Fragen

• Visualization designers must take into account three very different kinds of resource limitations: those of computers, of humans and of displays

  • Computational limits: Processing time / system memory

  • Display limits: Number of pixels, Information density (ratio of used space vs unused whitespace)

  • Human limits: Perception, attention and memory (e.g. change blindness)

• A general model of visualization process with 4 stages where the user can interact with the process at each stage

• 4 stages: data acquisition -> filtering / enhancement -> visualization mapping -> rendering

• 3 general cases: simulation, data bases, sensors

• with this 3 cases you get raw data as a result which then will be visualized

• Examples: global climate simulation, images of particles in fluid, weather radar data,…

• process to obtain useful data (e.g. 3D volume) / derived data computed from the raw data

• Examples:

  • data format conversion

  • co-registration of data sets

  • resampling to grid

  • interpolation / approximation of missing values

  • data reduction

  • clipping / cleaning / denoising

  • etc.

• Derived data that was computed during the filtering / enhancement step now is mapped to some rederable representation

• Examples:

  • scalar field mapped to (->) isosurface

  • 2D field -> height field

  • etc.

• Decide

  • which parts of the data are shown?

  • How to represent them?

• Graph.primitives: points, lines, surface, volumes

• Visual channels: color, texture, transparency

• from rederable representation to display images / video

• Generate 2D image / video

  • viewpoint specification

  • visibility calculation

  • lighting / shading, composition

  • compute values at sampling points

Filtering / enhancement step

Rendering stage

Rendering stage

Visualization mapping stage, for instance using a transfer function to assign color and opacity to each voxel.

Filtering and enhancement stage (?)

• independent variables refer to the dimensionality of the domain of the problem

  • e.g. 2D or 3D Space, time

  • Do not depend on anything else

• Dependent variables refer to the type and dimension of the data to be visualized

  • e.g. temperature, density values, velocity vectors

  • Depend on the location where we measured those, e.g. measured in respect to the independent variables

R would be independent variable and R3 woul be the dependent variable

Basically a function of a parameter and the output would always be a 3D location for instance

We have 3D space = independent variables

3D vectors given at every location so the vectors itself would be the dependent variables

TODO

• Cartesian grid = equidistant grid

• Spacing is constant in x and y (or z in 3D) dimension

• Difference to uniform / regular grid: same spacing within one direction, but spacing in x and y direction are different

• Information that has to be stored: Index, coordinates

• Positions of the individual cells can be computed from the indices - don’t have to be stored

• Neighborship information is implicit

• non-orthogonal grid

• Grid points / position of individual vertices specified explicitly

• still have regular grid cells so neighborhood information is still implicit

• Unstructured grid: both location of the individual vertices and neighborhood information has to be specified explicitly

  • cells are tetrahedra or hexahedra

Draw a circle aroung each of the triangles and whenever we draw such a circle we have to make sure that no vertex from another triangle is inside that circle. If this would happen then the Delaunay property is violated and its locally non-Delaunay and we would have to perform e.g. an edge-flip operation to get it Delaunay.

The use of computer-supported, interactive, visual representations of data to amplify cognition

Preoperative planning of tumor resection, Virtual fetoscopy (4D Ultrasound), MRI scans,…

• lets you see things that would rather go unnoticed (data trends, outliers, dependencies, etc.)

• gives answers faster

• lets you interact with your data, study causes and effects, etc

• helps to deal with increasing size and diversity of data

• produces pretty, informative and interactive pictures

Size of effect shown in graphic / Size of effect in data

• Visual exploration (Nothing is known about the data)

  • find the unknown / unexpected

  • generate new hypothesis

• Visual analysis (confirmative vis.) (There are hypotheses)

  • confirm or reject hypotheses

  • information drill-down

• Presentation („Everything“ is known)

  • effective / efficient communication of results

• bodies were frozen in a special material to preserve tissues and organs

• Sections were „shaved“ off the frozen block micro-thin layers to expose underlying tissues

• a picture is taken

• A „stack“ of 2D images is obtained

• complexity / technical demands: low

• benefits, possibilities: Low

• complexity / technical demands: middle

• benefits, possibilities: middle

• complexity / technical demands: high

• benefits, possibilities: high

• Attribute types (quantitative vs. qualitative)

• Domain (continuous vs. discrete)

• Value range (includes precision of values)

• Data type (categorical, scalar, vector, tensor data)

• Dimension (number of components)

• Error and uncertainty

• (physical) interpretation

• Quantitative: numerical, measurable

  • e.g. length, mass, temperature

  • metric scale - allows measure of distance

  • Continuous (real) or discrete (distinct & separate values)

Qualitative: categorical data, not measurable

• No metric scale; cannot be measured

• Requires a subjective decision in order to be categorized

• Discrete

• Nomial

  • No natural ordering or indication of values, only equivalence and membership (=, ≠)

