05 Visual Mappings

8/10/2019 05 Visual Mappings

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Weiskopf/Machiraju/Mller

Approaches to Visual

Mappings

CMPT 467/767

VisualizationTorsten Mller


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Weiskopf/Machiraju/Mller 2

Overview

Effectiveness of mappings

Mapping to positional quantities

Mapping to shape Mapping to color

Mapping to texture

Other mappings Glyphs


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Readings

Colin Ware:

Chapter 4 (Color)

Chapter 5 (Visual Attention and Informationthat Pops Out)

The Visualization Handbook:

Chapter 1 (Overview of Visualization)

Additional (background) reading

J. Mackinlay: Automating the design of

graphical presentations of relational

information.

ACM ToG, 5(2), 110-141, 1986


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Visual Language is a Sign

System Image perceived as a set of signs

Sender encodes information in signs

Receiver decodes information from signs

Jacques Bertin

French cartographer [1918-2010] Semiology of Graphics [1967]

Theoretical principles for visual encodings

Semiology of Graphics [J. Bertin, 83]

4


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Effectiveness of Mappings

Mapping from (filtered) data to renderable

representation

Most important part of visualization Possible visual representations:

Position

Size

Orientation Shape

Brightness

Color (hue, saturation)

.


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Efficiency and effectiveness depends on

input data:

Nominal

Ordinal

Quantitative

Good visual design

Based on psychology and psychophysics

Psychological investigations to evaluate the

appropriateness of mapping approaches


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Basic Types of Visual

Encodings

Position

Size

(Grey)Value

Texture

Color

Orientation

Shape

Semiology of Graphics [J. Bertin, 67]

Points Lines Areas

7


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Mapping to Data TypesNominal Ordinal Quantitative

Position

Size

(Grey)Value

Texture

Color

Orientation

Shape!= Good~ = OK

"= Bad8


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Mapping to Data TypesNominal Ordinal Quantitative

Position ! ! !

Size ! ! !

(Grey)Value ! ! ~

Texture ! ~ "

Color ! " "

Orientation ! " "

Shape ! " "

!= Good~ = OK

"= Bad9


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Weiskopf/Machiraju/Mller[Mackinlay, Automating the Design of Graphical Presentations

of Relational Information, ACM TOG 5:2, 1986]

Mackinlays Retinal Variables

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Effectiveness of visual variables According to Mackinlay

[J. Mackinlay: Automating the design of graphical presentations of relational information. ACM

Transactions on Graphics, 5(2), 110-141, 1986]


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Stolte / Hanrahan

Polaris: A System for Query, Analysis andVisualization of Multi-dimensional Relational DatabasesChris Stolte and Pat Hanrahan

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Effectiveness according to neurophysiology

Cells in Visual Areas 1 and 2 differentially tuned

to each of the following properties: Orientation and size (with luminance)

Color (two types of signal)

Stereoscopic depth

Motion

Grapheme Describes a graphical element that is primitive in

visual terms

Makes use of early stages of human vision


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Mapping to Positional

Quantities Mapping to positional quantities:

Position

Size Orientation

Geometric mapping

Typically, very effective visual parameters

Generic diagram methods

0.100

0.325

0.550

0.775

1.000

0.05 0.288 0.525 0.763 1


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Quantities Point diagrams

E.g. scatter plots: visual recognition of

correlations


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Quantities Line and curve diagrams:

Effective perception of differences in

Position and

Length

5000

6250

7500

8750

10000

0 7.5 15 22.5 30


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Quantities Bar graph:

Discrete independent variable (domain):

nominal/ordinal/quantitative

Quantitative dependent variable (data)

5000

6250

7500

8750

10000

1 2 3 4 5 6 7 8 9 10 11 12 13 14


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Quantities Pie charts:

Quantitative data that adds up to a (fixed?)

number

0.6188

0.9944

0.3258

0.4613

0.7847

0.1292


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Mapping to Shape

Especially useful for data with direct

relationship to locations

Convey spatial structures

Examples

Isolines (contour lines)

Height fields

Function graphs (function plots)

Direct encoding of qualitative data

Typically in the form of glyphs


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Mapping to Color

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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Mapping to Color

Possible problems:

Distract the user when inadequately used

Dependent on viewing and stimulus conditions

Ineffective for color deficient individuals (use

redundancy)

Results in information overload

Unintentionally conflict with culturalconventions

Cause unintended visual effects and discomfort


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Mapping to Color

Nominal data

Colors need to be

distinguished

Localization of data

Around 8 different

basis colors

co-citation analysis


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Mapping to Color

Nominal data


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Mapping to Color

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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Mapping to Color

Pre-shading vs. post-shading

Pre-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


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Mapping to Color

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

HSV color model

Perceptual issues

Temperature color table


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Mapping to Color

Bivariate and trivariate color tables are

problematic:

No intuitive ordering

Colors hard to distinguish

Many more color tables for specific

applications

Design of good color tables depends onpsychological / perceptional issues

Often interactive specification of transfer

functions to extract important features


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Mapping to Texture

Main parameters for texture Orientation

Size

Contrast

Alternatively

[Tamura 78]: Coarseness

Roughness Contrast

Directionality

Line-likeness

Regularity

[C.

