Data Visualization
References
Program
Tools
How do people use visualization?
 verification
 analysis
 exploration/discovery
 presentation/storytelling
 art/aesthetics
Provenance
The steps the user take in the process of visual exploration/analysis and the resulting visualizations and findings
We use provenance for:
 recall
 reuse and replicate
 Sharing
 Metaanalysis
Capture:
 datasets
 visualization and insight
 interaction
Visual Interaction Techniques
 Selecting/Highlighting/Brushing
 Using Lasso to update linked views
 sidebars for interactive filtering
A welldesigned interactive visualization interface should show the following
 Visualize
 use effective visual encodings
 Filter
 reduce visible data to relevant items
 Select
 Retrieve details about interesting items
 Navigate
 Pan, zoom, change view
https://github.com/juba/scatterD3 DeepTree http://www.visualcomplexity.com/vc/
Visual Design and Encoding  Westermann
The purpose of visualization is insight, not pictures.  Schneiderman
Why use Interactivity?
 Handle data complexity
 A single static view can show only one aspect of data
Overview first, zoom and filter, then detailsondemand
Why depend on vision?
 Visual system is highbandwidth channel to brain
Preattentive Processing
 Sequential vs. Parallel processing (popout)
 Combination of channels usually requires serial search
 Difficult if no unique visual property of the target
Gestalt Principles
Representations should be correct, accurate and truthful.
To bring up a change, you must attend to it. (Change blindness)
Visual Design
A good visualization depends on:
 data types
 context of the data
 tasks to perform e.g. identify trends
 questions to answer
 messages to deliver
\begin{equation} \text{Lie Factor} = \frac{\text{Size of effect shown in graphic}}{\text{Size of effect in data}} \end{equation}
Bad visualizations do not allow you to recover original data from the visualization. Keep proportions and relative sizes.
maximize dataink ratio
Steven’s Psychological Power Law
https://en.wikipedia.org/wiki/Stevens%27s%5Fpower%5Flaw
Steven’s psychophysical power law:
\begin{equation} \text{Perceived sensation} = \text{Physical Intensity}^T \end{equation}
Compensating for human’s over/underestimation:
Difficult to focus on one channel when multiple channels are presented. (Redudancy is bad!)
Visual mapping  Separable vs integral visual channels
 Color + position
 Color + size
 Width + height
 Red + green* Unfiled
 https://en.wikipedia.org/wiki/Tutte%5Fembedding
 ReingoldTilford Algorithm
Scientific Data Visualization  Stefan Bruckner
Types of Visualization
 Volume Visualization
 Visualization of scalar fields
 Important in medicine, biology, geoscience, engineering, …
 Flow Visualization
 Visualization of Vector Fields
 Data typically from computational fluid dynamics (CFD) simulations
Data Representation
 Inherent Spatial Domain?
 Yes: Do we recycle data space or not
 No: Select which representation space
 What dimension is used for what?
 Relationship data space <=> data attributes
 Available display space (2D/3D)
 Where is the focus?
 Where can you abstract?
Grids

Common way of storing datasets of field type (scalar, vector, tensor fields)

Typically a highperformance, spaceefficient representation

Data is organized in cells which contain samples.

Often used to define an interpolation function that defines data values between samples leading to a continuous representation.

Which data orginazation is optimal?

Where does the data come from?

Is there an explicit neighbourhood relationship?

How is the neighborhood information stored?

How is navigation within the data possible?

Calculations within the data possible?

Are the data structured?
Regular Grid
 Orthogonal, equidistant grid
 Sample distances not equal
 Implicit neighborhoodrelationship
Rectilinear Grid
 Orthogonal grid
 Varying sample distances (\(x[i], y[j]\) given)
 Allows you to place more samples in areas that are more important to you, not wasting storage in uninterested areas
Curvilinear Grid
 Nonorthogonal grid
 Gridpoints explicitly given (\(x[i,j]\))
 Implicit neighborhood relationship
Blockstructured Grid
 Combination of structured grids
Unstructured Grid
 Gridpoints and connections arbitrary
 Gridpoints and neighborhood explicitly given
 Cells: tetrahedra
TODO Other Grids SUMMARY OF GRID TYPES
 Noncartesian Coordinates
Scattered Data
 Gridfree data
Interesting to look at dimensionality of data space, vs dimensionality of data attributes
Data Enhancement
 Filtering
 Resampling
 Data derivation
 Data interpolation
Data, Visualization, Interaction
 Coupling varies considerably
 Data Generation (data acquisition)
 Mesaurement, simulation, modelling
 Can take very long, and be very costly
 Visualization (rest of visualization pipeline)
 Data enhancement, viz mapping, rendering
 Depending on implementation, fast/slow
 Interaction
 How can the user intervene, vary parameters
 Data Generation (data acquisition)
Interactive Steering
 Simulation and modelling generate data “on the fly”
 Allows realtime insight of the data
 User can interfere with the simulation, and change the design of the simulations
Volume Visualization
 the visualization of 3D scalar fields
 Mapping 3D > 2D
 Projection (e.g. MIP), slicing, volume rendering
 Volume data is 3Dx1D data
 Scalar data, 3D data space, space filling
 User wants to gain insight into 3D data, find structures of special interest + context