  • e.g. eye color (blue, green, brown)

• Ordinal

  • Logical order relation (<, >) but no relative size or degree of difference

  • e.g. judgement of size (small, medium, large), Attitudes (strongly disagree, disagree, neutral, agree, strongly agree)

Categorical data: Values from a fixed number of categories

Scalar data: Given by a function

Vector data: Represent direction and magnitude and given by an n-tupel; 2D vector field where every sample represents a 2D vector

Tensor data: A multi-dimensional matrix

• Deals with the reconstruction of a continuous real object from a given discrete representation

• Data that has some physical or geometric correspondence

• Deals with data that is discrete and more abstract

• Does not have a physical or geometric correspondence

• Symbolic, tabular, networked, graphs, textual information

• Grid-free data

• data points given without neighborhood relationship

• influence on neighborhood defined by spatial proximity

• Scattered data interpolation

• Curves on which all points have a certain (constant) value

• Are hyperbolas, not lines

• Construct a continuous function f from a given set of points and values which approximates the given values

• Independet of dimension of parameter domain (1D / 2D / 3D)

• Function represented as weighted sum of N radial functions

• Nearby points have higher influence than far-away points

• Each radial function is centered around a data point. Values decrease quickly the further away from this point / the functions center

• Interpolation: we want a curve which is going through the initial data points and changes smoothly in between them

• Drawbacks of radial basis functions

  • Every sample point has influence on whole domain

  • Adding a new sample requires re-solving the equation system

  • Computationally expensive (solving a system of linear equations)

• What can we do?

  • Find a different radial function

  • Give up finding a smooth reconstruction and try finding a piecewise (local) reconstruction function

• A measure for the quality of a triangulation is the aspect ratio of the so-defined triangles

• Avoid long, thin triangles

• Make triangles as „round“ as possible

• Maximize the minimum angle in the triangulation

• Maximize radius_of_in-circle / radius_of_circumcircle ratio

• A Delaunay triangulation is an optimal triangulation

• The circumcircle of any triangle does not contain another point of the set

  • Maximizes the minimum angle in the triangulation

  • Such a triangulation is unique (independet of the order of samples) for all but trivial cases

• Building a Delanuay triangulation from initial, non-optimal triangulation: successively improving the initial triangulation via local operations

  • Edge-flip operation:

    • An edge is local Delaunay if there exists an empty circumcircle / The circumcircle of any triangle does not contain another point if the set

    • If an edge shared by two triangles is illegal, a flip operation generates a new edge that is legal

• If a triangulation is locally Delaunay everywhere -> globally Delaunay

• Problem: Looking for nearest neighbor

• Partitions domain into Voronoi regions: Each Voronoi region contains one initial sample - the Voronoi samples

• Points in Voronoi region are closer to respective sample than to any other sample (blue circle)

• Centers of circumcircles of Delauney triangulation (borwn circle)

• The geometric dual (topologically equal) of Delaunay triangulation (blue = Delaunay, yellow = Voronoi)

• Points in a Voronoi region are closer to the respective sample than to any other sample

• An isoline (iso-contour) consists of all points at which the data has a specific value c: {(x,y) | f(x,y) = c} (Given a 2D scalar function and a scalar iso-value c)

• Can be seen as a special kind of data condensation

• Isolines are always closed curves (except when they exit the domain)

• Isolines never (self-) intersect, thus they are nested

• Isolines are always orthogonal to the scalar field’s gradient

• The true isolines within a cell are hyperbolas

• Approximates the surface by a triangle mesh

• Surface vertices are found by linear interpolation along cell edges

• Efficient triangulation by means of lookup tables

• the standard geometry-based surface extraction algorithm for 3D scalar field

• Computes isosurface for specific iso-value

• Cell consists of 8 vertices

• indices: (i+[0,1], j+[0,1], k+[0,1])

1. Consider a cell (defined by 8 vertices with associated data values) independently

2. Classify each vertex as inside or outside (outside the surface: value < iso-value, inside the surface: value => iso-value)

1. Use the binary labeling of each cell to compute an index: outside = 0, inside = 1

2. Get per-cell triangulation from index: look up the triangulation for every index from a pre-computed table

3. Interpolate the edge location : for each triangle edge, find the vertex location along the edge using linear interpolation of the vertex values

4. Compute gradients : Calculate normals at each cube vertex (via finite differences), and interpolate along the edges

5. Consider ambiguous cases: use asymptotic decider as in 2D for this

6. Go to next cell

• Summary:

  • 256 Cases, Reduce to 15 Cases by symmetry

  • Causes holes if arbitrary choices are made

  • Up to 5 triangles per cube

  • Not that triangulation is only approximation of true isosurfaces produced by trilinear interpolation

• Data values are initially given at vertices of a 3D grid = voxels (volume elements)

