ScientificVisualization

Leif Kobbelt

2Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Overview

• introduction to visualization

•mapping & rendering

• data cleanup & filtering

• data structures & implementation

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3Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

History

Map of Catal Hyük

6200 BC

Excavation

Reconstruction

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4Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

History

• Time series: inclination of planets

(10th century)

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5Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

History

Vector visualization (1686) Height field (1879)

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6Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

History

Napoleon‘s campaign against Russia (1812/13)

Cartography (1861)

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7Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

History

“The purpose of computing

is insight not numbers”

(Hamming 1962)

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8Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

History

• direct implications the data flood from super computer simulations can only

be dealt with visually

needs a visualization specialist and an interdisciplinary team

new developments in hard/software, nets, etc are necessary

• advantages in the long term will be faster insight

faster product–development cycles

stronger position in global competition

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9Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

The Visualization Pipeline

simulation data bases sensors

raw data

visualization data

rendering representation

images / video

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10Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

The Visualization Pipeline

simulation data bases sensors

raw data

visualization data

rendering representation

images / video

filtering

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11Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

The Visualization Pipeline

simulation data bases sensors

raw data

visualization data

rendering representation

images / video

filtering

mapping

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12Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

The Visualization Pipeline

simulation data bases sensors

raw data

visualization data

rendering representation

images / video

filtering

mapping

rendering

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13Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Filtering

• data format conversion

• clipping / croping

• denoising

• sub- / super- / re-sampling

• interpolation / approximation

• classification / segmentation

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14Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Mapping

• graphics primitives

points, lines, surfaces, volumes

polynomials vs. piecewise linear

color, texture, transparency

• iso-contours of scalar fields

• height fields

• vectors, glyphs, ...

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15Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Rendering

• geometric scenes

surfaces, volumes, images

• intuition

perspective, visibility

• realism

shadows, lighting, reflections

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16Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Reliability

• errors in ...

data acquisition

filtering

mapping / interpolation

rendering

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17Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Reliability

• errors in ...

data acquisition

sampling density → alias

quantization

filtering

mapping / interpolation

rendering

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18Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Reliability

• errors in ...

data acquisition

filtering

noise to signal ratio

features

mapping / interpolation

rendering

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19Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Reliability

• errors in ...

data acquisition

filtering

mapping / interpolation

approximation quality

intuition (plausible real world analogue)

rendering

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20Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Reliability

• errors in ...

data acquisition

filtering

mapping / interpolation

rendering

consider human perception

avoid distraction (too much information)

too much realism (pseudo information)

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21Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Types of Data

• domain dimension

• range dimension

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22Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Types of Data

• domain dimensionunivariate / „curves“ (d=1)

bivariate / „surface“ (d=2)

trivariate / „volumes“ (d=3)

quadvariate / e.g. „space-time volumes“ (d=4)

• range dimension

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23Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Types of Data

• domain dimension

• range dimension

scalar (n=1)

planar (n=2)

spatial (n=3)

multi-dimensional

vector valued

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24Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Types of Data

nD

3D

2D

1D

0D

1D 2D 3D nD

I J

G H

C D E F

A B

dimension of

domain

dimension of

data type

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25Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Applications

• Flow Visualization

© N. Max, LLNL

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26Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Applications

• Flow Visualization

© N. Max, LLNL

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27Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Applications

• Information Visualization

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28Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Applications

• Information Visualization

Web hyperlinks

(quasi-hierarchical

graphs)

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29Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Volume Visualization

• Visualization of numerical simulation results large and unstructured data sets

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30Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Volume Visualization

• Visualization of medical data setsanalysis and pre-operative planning

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31Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Vector Field Visualization

• Visualization of flow phenomena

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32Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Vector Field Visualization

• Feature extraction

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33Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Grids

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34Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Data Structures

• domain structure

regular / grid

semi-regular (piecewise regular)

unstructured / scattered

• topology vs. geometry

linear, rectilinear, curvilinear

multigrids

sparse grids

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35Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Data Structures

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36Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Data Structures

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37Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Data Structures

• Example

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38Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Data Structures

• Example

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39Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Data Structures

• Example

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40Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Volumetric Representations

• Voxel grid O(h-3)

• Adaptive octree Three color octree O(h-2) Adaptively sampled distance fields O(h-1)

• kD-Tree

• Binary space partition Partition the space along arbitrary planes Piecewise linear C-1 approximation Align cells to surface

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41Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Three Color Octree

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42Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Three Color Quadtree

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12040 cells1048576 cells

43Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Three Color Quadtree

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12040 cells1048576 cells 895 cells

44Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Adaptively Sampled Distance Fields

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12040 cells1048576 cells 895 cells

45Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Adapively Sampled Distance Fields

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12040 cells 895 cells

46Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Adaptively Sampled Distance Fields

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12040 cells 895 cells 254 cells

47Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Binary Space Partitions

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12040 cells 895 cells 254 cells

48Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Binary Space Partitions

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254 cells895 cells

49Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Color Coding

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50Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Color Coding

• Issues: What kind of data can be color-coded ? What kind of information can be efficiently visualized?

