lecture%202%20:%20Visualization%20Basics

1
lecture 2 Visualization Basics

• Bong-Soo Sohn
• School of Computer Science and Engineering
• Chung-Ang University

2
Data Acquisition

• Scanned/Sampled Data
• CT/MRI/Ultrasound
• Electron Microscopy
• Computed/Simulated Data
• Modeled/Synthetic Data

3
Time-Varying Data

• Time-Varying Data from Scanning

4
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 lt 1µ
• Ultra microscopy like Cyro EM 50Å-100Å

5
Imaging Techniques

• 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
• 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 idx, jdy,
  kdz.
• 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)

• Unstructured
• 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

• Union of balls
• Triangulation Dual

13
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

• p0 p p1
• The Barycentric coordinates a (a0 a1) for any
  point p on line segment ltp0 p1gt, are given by

f
f1
fp
f0
which yields p a0 p0 a1 p1 and
fp a0 f0 a1 f1
16
Linear interpolation over a triangle

• p0
• p1 p p2
• For a triangle p0,p1,p2, the Barycentric
  coordinates
• a (a0 a1 a2) for point p,

17
Linear interpolant over a tetrahedron

• Linear Interpolation within a
• Tetrahedron (p0,p1,p2,p3)
• a ai 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
• p1 p2
• p3 p4
• p
• p5 p6
• p7 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)
• 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
ltmedicalgt
lt ocean temperature function gt
lt two isosurfaces (blue,yellow) gt
ltbio-moleculargt
23
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)xF(x)-w0 , ( w is isovalue and x is
  domain R3 )

1.0
1.0
1.0
0.8
0.4
0.3
0.8
0.4
0.3
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
0.4
0.4
0.4
0.8
0.4
0.6
0.8
0.4
0.6
0.8
0.4
0.6
0.4
0.4
0.4
0.3
0.25
0.3
0.25
0.3
0.25
0.35
0.35
0.35
( Isocontour in 2D function isovalue0.5 )

• Marching Cubes for Isosurface Extraction
• Dividing the volume into a set of cubes
• For each cubes, triangulate it based on the
  28(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 -gt 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
Volume Rendering

• Popular Visualization Techniques for Scalar
  Fields

1. Volume Rendering Drebin88,
C color ?C opacity
C , ?C
I
I
Light traversal from back to front
I C ?C (1- ?C)I
ltemissiongt
ltincoming lightgt
ltproduced by CCV vistoolgt

• Hardware Acceleration ( 3D Texturing )
  Westermann98

1. Slicing along the viewing direction
2. Put 3D textures on the slice
3. Interactive color table manipulation

27
Volume Rendering

• 3D volumetric data -gt 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