• Voxel = point sample in 3D

• Considers ambient light and point lights as well as the material color and reflection properties

• Ambient light: background light, constant everywhere

• Diffuse reflector: reflects equally into all directions

• Specular reflector: reflects mostly into the mirror direction

• Necessary to emphasite iso-surface shape: simulate reflection of light and effect on color

• Phong’s illumination model

C = ka Ca Od

• Background light

• constant everywhere

• ka = ambient reflection coefficient aus [0,1]

• Ca = Color of the ambient light

• Od = object color

• Scatters light equally in all direction

• C = kd Cp Od cos θ bzw. C = kd Cp Od (l * n)

  • kd = diffuse reflection coefficient aus [0,1]

    • if kd = 0 -> black, kd = 1 -> am hellsten

  • Cp = color of the point light

  • Od = object color

  • cos θ = angle between light vector l and normal n

• if l = n meaning light is precisely above the point and θ = 0 the cos 0° = 1 -> 100% intensity

• if light shines onto point in a 45° angle -> cos 45° ≈ 0.7 -> 70% intensity

• if 90° angle = 0% intensity

• highest diffuse reflection when normal vector = light vector, point precisely below light source

• Highlight = reflection of light source

• Glossy surfaces

• Reflects mostly into the mirror direction

• view dependent!

• C = ks Cp Od cos^n 𝞅 bzw. C = ks Cp Od (r * v)^n

  • ks = specular reflection coefficient aus [0,1]

  • Cp = color of the point light

  • Od = object color

  • cos 𝞅 = angle between the reflected light ray r and the vector to the viewer v

  • ^n = shininess factor (controls extend of highlight)

    • the larger n the smaller the highlight / intensity

• highest specular reflection when reflected vector = view vector

when the expont in the Specular reflection formula (shininess factor) gets close to infinity we have almost a perfect mirror

Camera position vector minus surface point vector

Vector of position of a point light source minus vector of surface point

• medical scanners e.g. CT scan

• automotive engineering

• Techniques for 2D scalar fields (e.g. slicing)

• Indirect volume rendering techniques (e.g. surface fitting)

• direct volume rendering techniques

• e.g. surface fitting

• Convert / reduce volume data / raw data to intermediate representation (surface representation) first, which can then be rendered with traditional techniques

• MC-algorithm (Marching-cubes algorithm)

• consider data as a semi-transparent gel with physical properties and directly get a 3D representation of it

• e.g. Ray-casting

• Volume material attenuates reflected or emitted light

• Get a 3D representation of the volume data taking into account emission and absorption (without making an intermediate representation first)

• considers the physics of light transport in a dense medium

  • Optical properties are mapped to each voxel (emission = color, absorption = opacity)

  • The light reaching the viewer is simulated by ray casting

Display volume data, mapped to colors, on a slice plane

Generate opaque / semi-opaque surfaces (e.g. via the MC-Algorithm)

• performs mapping of data values to visual properties like color and opacity

• associate distinct materials (value ranges) to disting properties (color & opacity: as (RGBa))

• assign a different color to each scalar value (for scalar data)

• Opacity alpha = 1 -> completely opaque

• Opacity alpha = 0 -> completely transperent

• Numerical approximation of the volume rendering integral

  • A ray is cast into volume for each output pixel -> volume is resampled at equidistant intervals along the ray (integral as a sum over samples) -> Sample values are tri-linearly interpolated -> apply transfer function

• Or Volumetric ray integration using front-to-back strategy (alpha-compositing), first-hit, average or maximum

• Defines a virtual image plane where viewer is looking through

• Cast a ray through every pixel on the screen

for each pixel on the image plane

compute entry- and exit-point in volume

while current position inside volume

read density at current position

apply transfer function: scalar value -> color + alpha-value

compute shading

apply compositing

compute new position along ray

end while

set pixel color in image plane

end for

accumulation of color and opacity along rays

• alpha-compositing

• Surface rendering / first hit

• Average

• Maximum

• stop ray traversal if an iso-surface is hit (larger than a certain threshold), and shade the surface points

• produces same result as marching cubes, but with higher accuracy

• simply accumulate colors but does not account for opacity

• values along the viewing ray are averaged

• produces an x-ray image

• only takes the maximum color along the ray and displays it

• doesn’t account for opacity

• Often used for magnetic resonance angiograms

• good to extract vessel structures

• Too few samples along the ray

• Interrupted artifacts -> no smooth surface of the visualization

• Solution: Increase sampling rate to Nyquist frequency -> at least 2 samples per voxel

• remove artifacts by stochastic jittering of ray-start position

Direct volume rendering

• Direct representation

• Conveys volume impression

• Often realized in software (slow?!)

• Transfer function specification

Surface rendering

• Indirect representation

• conveys surface impression

• Hardware supported rendering (fast?!)

