3D Volume Visualization

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3D Volume Visualization
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Volume Graphics

• Maintains a 3D image representation that is close
  to the underlying fully-3D object (but discrete)
• ????(Boundary Surface)?? ??? ? ?? ???? ????
  ?????? ??

N x 2D arraies 3D
array
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Input Data 3D Images (Volumetric Image)

• it is a 3D array of point samples, called voxels
  (volume elements)
• the point samples are located at the grid points
• the process of generating a 2D image from the 3D
  volume is called volume rendering

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Data Acquisition

• Scanned Data
• CT
• MRI
• Ultrasound
• Electron Microscopy
• Simulated Data

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Volume Visualization Methods

• Volume Rendering
• Ray casting
• Isosurface Extraction
• triangulation

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Volume Rendering (Basic Idea)
Based on the idea of ray tracing

• Trace from each pixel as a ray into object space
• Compute and accumulate color/opacity value along
  the ray
• Assign the value to the pixel

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Transfer Function

• Maps voxel data values to optical properties
• Color/opacity map
• Emphasize or classify features of interest in the
  data

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Raycasting
volumetric compositing
color
opacity
object (color, opacity)
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Raycasting
Interpolationkernel
volumetric compositing
color
opacity
1.0
object (color, opacity)
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Raycasting
Interpolationkernel
volumetric compositing
color c c s ?s(1 - ?) c
opacity ? ? s (1 - ?) ?
object (color, opacity)
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Raycasting
volumetric compositing
color
opacity
1.0
object (color, opacity)
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Raycasting
volumetric compositing
color
opacity
1.0
object (color, opacity)
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Raycasting
volumetric compositing
color
opacity
1.0
object (color, opacity)
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Raycasting
volumetric compositing
color
opacity
1.0
object (color, opacity)
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Raycasting
volumetric compositing
color
opacity
object (color, opacity)
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Volume Ray Marching

• Raycast once per pixel
• Sample uniform intervals along ray
• Interpolate trilinear interpolate, apply
  transfer function
• Accumulate integrate optical properties

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Composition (alpha blending)
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3D Texture Based Volume Rendering
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Use Image-space axis-aligned slicing plane
the slicing planes are always parallel to the
view plane
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Isosurface

• Isosurface (i.e. Level Set )
• C(w) x F(x) - w 0
• ( w isovalue , F(x) real-valued function ,
  usually 3D volume data )

isosurfacing
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?? CT ?? ?? ???? F(x,y,z)
?? ?? ??? w ?? ???
??? ?? F(x,y,z)w
??? ??? w ? ???
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Marching Cubes

• Lorensen and Cline, ACM SIGGRAPH 87
• Goal
• Input 2D/3D/4D imaging data (scalar)
• Interactive parameter isovalue selection
• Output Isosurface triangulation

isosurfacing
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Surface Intersection in a Cube

• assign ZERO to vertex outside the surface
• assign ONE to vertex inside the surface
• Note
• Surface intersects those cube edges where one
  vertex is outside and the other inside the surface

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Surface Intersection in a Cube

• There are 28256 ways the surface may intersect
  the cube
• Triangulate each case

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Marching Cubes Table

• Using symmetries reduces 256 cases into 15 cases

ltwrong surfacegt
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Surface intersection in a cube

• Create an index for each case
• Interpolate surface intersection along each edge

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Calculating normals

• Calculate normal for each cube vertex
• Interpolate the normals at
• the vertices of the triangles

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Problems in Marching Cubes

• May Generate very large meshes
• Simplification
• Can we generate 3D mesh?
• Interval Volume Tetrahedrization
• Computationally Slow
• Acceleration techniques , CUDA
• Ambiguity problem
• Trilinear isosurface
• How to select isovalue?
• Contour spectrum

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Problems in Marching Cubes

• How to preserve sharp features?
• Dual contouring
• Hard to deal with extremely large volume data
• Parallel
• Out-of-core
• Segmenting Isosurface Components?
• Contour Tree
• Volume Structure
• Contour Tree , Morse Complex

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Comparison

• Volume Rendering
• ??? ??? ?? 3D?? ??? 2D??? ???
• ??? ???? ?? ??? ????? ???
• Transfer function? ??? ?? ?? ??? quality? ?? ???
  ? ????, ??? ??? ??? ?.
• Isosurface Extraction
• Triangulation? ?? ??? Surface Mesh ???? ??(fast
  rendering, shading, ?)? ??
• ??? isosurface? ?? ??? ???? ?? ??? ??? isovalue??
  ??? ?? ??? ???.

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Visualization SW

• Volume Rover
• http//www.cs.utexas.edu/bajaj/cvc/software/volro
  ver.shtml

Transfer function