Definitionen

1. data acquisition

• sources: data bases, simulation, sensors

1. filtering and enhancement: process to obtain useful data

• data format conversion

• resampling to grid

• interpolation/approximation of missing values

• clipping/cleaning/denoising

1. visualization mapping: map derived data to graphical primitives (how to represent data?)

• scalar field —> isosurface

• vector field —> vectors

• 2D field —> height field

• tensor field —> glyphs

• 3D field —> volume

1. rendering: generate 2D image/video

• viewpoint specification

• visibility calculation

• lighting/shading

• compute values at sampling points

• Passive Vis

• interactive vis

• visual steering (change data)

• velocity

• volume

• variety

• value

• veracity (Richtigkeit)

R^n (ind.) —> R^m (dep.)

independent:

• dimension of the domain of the problem

• 3D/2D space, time

dependent:

• type of dimension of data

• depends on domain (independent vaiable)

• temperature, velocity, density values, vectors)

• categorical data

• scalar value (given by function R^m —> R)

• vector data ("2D vector field)

• tesor data (multi dim matrix)

• cartesian grid

  • dx = dy

  • stored information (get grid points by): cell indices + origin

• uniform/regular grid

  • dx !=dy

• rectilinnear grid

  • Varying sample distances

• curvilinar grid

  • non orthogonal grid

  • specify grid points!

  • but still inplicitly given neighbors

• unstructured grid

  • gridpoints + neighborhood has to be specified ecplicity

• scattered data

radial basis function:

• points have global influence

• for each new sample point have to resolve equation system

• computationally expensive (inear eq. system)

inverse distance weighting

• no system of linear equations to find weights

• but still global influcence of points

• still computationally expensive

—> triangulation instead of continous functions for interpoltion

• connect sample point to triangles —> triangulation

• piecewise interpolate inside triangles

• good triangualation:

  • maximize minimum angle: radius-in-circle/radius-out-circle

  • delauny triangulation

    • out-circle does not contain other points of the set

    • build form non-oprimatl Delauny by local operations: Edge flipping

    • 
      

• each vonoroi region contains one initial sample point (sample)

• point in vonoroi region are closer to respective sample than to any other sample

• vonoroi samples are vertives in delauny trinagulation

• vonoroi vertives are midpoint of delauny triangulation

• sinc function

  • optimal reconstruction but very expensive

• bicubic interpoplation (Catmull-Rom spline)

  • mimics sinc

• Cubic B-spline

  • does not go through center points —-> approximation

• trillinar interpolation (tent (function look like tent))

  • fast but low quality

• 
  

= isocontour

all points at which data has specifc value

• always closed curves

• are nested (not (self)intersecting)

• orthogonal to scalar fields gradient

compute via

• marching square /cubes

• 16 different sign (+/-) configuarations - 4 base cases

• only consider cellls having differnet signs

• ambigous case:

  • midpoint decider (f_center >= c —> x

    • doe not work if f_center and delta are in diffenent sign zones

  • exact assympotic decider (delta >= c —> +

• 256 cases (2^8 , 15 base cases)

• ambiguity in case 3,6,7,10,12,13 —> use decider like in 2D

• can cause holes if abitrary choices are made

  • up to 5 triangles per cube

• ambient light

  • background light, contant

• diffuse refeflector

  • scatter light equally in all directions

• specular reflector

  • highlight = refelction of light source ,refelcts mostly in mirrir direction

  • if n increases —> intensity decreases, shininess increases

• forward differences

  • needs one extra point

  • see underlying grid structure

• central differences

  • needs two extra points —> but more smooth —> preferred

• sobel operator —> better approx. scheme

• indirect

  • convert volume data to intermediate representation whcih then can be rendered with traditional techniques (MC algo)

  • conveys surface impression

• direct

  • drecty get 3D representation from data

  • conveys volume impression

• map data values to visual properties

  scalr value —> color + alpha value

  • color C

  • opacity alpha

  • —> Color quadrupel (RGBalpha)

Direct volue rendering

• optical properties are mapped to each voxel (emission = color, absorption = opacity) —> emission/absorption model

• the light reaching the viewer is simualted by ray casting

• front to back(alpha compositing)

• average compositiong

  • produces xray image, does not acount for opactiy

• maximum intenstity projection MIP

  • does not acount for opactiy

  • good for magnetic ressonance

  • vessel structure extraction

• fist hit /surface rendering

  • same result as marching cubes but higher quality

due to too samples along the ray

—> increas sampling rate to Nyquist frequency

>= 2 samples per voxel

• dimension(2D, 3D)

• time dependency (steady vs time-varying)

• direct vs indirect

• Direct flow vis

  • arrows (glyphs), color coding

• geometrical (indirect flow vis)

  • stream lines, path lines, treak lines, surfaces

  • show particle movement along trajcetories

• sparse

  • feature based (critical points, sink, source, saddle, ..)