• Iso-value-definition

• Data in volumetric datasets are usually given in some kind of grid

• ray casting: interpolation scheme e.g. trilinear interpolation or some other higher-order interpolation scheme

Visualize stuff that is moving, e.g. wind tunnel / wind fields, weather / climate simulations, aerospace / car / ship design

• Flow simulation:

  • Design of ships, cars, airplanes

  • Weather simulations (e.g. atmospheric flow)

  • Medical blood flows

• Measurements

  • wind tunnel

  • schlieren imaging

• Modeling

  • Differential equations systems (dynamical systems)

• Motion of fluids (gases, liquids)

• Geometric boundary conditions

• Velocity / flow field v(x,t)

• Conservation of mass, energy, and momentum

• Navier-Stokes equations

• Computational fluid dynamics (CFD)

• Dimension (2D or 3D)

• Time-dependency: steady vs. time-varying flows

• Direct vs. indirect flow visualization

Steady (time-independent) flow:

• flow static over time

• e.g. laminar flows

• simpler interrelationships

time-dependent (unsteady) flow

• flow changes over time

• e.g. turbulent flows

• more complex interrelationships

• Direct flow visualization (arrows, color coding,…)

• Geometric flow visualization (stream lines/surfaces,…)

• Sparse (feature-based) visualization

• Dense (texture-based) visualization

• e.g. color coding, arrow plots, glyphs

• Gives overview on current flow state

• Visualization of vectors

• Visualize local features of the vector field

• Map vector or curl to arrow glyphs

• Can visualize more features of vector field, e.g.using Velocity, Curvature, Rotation, Convergence,…

• Vector per grid point pointing into the flow direction

• use arrow length and / or color to highlight special regions

Advantages

• Simple

• 3D effects

Disadvantages

• Ambiguity

• Difficult spatial perception (1D-objects in 3D)

• Inherent occlusion effects

• Poor results if magnitude of velocity varies significantly and changes rapidly

-> Use 3D arrows of constant length and color code magnitude

• Use intermediate representation (vector-field integration over time)

• Visualization of temporal evolution (also consider data over time)

• Stream lines, path lines, streak lines

Basic idea: trace particles along characteristic trajectories and map trajectories to particles, lines, balls, bands

• Stream lines: trajectories of massless particles in a “frozen” (steady) vector field

  • trajectories of massless particles at one time step

  • doesnt show its movement over time but within a frozen flow / vector field

• Path lines: trajectories of massless particles in (unsteady / time-varying) flow

  • follow one particle through time and space

• Streak lines: trace of dye that is continuously released into (unsteady / time-varying) flow at a fixed position

  • connect all particles that started at the same seed point

  • a new particle is continuously injected at the same seed point

  • all existing particles are advected and connected (from youngest to oldest)

-> Comparison of path / streak / stream lines: Identical for steady flows

• we liked to see places where the flow twists (vortices)

• Trace two close-by particles (keep distance constant)

• Or rotate band according to curl

• simultaneously release aprticles along a seeding structure (line) and connect all them to form a surface

• e.g. particle-based, triangulated, or semi-transparent streak surface

• means that the line tangent (1st derivate) is aligned to the vector field / is in vector field direction

Select start point (seed point)

Find cell that contains start point

While (particle in domain) do

interpolate vector field at current position

integrate to new position

find new cell

draw line segment between latest particle positions

EndWhile

• irregular results when using regular grid

• Evenly-spaced streamlines:

  • Idea: streamlines should not get too close to each other

  • Choose seed point with distance d_sep from existing stream line

  • forward- and backward-integration until distance d_test

• Stop stream line integration

  • when distance to neighboring stream line <= d_test

  • when stream line leaves flow domain

  • when stream line runs into fixed point (v(x*)=0)

  • When stream line gets too close to itself

  • after a certain number of maximal steps

• the smaller d_sep the nearer together the streamlines are

• the smaller d_test in relation to d_sep the nearer together the streamlines are

• Image-space technique

  • Vector field is first projected to 2D image

    • 2D image is scanned at intervals d_sep

    • Seedpoint is found and stream lines are traced in that region

    • Scanning continues until seedpoint in new region is found

  • Seeding and integration happen in image space

• Discontinuity detection

  • Stop stream line integration when z-depth drops to zero (edge of model) or when z-depth changes too abruptly (edge of overlapping regions)

due to the perspective it is unclear in which direction the vector is pointing so there is some ambiguity assigned to having arrows in 3D for instance, or there can be occlusion effects

Examples:

• Streamlines

• Streaklines

• Pathlines

-> When using direct flow visualization we directly show the flow.

-> With geometric (integration-based) visualization we consider movement of particles along trajectories in the flow.