Ware,

InformationVisualization]


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Mapping to Texture

Goal:

Avoid visual "crosstalk

Orthogonal perceptual channels

Restricts range of parameters

E.g. approximately 30 degrees difference in

orientation needed to distinguish textures

Main application for textures: nominal data

Some applications for direct visualization of

orientations


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Mapping to Texture

Generate texture

Gabor func. as primitives

Parameters:

Orientation

Size

Contrast

Randomly splatter down

Gabor functions Blending yields continuous

coverage

Stochastic texture model

[C.

Ware,

InformationVis

ualization]

Visualization of a magnetic field


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Mapping to Texture

Other stochastic texture models:

LIC (Line integral convolution) for vector field

visualization

Structural models

Procedural description of texture generation

E.g. Lindenmayer systems (L-systems)


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Other Mappings

More advanced mappings possible

Examples for other visual variables Motion

Blink coding

Explicit use of 3D

Multiple attributes

Typical combination of

attributes:

Geometric position,e.g., height field

Color: saturation,

intensity, tone

Texture

Issue: Interference?


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Glyphs

Glyphs and icons

Consist of several components

Features should be easy to distinguish andcombine

Icons should be separated from each other

Mainly used for multivariate

discretedata


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Glyphs

Multi-dimensional coding Perceptual independence?

Integraldisplay dimensions Two or more attributes perceived holistically

Separabledimensions Separate judgments about each graphical

dimension

Simplistic classification, with a large

number of exceptions and asymmetries

More integral coding pairs

More separable coding pairs

[C.W

are,

InformationVisualization]


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Glyphs

Interesting graphical attributes for basic glyph design

[according to C. Ware, Information Visualization]

Visual variable Dimensionality

Spatial position of glyph 3 dimensions: X, Y, ZColor of glyph 3 dimensions: defined by color opponent theory

Shape 23? dimensions unknown

Orientation 3 dimensions: corresponding to orientation about each

of the primary axes

Surface texture 3 dimensions: orientation, size, and contrastMotion coding 23? Dimensions largely unknown, but phase may be

useful

Blink coding: The glyph

blinks on and off at some

rate

1 dimension


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Glyphs

Color icons [Levkowitz 91]

Subdivision of a basic figure (triangle,

square, ) into edges and faces

Mapping of data to faces

via color tables

Grouping by emphasizing

edges or faces


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Glyphs

Stick-figure icon [Picket & Grinstein 88]

2D figure with 4 limbs

Coding of data via Length

Thickness

Angle with vertical axis

12 attributes

Exploits the human

capability to recognize

patterns/textures


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Glyphs

Stick-figure icon


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Glyphs

Circular icon plots:

Star plots

Sun ray plots

etc

Follow a "spoked wheel" format

Values of variables are represented by

distances between the center ("hub") of the

icon and its edges


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Glyphs

Star glyphs[S. E. Fienberg: Graphical methods in statistics.

The American Statistician, 33:165-178, 1979]

A star is composed of equally spaced radii, stemming

from the center

The length of the spike is proportional to the value of

the respective attribute

The first spike/attribute

is to the right

Subsequent spikesare counter-clockwise

The ends of the rays

are connected by a line


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Glyphs

Sun ray plots

Similar to star glyphs/plots

Underlying star-shaped structure


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Glyphs

Chernoff faces/icons[H. Chernoff (1973). The use of faces to represent points in k-dimensional space

graphically. Journal of the American Statistical Association , 68 :361-368]

Each facial feature represents one variable

Human ability to

distinguish small

features in faces


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Glyphs

Chernoff faces/icons

Possible assignment in the decreasing order of importance: Area of the face

Shape of the face

Length of the nose Location of the mouth

Curve of the smile

Width of the mouth

Location, separation, angle, shape, and width of the eyes

Location of the pupil

Location, angle, and width of the eyebrows

Coding of 15 attributes

Additional variables could be encoded by making faces

asymmetric


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Glyphs

Chernoff faces/icons


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Glyphs

Face morphing [Alexa 98]

Documents

05 Visual Mappings