• dense( texture-based)

  • convolution along chaarcteristic lines

  • flexibility: from fuzzy to crisp

  • LIC (global, L increases —> smoother)

  • OLIC (not globa)

  • 3D LIC

• inherent occlusion effects

• ambiguity

• difficult spatial perception (1 D objects in 3D)

• are tangential to the flow

  • 1st derivative (gradient) points in vector field direction

• do not intersect

• are solution to initial value problem of ODE

Numerical Integration of ODEs

• Euler method (first order method)

• Runge kutta 2nd order / 4th order

• stream linkes should not get to close to each other

• choose seed point with distance d-sep from existing stream line

• forward and backward integration until d_test reached

• dsep increasing —> lines are narrow

• dtest increasing —> shorter stream lines

graphical primatives

• points, lines, areas, surfaces

visual channels (appearence of graphical primatives)

• color

• position

• shape

• slope tilt

• size

• Pop out (preattentive processing)

  • auomatic, parallel detection of basic features (250 ms)

• discriminability

  • How many usable steps (like bins)

• seperability

  • seperable vs integral channels

  • seperable: able to judge visual channels independently

  • integral: channels are viewd holistically (ganzheitlich)

• Relative vs absolute judgement

  • perception highly context depenent

  • Webers Law

  • e.g color, lenght, size

• Categorial + Quantitative Data

  • Bar, Pie,

  • stacked bar (quantitative wrt 2 categorical vars)

  • parallel sets (quantitative wrt multiple categorical vars)

• Time dependent data

  • line graph (most accurate angel judgement: 45 °)

  • Theme river

    • categories over time,

    • occurence/freq of topic/catagorical data mapped to width of river band

  • horizon graphs

    • reduce vertival space

• single + multiple varibles

  • histgram (binning, group value sinto equally spaced intervals)

  • boxplot —-> summary stats (median, max, min interquatile range)

    • variations: turkey’s, Trufte’s

  • Scatter plot

  • scatterplot matrix

    • all attribute combinations —> overview of correlations

  • parallel coordinates

  • radar chart (radial axis arrangement, items are polylines)

  • function plots

  • Glyphs, color mapping

• small, independent visual onjects that depict attributes of a data record

• 2D, 3D, surface

• star glyphs

  • equally spaced spikes

  • lenght of spike represents attribute value

  • end of spikes connected

• stick figures

  • data encoded by lenght, angle, thickness

  • recognize texture patterns

• chernoff faces

• Hue: dominant wavelenght

• saturation: pureness, amamount of white light

• luminance / brightness, intensity of light

equal steps in color map should be perceives equally

(rainbow NOT)

irdering of data should be represented by ordering of colors

(rainbow NOT)

• visual exploration

• confirmative analysis/ visual analysis

• presentation

• spatiotemporal data

  • time dependent

• multi-variate data

  • attribute views

  • volume rendering

  • clustering, dimensionality reduction

• multi-modal data

  • carious types of grids with different resolutions

  • visual data fusion

  • comparative vis

• muti-run data

• multi-model data

  • couples climate models

• use a common frame (axes)

• Layering techniques (glyphs, color, transparency)

• multi volume rendering (segmentation)

• side by side composition (juxtaposition)

• overlay in same coordiante system (superposition)

• explicit encoding of differences

change item visabiility

zoom, pan, rotate

• true dimensionality of dataset assumed to be smaller than dim of meassurements

• PCA

  • find direction if largest variance

  • coordinate system transformation

glyphs, laxering, feature-based

• layering (glyphs, color, transparency)

• multi-volume rendering

• common frame by shared axes

• juxtrapostion: side by side

• superposition: overlay

• explicit encoding of differences

show focus/important information and context information together

• overview + detail: seperates focus and context information

color, zooming, transparency

• fish eye lense

• Perspective wall

• reduce the number of features or variables in a dataset while retaining as much useful information as possible

• find interesting features in lower dimensionality easier

• PCA:

• PCA works by identifying the linear combinations of the original variables that explain the most variance in the data. These combinations are called principal components, and they can be used as new variables that capture most of the information in the original dataset. PCA then discards the least important principal components, effectively reducing the dimensionality of the dataset.

pca reduces the number of variables or features needed to represent the data while retaining most of the information in the original dataset.