False

False

True

True

False

• Global computation of flow features

• Vortices, shockwaves, vector field topology

• one of the most prominent features

• Important in many applications (turbulent flows)

• No formal, well accepted definition yet (“something swirling”)

• characterized by sharp discontinuities in flow attributes (pressure, velocity magnitude,…)

• Idea: do not draw “all” stream lines, but only the “important” ones

• show only tological skeleton

  • Connection of critical points

  • Characterization of global flow structures

• Critical points: singularities in vector field such that v(x*) = 0 (source, saddle, sink)

  • Points where magnitude of vector goes to zero and direction of vector is undefined

  • Stream lines reduced to single point

  • Type of critical point determines flow pattern around it

Critical points in 3D

• More complicated

• Line and surface separatices exist

The intersection of the separation surfaces of the two saddles is the saddle connector

• Global method to visualize vector fields

• Dense sampling

  • better coverage of information

  • Critical point detection and classification

  • (Partially) solved problem of seeding

• Flexibility in visual representation

  • Good controllability of visual style

  • From line-like (crisp) to fuzzy

• Global visualization technique (not only one particle path)

• Dense representation of flow fields

• Convolution along characteristic lines -> correlation along these lines

• for 2D and (3D flows)

• Start with a random texture (white noise)

• Smear out the texture along trajectories of vector field

• Results in low correlation between neighboring lines but jigh correlation among them (in flow direction)

• look at stream line that passes through a pixel

• Smear out -convolve- noise texture in direction of vector field (along stream line)

• LIC is a convolution of

  • a noise texture T(x,y)

  • and a smoothing filter

Algorithm:

• Stream line containing the point

• randomly generated noise texture

• compute intensity using an integral

• smoothing filter kernel, normalized and usually symmetric

Influence of filter length: The bigger the L the finer the lines

• Sliding a function g(x) along a function f(x)

• Function f is averaged with a weight function g

  -> Horizontal / Vertical Gaussian blur

• Visualizes orientation (in addition to direction)

• uses a sparse texture; i.e. smearing of individual drops

• Asymmetric convolution kernel

• only good if non-relevant data is discarded

False, its a global method

False

False

False

False

• represent data items or links

• points, lines, areas, surfaces

• representation of links between data items: Connection, Containment

• control appearance of graphical primitives based on data attributes

• Position (horizontal, vertical, both), Color, Slope, Size (length (1D), 2D area, 3D volume), Shape

• some visual channels are better than others

• encode most important data attributes with most effective / accurate channels

match type of visual channel to data type

• Pop-out (emphasize important information)

• Discriminability (how many usable steps?)

• Separability (judge each channel independently)

• Relative vs. absolute judgement

-> Perceived color is highly context depenent

-> percetion is relative

-> use popout to emphasize data

-> choose carefully with the mapping and color

• Preattentive processing: automatic and parallel detection of basic features in visual information (200-250 msec)

• Speed independent of distractor count

• Works on many individual channels

• How many usable steps?

• Must be sufficient for number of discriminable bins

• we can only distinguish a limited number of colors / brightness level

• Perception highly context-dependent

• Perceptual system mostly operates with relative judgements, not absolute ones

• Weber’s Law: just-noticeable difference is a fixed percentage of the magnitude of the stimuli (e.g. bar length) -> if i have a visual stimuli, to see the difference between the two, if the difference is smaller than a certain percentage of the total, you cannot see the difference anymore

• Categorical + quantitative data: Bar / pie chart, stacked bars

• Time-dependent data: Line graph, ThemeRiver, Horizon graph

• Single and multiple variables: Histogram, scatterplot, parallel coordinates, Glyphs, color mapping

• numerical, measurable

• objective data produced through a systematic process, not subject to interpretation (e.g. lenght, mass, temperature)

• Metric scale: allows measure of distance

• Continuous (real) or discrete (distinct & separate values)

• categorical, not measurable

• no metric scale, cannot be measured

• Requires a subjective decision in order to be categorized

• Discrete

• Attribute 1: categorical -> horizontal position

• Attribute 2: quantitative (dependent) -> length / vertical position

• Bars should always start at zero!

• Bars support comparison

• Attribute 1: categorical -> color

• Attribute 2: quantitative (dependent) -> angle

• angle / area judgement less accurate than bar length

• often bar chart better choice

• Quantitative data wrt 2 categorical vars (horizontal & vertical)

• Investigate part-to-whole relationship (100%)

• Length and color hue

• Quantitative data wrt. multiple categorical attributes

• Shows connections and proportions

B

C

• quantitative data on common scale(s) wrt. time

• Connection between points - trends, structures, groups

• banking to 45 degrees

  • Perecptual principle: most accurate angle judgment around 45°

  • Pick aspect ration (height/width) accordingly

• Lines imply trends

• Thematic changes in documents

• Occurrence per topic / category mapped to width of river band

• less distorted around center

• Rearranging bands

• Reduces vertical space without losing precision

• Split vertically into layered bands

• Collapse color bands to show calues in less vertical space

• Optional mirroring of negative values

• pre-attentive processing: automatic and parallel detection of basic features in visual information (200-250 msec)

