Data Ink Ratio

= (data-ink) / (total ink to produce graphic)

= proportion of ink devoted to non-redundant display of information

= 1.0 – proportion of graphic that can be deleted without loss of data-information

Data InkA low value of data ink ratio!

How much can be removed from this graphic?

1

2

3

4

5

6

ExerciseAnswer at:

http://home.ched.coventry.ac.uk/Volume/vol0/dataink.htm

Fundamental purpose of a graph is to show changes in the data

Design variation – where the same data is displayed differently for decoration - is to be avoided

Leads to ambiguity and deception

Design VariationWhat is wrong with this?

Summary

- Use the correct type of graph
- Line graph for response against continuous control
- Bar chart when control is categorical
- Pie chart when viewing as proportions
- Histograms when aggregating over intervals
- Scatter plots to see relationships between two variables
- Remember Tufte’s principles when creating a graphic
- Thanks to Statistics Canada – an excellent web site for simple data presentation
- http://www.statcan.ca/english/edu/power/toc/contents.htm

Data defined over 2D regions and 3D volumes

In contouring we are extracting lines of constant ‘height’ from data defined over a 2D region… sometimes called isolines

What is the analogy for data defined over a 3D volume?

Data over 2D Region - ContouringTopographic map with isohypses

of height -wikipedia

The analogy for 3D data is the isosurface: points where the measurements have a constant value…

Here we see surface of brain extracted from a 3D medical dataset

What limitations do you notice compared with contours in 2D??

Isosurfacinghttp://www.csit.fsu.edu/~futch/iso/

Famous isosurfacing algorithm is marching cubes

Each cube processed in turn

For zero isosurface, create surface separating positive and negative vertices of cube

After each cube is processed we have a surface (or surfaces) separating all positive vertices from all negative ones

Marching CubesLobster – Increasing the Threshold Level

From University of Bonn

Isosurfacing by Marching Cubes Algorithm

- Advantages
- isosurfaces good for extracting boundary layers
- surface defined as triangles in 3D - well-known rendering techniques available for lighting, shading and viewing ... with hardware support
- Disadvantages
- shows only a slice of data

Isosurfacing can be applied to rendering of objects… here an engineExample – mechanical engineering

Computer Science, UC Davis

Image Presentation of Data over 2D Region

Note here that in addition to the contour lines the height

of each ‘dot’ is individually coloured – so there is a mapping

from ‘height’ to colour … this is known as a transfer function.

What is the analogy in 3D?

Volume Rendering

- The analogy in 3D is known as volume rendering
- To overcome the step to 3D, we transfer values to colour and opacity
- Volume is a partially opaque gel material
- By controlling the opacity, we can:
- EITHER show surfaces through setting opacity to 0 everywhere except at a specific value where it is set to 1
- OR see both exterior and interior regions by grading the opacity from 0 to 1

[Note: opacity = 1 - transparency]

a

1

0

CT value

fsoft_tissue

Data Classification – Assigning Opacity to CT data- CT will identify fat, soft tissue and bone
- Each will have known absorption levels, say ffat, fsoft_tissue, fbone

This transferfunction will highlight soft tissue

a

1

0

CT value

fsoft_tissue

Data Classification – Assigning Opacity to CT Data- To show all types of tissue, we assign opacities to each type and linearly interpolate between them

In practice, a is

also increased in

areas where data

changes rapidly –

This accentuates

boundaries

ffat

fbone

Data Classification – Constructing the Gel – CT Data

- Colour classification is done similarly

Known as colour transfer function

white

red

yellow

CT number

Soft

Tissue

Air

Fat

Bone

Isosurface and Volume Rendering

Storm cloud

data rendered

by IRIS Explorer –

Isosurface & volume

rendering

Summary

- Scientific visualization allows us to understand data defined over 2D and 3D regions
- Traditional 2D methods have been generalised to 3D:
- Contouring – isosurfacing
- Image representation – volume rendering
- Excellent new text book
- Helen Wright
- Introduction to Scientific Visualization – Springer Verlag

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