• Areas of application Provide information coding Designate or emphasize a specific target in a crowded display Provide a sense of realism or virtual realism Provide warning signals or signify low probability events Group, categorize, and chunk information Convey emotional content Provide an aesthetically pleasing display

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51Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Color Coding

• Possible problems:Distracts the user when inadequately used

Dependent on viewing and stimulus conditions

Ineffective for color deficient individuals

Results in information overload

Unintentional conflicts with cultural conventions

Cause unintended visual effects and discomfort

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52Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Color Coding

• Nominal dataColors need to be

distinguished

Localization of data

Around 8 different

basis colors

co-citation analysis

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53Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Color Coding

• Ordinal and quantitative data Ordering of data should be represented by ordering of colors

Psychological aspects

x1 < x2 < ... < xn E(c1) < E(c2 ) < ... < E(cn )

• Color coding for scalar data Assign to each scalar value a different color value

Assignment via transfer function T

T : scalarvalue colorvalue

Code color values into a color lookup table

0

Scalar (0,1)

RiGiBi

(0,1) (0,N-1)255

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54Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Color Coding

• Pre-shading vs. post-shadingPre-shading Assign color values to original function values (e.g. at vertices of a cell)

Interpolate between color values (within a cell)

Post-shading Interpolate between scalar values (within a cell)

Assign color values to interpolated scalar values

• Linear transfer function for color coding Specify color for fmin and for fmax

(Rmin ,Gmin , Bmin) and (Rmax , Gmax , Bmax)

Linearly interpolate between them

)()( maxmaxmax

minmax

maxminminmin

minmax

min ,B,GRff

ff,B,GR

ff

fff

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55Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Color Coding

• Different color spaces lead to different interpolation functions

• In order to visualize (enhance/suppress) specific details, non-linear

color lookup tables are needed

• Gray scale color table Intuitive ordering

• Rainbow color table Less intuitive

• Temperature color table

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56Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Color Coding

• Bivariate and trivariate color tables are not very useful: No intuitive ordering

Colors hard to distinguish

• Many more color tables for specific applications

• Design of good color tables depends on psychological /

perceptional issues

• Often interactive specification of transfer functions to

extract important features

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57Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Color Coding

• Example Special color table to visualize the brain tissue

Special color table to visualize the bone structure

Original Brain Tissue

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58Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Color Quantization

• Task: Select a set of colors to represent the color gamut of an

image

Compute mapping from color space to representrative

color

• „True color“ image: 24 bits per pixel

• Colormap: 1 color index per pixel adresses color

lookup table

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59Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Color Quantization

• Naive idea: Uniform quantizationDrawback: many colors in colormap are not used in final

image

bad image reproduction

• Better: Median Cut AlgorithmChoose color map based on color distribution in original

image

Pro: uses every color in the colormap

closer image reproduction

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60Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

RGB Space

R

G

B

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61Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

RGB Space

R

G

B

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62Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Median Cut (2D)

8 colors

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63Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Median Cut (2D)

8 colors

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64Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Median Cut (2D)

8 colors

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65Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Median Cut (2D)

8 colors

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66Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Median Cut (2D)

8 colors

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67Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Median Cut (2D)

8 colors

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68Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Median Cut (2D)

8 colors

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69Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Median Cut (2D)

8 colors

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70Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Median Cut Algorithm

Color_Quantization(image I, k) {

for each pixel in I

map to RGB space

B = {RGB space}

for (i = 1 to k-1) {

L = Heaviest(B)

split L at median along longest dimension into L1 and L2

remove L from B and add L1, L2

}

for each box in B

assign color representative

for each pixel in I

map to representative

}

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71Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Color Quantization

16 Mio.

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72Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Color Quantization

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73Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Color Quantization

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74Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Color Quantization

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75Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Color Quantization

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76Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Color Quantization

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77Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Color Quantization

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78Visual Computing Institute | Prof. Dr. Leif Kobbelt

Computer Graphics and Multimedia

Data Analysis and Visualization

Color Quantization

16 Mio.

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