• independent of the number of distractors

• usually only works on individual channels, when having a combination of channels it usually requires a serial search instead of pre-attentive processing

• quantitative data: length - angle / slope - 2D area - curvature

• qualitative / categorical data: different ranking but didn’t talk about it in the lecture

• two visual channels that are separable (color and position): we can focus on one group (either one color or one position) -> separable visual channels

• integral visual channels: not possible to see the different channels separately

• fully separable visual channel: color + position, fully separable, 2 groups each

• fully integral visual channel: red + green make different colors, major interference, 4 groups total: integral color

• Attribute 1: categorical -> horizontal position

• Attribute 2: quantitative (dependent) -> length / vertical position

• Pie chart: usually estimate the angle or area

• Bar chart: length and precision of the ending is read out

• humans ar much better at comparing length and position instead of angle and ares -> Bar chart better

• quantitative data with respect to multiple categorical attributes

• shows connections and proportions

• usually have categorical data with a certain frequency (how often it appears)

• split an original graph into some layers and use color coding to distinguish different layers, those layers can be collapsed on top of each other

• Binning: group values into equally spaced intervals (bins)

• Bin width affects representation

• shows summary statistics of a distribution (1 variable)

• Probability density function (PDF)

  • q1: lower quartile: 25% of data below

  • q2: median

  • q3: upper quartile: 25% of data above, 75% of data below

• Interquartile range: between q1 and q3

• Variations:

  • Tukey’s box plot

  • Tufte’s quartile plot

    • median = dot

    • easier to follow trend of median, more compact

• Show correlations between 2 dependent variables

• Typically quantitative (measurable) data attributes

• find trends, outliers, distributions, correlations, clusters,…

• encode additional attributes by size, color, shape,…

• show (all possible) combinations of attributes in a scatterplot matrix

• Each row / column is one attribute

• overview of correlation and patterns between data attributes

-> Brushing: mark data subset

-> Linking: highlight brushed data in linked views

-> Move / alter / extend brush

• Represent multiple data variables

• each variable is represented by a vertical axis, which are organized as evenly spaced parallel lines

• Data on each axis is normalized to min / max

• One data sample is represented by a connected set of points, one on each axis

• recognize patterns between adjacent axes

• steep learning curve for novices

• Axis ordering is major challenge: order by quality metrics

Line point duality

• Points in scatterplot map to lines in parallel coordinates

• points in parallel coordinates map to lines in scatterplot

• Radial axis arrangement

• Items are polylines

• axes in center very crowded: too much information in the center

• showing single variable

• 1D curve

• Mapping of a discrete set of points to a set of lines by connecting adjacent points

• function plot for 2 independent variables x and y and 1 dependent variable

• 2D surface, f(x,y) can be interpreted as height value at (x,y)

• Mapping of a discrete set of points to a set of faces by connecting adjacent points

• small independent visual objects that depict attributes of a data record

• Discretely placed in a display space

• Data attributes are represented by different visual channels (e.g. shape, color, size, orientation)

• Visual channels should be easy to distinguish and combine

• Mainly used for multivariate data

• A star is composed of equally spaced spikes, originating from the center

• Length of spikes represents value of respective attribute

• end of rays connected by line

• 2D figures with limbs

• Data encoded by

  • length

  • line thickness

  • angle between lines

• recognize texture patterns: see changes looking at texture and neighborship, not individual glyphs but patterns that they form

• Data attributes represented by features of a face (eye position, nose length, mouth form,…)

• Problem:

  • Faces are preceived holistically: we interpret mood of glyphs but its actually data visualization

  • Efficiency?

• light is electro magnetic radiation

• different wavelengths are perceived as different colors

  • Human eye can only see light between 380nm and 780nm (visible spectrum)

• Hue: dominant wavelength

• Saturation: pureness, amount of white light

• Luminance / Brightness: intensity of light

• Emphasize a specific target in a crowded display (pop-out)

• Group, categorize, and chunk information

• Possible problems:

  • Dependent on viewing and stimulus considtions

  • distract the user when inadequately used

  • Ineffective for color deficient individuals

  • Results in information overload

• Color maps can be

  • categorical vs. ordered

  • sequential vs. diverging

  • discrete vs. continuous

• equal steps in color map (i.e. magnitude of data) should be perceived equally

• equal steps in color map don’t mean equal steps in reality

• ordering of data should be represented by ordering of colors

• rainbow colormap is perceptually unordered

• Perceived color is highly context dependent

• Size matters

• vary luminance too

• make sure contrast is high

• Colors are more useful for qualitative statements

• do not use color if it is necessary to read our precise values

• use “good” color maps

• size

• color

• shape

• …

• used to show more than two variables: but the combination of a lot of variables

