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lecture 2 : Visualization Basics

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lecture 2 : Visualization Basics Bong-Soo Sohn School of Computer Science and Engineering Chung-Ang University – PowerPoint PPT presentation

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Title: lecture 2 : Visualization Basics


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
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