1. lecture 2 : Visualization Basics
Bong-Soo Sohn
School of Computer Science and Engineering
Chung-Ang University

2. Data Acquisition Scanned/Sampled Data Computed/Simulated Data
CT/MRI/Ultrasound
Electron Microscopy
Computed/Simulated Data
Modeled/Synthetic Data

3. Time-Varying Data
Time-Varying Data from Scanning

4. Scanners can yield both domains and functions on domains
Imaging Scanners
Scanners can yield both domains and functions on domains
Scanners yielding domains
Point Cloud Scanners: 300μ-800μ
CT, MRI: 10μ-200μ
Light microscopy: 5μ-10μ
Electron microscopy: < 1μ
Ultra microscopy like Cyro EM 50Å-100Å

5. Imaging Techniques Ultrasound Computed Tomography (CT)
Measures spacially varying X-ray attenuation coefficient
Each slice 1-10mm thick
High resolution , low noise
Good for high density solids
Magnetic Resonance Imaging (MRI)
Measures distribution of mobile hydrogen nuclei by quantifying relaxation times
Moderate noise
Works well with soft tissue
Ultrasound
Handheld probe
Inexpensive, fast, and real-time
High noise with moderate resolution

6. Various Data Characteristics
Time varying data
Vector , Tensor
Meshless
Sparse
Static
Scalar
Meshed
Dense

7. Data Format Mesh (Grid) Type Mesh type conversion Regular Rectilinear
Unstructured
Meshless
Mesh type conversion
Meshless to meshed

8. Mesh Types Mesh taxonomy regular rectilinear meshes:
There is an indexing scheme, say i,j,k, with the actual positions being determined as i*dx, j*dy, k*dz.
In 2-D, we get a pixel, and in 3-D, a voxel. dx
A 2-D regular rectilinear cartesian grid dy

9. Mesh Types (contd) Irregular rectilinear meshes:
Individual cells are not identical but are rectangular, and connectivity is related to a rectangular grid
dx, dy are not constant in grid,
but connectivity is similar in topology
to regular grids.

10. Mesh types (contd) Curvilinear (structured) grid:
a regular grid subjected to a non-linear transformation so as to fill a volume or surround an object.
A 2-D curvilinear grid

11. Mesh Types (contd) Dynamic (Time-varying) meshes Unstructured: Hybrid:
Cells are of any shape (tetrahedral) hexahedra, etc with no implicit connectivity
Hybrid:
Combination of curvilinear and unstructured grids.
Dynamic (Time-varying) meshes

12. Triangulations (Delaunay) & Dual Diagrams (Voronoi)
Meshless (particle) Data  Meshed Data
Triangulations (Delaunay) & Dual Diagrams (Voronoi)
Union of balls
Triangulation & Dual

13. Multivariate Time Series
Field Data
Scalar
temperature, pressure, density, energy, change, resistance, capacitance, refractive index, wavelength, frequency & fluid content.
Vector 
velocity, acceleration, angular velocity, force, momentum, magnetic field, electric field, gravitational field, current, surface normal
Tensor
stress, strain, conductivity, moment of inertia and electromagnetic field
Multivariate Time Series

14. Interpolation
Interpolation/Approximation are often used to approximate the data on the domain
In other words, it constructs a continuous function on the domain

15. Linear Interpolation on a line segment
p p p1
The Barycentric coordinates α = (α0 α1) for any point p on line segment <p0 p1>, are given by fp f1 f f0
which yields p = α0 p0 + α1 p1
and fp = α0 f0 + α1 f1

16. Linear interpolation over a triangle
p1 p p2
For a triangle p0,p1,p2, the Barycentric coordinates
α = (α0 α1 α2) for point p,

17. Linear interpolant over a tetrahedron
Linear Interpolation within a
Tetrahedron (p0,p1,p2,p3)
α = αi are the barycentric coordinates of p p3 p
p0 p2 p1
fp3 fp
fp2
fp0
fp1

18. Trilinear Interpolation
Unit Cube (p1,p2,p3,p4,p5,p6,p7,p8)
Tensor in all 3 dimensions
p p2
p p4 p
p p6
p p8
Trilinear interpolant

19. comparison
Bicubic vs Bilinear vs nearest point

20. Resampling Used in image resize or data type conversion
Rectilinear to rectilinear
Unstructured to rectilinear

21. Rendering Isocontouring (Surface Rendering) Volume Rendering
Builds a display list of isovalued lines/surfaces
Volume Rendering
3D volume primitives are transformed into 2D discrete pixel space

22. Isosurface Visualization
Isosurface (i.e. Level Set ) :
C(w) = { x | F(x) - w = 0 }
( w : isovalue , F(x) : real-valued function )
isosurfacing
<medical>
< ocean temperature function >
< two isosurfaces (blue,yellow) >
<bio-molecular>

23. Popular Visualization Techniques for Scalar Fields
Isocontouring
Popular Visualization Techniques for Scalar Fields
2. Isocontouring [Lorensen and Cline87,…]
Definition of isosurface C(w) of a scalar field F(x)
C(w)={x|F(x)-w=0} , ( w is isovalue and x is domain R3 )
1.0
0.8
0.4
0.3
1.0
0.8
0.4
0.3
1.0
0.8
0.4
0.3
0.7
0.6
0.75
0.4
0.7
0.6
0.75
0.4
0.7
0.6
0.75
0.4
0.6
0.4
0.8
0.4
0.6
0.4
0.8
0.4
0.6
0.4
0.8
0.4
0.4
0.3
0.35
0.25
0.4
0.3
0.35
0.25
0.4
0.3
0.35
0.25
( Isocontour in 2D function: isovalue=0.5 )
Marching Cubes for Isosurface Extraction
Dividing the volume into a set of cubes
For each cubes, triangulate it based on the 2^8(reduced to 15) cases

24. Cube Polygonization Template

25. Surface Rendering (Geometry Rendering)
Objects are defined in terms of surfaces
Converts data into intermediate surface representation before rendering
Volume data -> geometric primitives
Surface reconstruction
Can use HW of the geometry engines for realtime rendering
Compact storage and transmission
Amorphous data does not have thin surfaces

26. Popular Visualization Techniques for Scalar Fields
Volume Rendering
Popular Visualization Techniques for Scalar Fields
1. Volume Rendering [Drebin88,…]
C : color
C: opacity I’
C , C I
Light traversal from back to front
I’= C C (1- C)I
<emission>
<incoming light>
<produced by CCV vistool>
Hardware Acceleration ( 3D Texturing ) [Westermann98]
Slicing along the viewing direction
Put 3D textures on the slice
Interactive color table manipulation

27. Volume Rendering 3D volumetric data -> 2D image
Show the information inside volume entities
Good for rendering soft and amorphous objects
Good for block (boolean) operation : CSG
Insensitive to scene complexity
Insensitive to object complexity
Sensitive to image resolution

28. Transfer Function
Mapping from density to (color, opacity)

29. Medical applications