• positive correlation: von links unten nach rechts oben

• negative correlation: von links oben nach rechts unten

• brushing: mark (interesting) data subset

• Linking: highlight brushed data in linked views

number of data point is selected in one plot of the scatter plot matrix and the corresponding data points are also highlighted in the other scatter plots in a scatter plot matrix

• if the lines of a parallel coordinates plot meet in one point it means that we have a negative correlation between the two axes / attributes

• small independent visual objects that show attribtues of a data record

• can be placed individually somewhere in the visualization in display space

• different data attributes can be encoded by different visual channels of a glyph (e.g. shape, color, size, orientation)

• visual channels should be easy to distinguish and combine

• mainly used for multivariate data to show different data attributes of a data record

• star glyphs:

  • show multiple attributes of a data record

  • composed of equally spaced spikes that start in the center, and the length of wach of the spikes represent a value of a data attribute, the ends of the spikes are connected by lines

• stick figures:

  • data attributes can be mapped to the angle between the different limbs of the stick figure and the length / thickness of the individual limbs can be used to encode data

  • usually not perceived individually but in combination

  • recognize texture patterns

Disadvantages:

• since it uses color hue to encode the information, some of the details may be lost

• perceptually non linear, means that the same step in the data is not represented in the same perceived difference

• perceptually unordered: no naturally ordering of the colors

Advantages:

• many colors

• good for categorical data, but not for quantitative data because of non-linear, perceptually unordered,…

• perceptual linear: equal steps in color map (i.e. magnitude of data) should be perceived equally

• perceptual ordering: ordering of data should be represented by ordering of colors

• Sequential:

  • are suited to ordered data that progress from low to high / min to max

• Diverging:

  • has neutral center

  • put equal emphasis on mid-range critical values and extremes at both ends of the data range.

oben: sequential, unten: diverging

• Visual exploration

  • find unknown / unexpected

  • generate new hypotheses

• Visual analysis (confirmative vis.)

  • verify or reject hypotheses

  • information drill-down

• Presentation

  • show / communicate results

• Combines computational & interactive visual methods

• multiple linked views

• Interpret large & complex data

• Drill-down into information

• Find relations (“read between the lines”)

• Detect features / patterns that are difficult to describe

• Integrate expert knowledge

• Spatiotemporal data

• Multi-variate / multi-field data (multiple data attributes, e.g. temperature or pressure)

• Multi-modal data (CT, MRI, large-scale measurements, simulations, etc.)

• Multi-run / ensemble simulations (repeated with varied parameter settings)

• Multi-modal scenarios (e.g. coupled climate model)

• Cartography, geovis, etc.

• Linear vs cyclic time

• automatic animations

• Flow visualization

• Visualize summary statistics

-> comes from 1 simulation / measurement device

-> multiple data attributes, e.g. temperature or pressure

• Attribute views (scatterplots, parallel coordinates, etc.)

  • Find patterns such as correlations or outliers

  • lack spatial relationships of data

  • which of the many data variables to show?

• Volume rendering

  • Difficult to see multi-variate patterns

  • Layering and glyphs

  • Feature-based visualisation (brushing, segmentation,…)

• Clustering, dimensionality reduction, etc.

-> comes from different data sources / different modalities

-> CT, MRI, large-scale measurements, simulations, etc.

• Various types of grids with different resolution

• Coregistration and normalization

• Multi-volume rendering

• Visual data fusion

• Comparative visualization

• Side-by-side comparison (juxtaposition)

• Overlay in same coordinate system (superposition)

• Explicit encoding of differences / correlations

• Change item visibility

• Change which items are visible

• Camera metaphor

• Zoom, pan, rotate (3D)

-> Guided navigation between characteristic views

-> Based on information-theoretic measures

• Compute rating for each view v_i and obejct o_j

• Optimal viewpoint estimation based on obejct visibility, location in image, and distance to viewer

• Animated transition

  • View 1 optimal for o1 (emphasize o1)

  • Overview optimal for o1 and o2

  • View 2 optimal for o2 (emphasize o2)

• Automatically order views / axes by quality metrics

• Enhance clustering, correlations, outliers, image quality, etc.

• Spatially separate overview / detail (e.g. juxtaposed views)

• User has to switch attention between representations

• Seamlessly integrates focus / context in single visualization

• Originally spaced distortion used

• More space for focus

• Keep context, without cropping away data outside of zoom area

• emphasize data in focus

• keep context for orientation / navigation

• focus specification, e.g. by pointing, brushing or querying

• Select function graphs that intersect with user-specific line

• Select function graphs by similarity to user-sketched pattern

• Similarity evaluated based on gradients (1st derivative)

• Supervised learning: leatning with a labeled training set

• Unsupervised learning: discovering patterns in unlabeled data

• Reinforcement learning: Learning based on feedback or reward

• Labeling of large time series data by domain experts

• Integrates supervised & unsupervised segmentation methods

• User can iteratively improve labeling

• Dimensionality reduction

• Aggregation, summary statistics

• Clustering, classification, outliers, etc.