Organization of Volume Data
 Cartesian or Regular grid
 CT/MR, often dx=dy<dz
 Data enhancement: isostackcalculation
 Curvilinear, unstructured grid
 Cartesian or Regular grid
Challenges
 So much information, so few pixels
 How to identify and enhance relevant features in the data.
 Speed and interaction very important
Voxels vs Cells
 pixels = picture element, voxels = volume element
 A voxel is a point sample in 3D, not necessarily interpolated
 Cell is a cube primitive, and the corners are 8 voxels. Values in cell use interpolation.
Linear Interpolation
 Current GPUs automatically do trilinear interpolation of 3D textures
Evaluating Quality of Reconstruction
 MarshnerLobb function is a common test signal to evaluate the quality of reconstruction filters
 Signal has a high amount of energy near its Nyquist frequency
Classification
 Using data values, gradiant and curvature, segment data into multiple semantic regions
 Often semiautomatic or fully manual
 Automatic approximation: transfer functions
 Simplest example of 1D transfer function: data value > color
Visualization Approaches
 Slicing
 display of 2D cross sections
 Indirect Volume Rendering
 Extraction of an intermediate representation
 Direct Volume Rendering
 Direct display of representation
TODO Isosurface Similarity
Visualization in the Spatial Domain

Slicing
 Reduce the dimensionality of 3D t o2D by showing a cross section
 Usually without a transfer function
 Orthogonal slicing often used to slice along anatomical planes in medical imagery
 Oblique slicing has arbitrary slice orientation, often used in an multiplanar reformation (MPR) setup.
 Curved slices often tailored towards specific applications, e.g. visualization of blood vessels.

Direct Volume Rendering
 Dense representation of underlying scalar field: transfer function defines visible structure.
 Image order (ray casting) fast and easy to implement, and are well supported by current GPUs
 Object order (splatting, texture slicing) also supported by older GPUs, but difficult to skip nonvisible regions. Easy to skip…(?)
 Nowadays: shading/classification after interpolation/resampling
 post/preinterpolative classification order
 Ray Tracing vs Ray Casting
 Ray tracing
 method from image generation, usig rayobject intersection and tracing secondary rays.
 Ray casting
 no objects, density values in 3D, only viewing rays.

Shading
 lambertian reflection
 light reflected equally in all directions
 specular reflection
 light reflected more in one direction
Make structures in volume data sets more realistic by applying an illumination model
 Shade each sample in the volume like a surface: BlinnPhong illumination model commonly used.
 Use normalized gradient vector as estimation for surface normal.
Indirect Volume Rendering
 Extract an intermediate representation from the volume (geometric surface), then use traditional rendering methods
 Cuberille regards each xovel as a little cube, classify as either part of the object or not.
Marching Cubes is a standard method for the extraction of isosurfaces from volume data
Flow Visualization
 Airplane/ship/car design
 Weather simulation
 Medicine (blood flows etc.)
 Gaseous, liquid flow
 Flow models: Differential Equation Systems (ODEs)
 Common techniques for solving NavierStokes equations:
 Lagrangian approach (particlebased)
 Treat the fluid as discrete particles, and apply interaction forces.
 Pros: momentum conservation/more intuitive, and fast, no linear equation solving
 Cons: connectivity information/surface reconstruction
 Eulerian approach
 Discretize the domain using finite differences
 Use the operator splitting technique to solve each term separately
 Pros: derivative approximation, adaptive time step/solver
 Cons: memory usage & speed, grid artifact/resolution limitation.
 Lagrangian approach (particlebased)
Data Visualization of Text Data  Jaegul Choo
Overview
 Vector encoding techniques of text
 Bagofwords vectors and word embedding
 Basic text visualization techniques
 Word cloud, wordle, word tree, phrase nets, ThemeRiver
 Topic Modeling
 Nonnegative matrix factorization
 UTOPIAN and visual analytic systems
 Dimension reduction
 Multidimensional scaling and tSNE
 Interactive dimension reduction techniques and systems
 Interactive visualization of deep learning
 Toolkits: Tensorboard, Embedding Projector, Visdom
 Advanced visual analytics systems: CNNVis, LSTMVis, DeepEyes