• Given some data points, we’d like to understand their structure

• Given a set of data points with some notion of distance between points, group them into clusters such that

  • members of a cluster are close / similar to each other

  • members of different clusters are dissimilar

• Usually

  • points are in high-dimensional space

  • similarity defined by distance measure (e.g. EUklidean)

• Clustering is a hard problem: many applications involve 10 or 10000 dimensions, and distances in high-dimensional spaces are at similar distance

• Time series clustered by similarity (K-means)

• Cluster affiliation of daily pattern shown in calendar

• Identify dense regions in data

• Clusters can be arbitrarily shaped

• Difficult to find good parameter settings

• 2 parameters: Radius epsilon and Number of Minimum Points MinPts

• core point: epsilon-neighborhood contains at least minimum number (MinPts) of points

• border point: in the epsilon-neighborhood of core point

• noise: neither a core object nor a border object

• Derive low-dimensional target space from high-dimensional measured space

• use when you can’t directly measure what you care about

  • True dimensionality of dataset assumed to be smaller than dimensionality of measurements

  • Latent factors, hidden variables

• Find directions of largest variance

• neglect directions of small variance (not descriptive)

• Coordinate system transformation (rigid rotation)

• Result:

  • new axes (eigenvectors) & explained variances (eigenvalues)

  • New axes usually don’t mean anything physical

• start with unknown dataset -> don’t know which features are in the data set, we want to explore it to find some hidden / unknown information

• Purpose: to generate new hypotheses -> which we can verify / reject later in visual analysis step

• Visualization (e.g. Information / Scientific Vis., Computer Graphics)

• Interaction techniques (e.g. Human Computer interaction)

• Data Analysis (e.g. machine learning, data mining)

-> Visual Analytics aims to combine those areas in different approaches

• 2 ways to show multivariate data:

• using attrubute views (scatterplots, parallel coordinates,…) that mainly focus on the attributes -> problem: don’t see spatial context in this examples

• using volume rendering: show data frames in a spatial context using e.g. glyphs or layering

• here we usually have data coming from different data sources (e.g. tumor from MR scan, vessels from MRA scal, skull from CT scan…)

• means data can be on various types of grids with different resolutions

• challenge:

  • what should be hidden and which data should be visible and shown to the user

  • comparison of multiple modalities -> need different techniques for that

• Layering techniques (e.g. glyphs, color, transparency)

• Multi-volume rendering (coregistration, segmentation)

• Helix glyphs

• side-by-side comparison (juxtaposition)

• Overlay in same coordinate system (superposition)

• Explicit encoding of differences / correlations

• idea: to combine both the important area / focus and the context information in one single visualization

  • e.g. highlight with color, opacity / transparency, blurring, enlargement of focus

• in overview + detail visualization the overview and the detail are shown next to each other (spatially separated)

  • issue: user has to switch attention between the representations

• color

• style

• frequency / blurring

• opacity / transparency

• fisheye views

• unsupervised method -> tries to find structures in the dataset by itself

• given a dataset with data points and some idea between the distance between the data points, group them into clusters -> data points that are similar should be grouped together in a cluster, and not similar /dissimilar data points should be in different clusters

• idea: if we have given some high dimensional data, then often it is possible to derive some low-dimensional target space where its easier to find the interesting features

• use when you can’t directly measure what you care about

  • true dimensionality of dataset assumed to be smaller than dimensionality of measurements

• example method: principal component analysis

• transformation of the coordinates system

• since the new axis is more aligned with the variance it is easier to distinguish / find groups and thats why we can dismiss other principal components

• Samples at equidistant intervals along Cartesian coordinate axes

• Neighboring samples are connected via edges

• Cells formed by 4 (2D) or 8 (3D) samples

• Cells and samples (grid vertices) are numbered sequentially with respect to increasing coordinates

• It is a structured grid:

  • Neighboring information (topology) is given implicitly

  • Neighbors obtained by incrementing / decrementing indices

• Structured Grids:

  • Uniform / Regular grid: orthogonal and quidistant grid

  • Rectilinear grid: varying sample-distances

  • Curvilinear grid: non-orthogonal grid, Grid-points specified explicitly, implicit neighborhood relationship

• Unstructured Grids: grid points and neighborhood specified explicitly; Cells: tetrahedra, hexahedra

• Grid-free data

• data points given without neighborhood relationship

• influence on neighborhood defined by spatial proximity

• Scattered data interpolationIs