Volume Rendering

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Volume Rendering Shear-Warp Factorization

• Joe Zadeh
• January 22, 2002
• CS395 - Advanced Graphics

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Volume Rendering (Part II)
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3D Radiology Lab, Stanford
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Start with Slices (usually)
Stanford
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Classification

• What does this voxel represent?
• Classification via probability
• Assign (R,G,B,?)
• Create Isosurfaces

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Marching Cubes
Lorensen and Cline
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Watt, pg 385
OBJECT
IMAGE
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Image Order Ray Casting

• Cast set of parallel rays
• Remain Traveling
• Two Issues
• Find voxels through which the ray passes
• Find a value for the voxel
• NOT RAYTRACING!!!

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Image Order Casting Image
Watt, pg 386
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Image Order Compositing with Resampling
Watt, pg 387
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Image Order Resampling (Shear) then Compositing
Watt, pg 388
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Object Order Voxel Projection

• Splatting

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Watt, pg 389
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The Paper

• Fast Volume Rendering Using a Shear-Warp
  Factorization of the Viewing Transform
• SIGGRAPH 94

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The Authors

• Philippe Lacroute
• Computer Systems Laboratory, Stanford
• PhD Dissertation with same title
• SGI for 3 years
• Marc Levoy
• Computer Science Dept, Stanford
• 1996 SIGGRAPH Achievement Award for Volume
  Rendering

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History of the Stanford Bunny
OBrien, Hodgins Animating Fracture
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Input Data
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Input Data
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Output Data
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Image Order vs. Object Order

• Image Order (ray-casting)
• Redundant Traversals of Spatial Data
• Early Ray Termination
• Object Order (splatting)
• Traverse through complete spatial data
• Only Traverse Once

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The Shear-Warp Revolution

• Takes the good of both Object and Image Order
  Algorithms

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Lacroute, Levoy
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3 Steps

• Factorization of the viewing matrix into a 3D
  shear parallel to the slices of volume data
• a projection to form a distorted intermediate
  image
• and a 2D warp to produce the final image

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In a Nutshell

• Shear (3D)
• Project (3D ? 2D)
• Unwarp (2D)

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The Shear (Parallel)
Lacroute, Levoy
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The Shear (Perspective)
Lacroute, Levoy
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Sheared Object Space

• Intermediate Coordinate System
• Simple mapping from object oriented system
• All viewing rays are parallel to the third axis

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Properties of Sheared Object Space

1. Pixel scanlines of intermediate are parallel to
   voxel scanlines
2. All voxels in a slice scaled by same factor.
3. (Parallel) Every voxel slice has same scale
   factor (voxel?pixel is one-to-one)

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Algorithm, again

• Transform volume to sheared object space by
  translation and resampling
• Project volume into 2D intermediate image in
  sheared object space
• Composite resampled slices front-to-back
• Transform intermediate image to image space using
  2D warping

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Three Shear-Warp Algorithms

• Parallel Projection
• Perspective Projection
• Fast Classification
• (SW Parallel Projection first described by
  Cameron and Undrill, 1992)

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Parallel Projection Rendering

• Recall Voxel scanlines in sheared volume are
  aligned with Pixel scanlines in intermediate
• Both can be traversed in scanline order
• Simultaneously

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Compress Voxel Scanlines

• Run-length encoding
• Skip transparent voxels
• RTAAAASDEEEEE RT4A SD5E
• Effectiveness depends heavily on image type

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Compress Intermediate Image

• Recall Splatting doesnt account for occlusion
• Solution Keep run-length encoding of opacity
  while creating the intermediate image
• If a pixel exceeds an opacity threshold, we know
  we dont have to go to deeper slices (I.e. ray
  termination)

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Lacroute, Levoy
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For the Uncompressed

• Recall All voxels in a given slice are scaled
  by the same factor
• Other rendering algorithms require a different
  scaling weight for each voxel
• Use Bilinear Interpolation and backward
  projection
• Two voxel scanlines ?single intermediate scanline

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Warping

• We now have composited intermediate image
• Warp Affine image warper with bilinear filter
• We now have our image

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Some Costs

• Run-length encoded volume
• Preprocessing created
• View Independent
• Three encodings (x,y,z)
• Still less data than original volume because
  omits transparency

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Lacroute, Levoy
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256x256x225 on SGI Indigo R4000
Lacroute, Levoy
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Perspective Projection

• Majority of Volume Rendering Parallel (94)
• Perspective mostly useful in radiation beam
  planning
• Viewing rays diverge, complicating sampling

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Perspective Projection Algorithm

• Almost exactly like Parallel
• In addition to translation during shear, scale as
  well then composite.
• Tends to create a many-to-one mapping from voxels
  to pixels
• Slower in calculating volumes and intermediate
  scanlines not traversed at same rate

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Fast Classification Algorithm

• Recall Previous two algorithms require intense
  preprocessing classification step
• Not acceptable when experimenting with different
  opacities
• Solution Classification opacity via scalar
  function

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The Algorithm
Lacroute, Levoy
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A bit more detail

• For some block of volume, find extrema of
  parameters to opacity function
• If function returns transparent opacity, discard
  scanline portion
• Subdivide scanline and repeat recursively until
  size of portion is smaller than a threshold

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Further Analysis

• 1283 5x speed increase over traditional
  ray-casting (.5 sec)
• 2563 10x speed increase (1 sec)
• General Shear-Warp O(n)
• Classification with Render O(n2)

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Pitfalls of Shear-Warp

• Two resampling steps
• No noticable degradation
• Uses 2D reconstruction filter to resample the
  volume data
• Not really applicable

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Futher Research

• Algorithm is parallelizable
• Real-Time Rendering on Shared Multiprocessors
  (approx 10 fps) SGI Challenge 16 Processor
  multiprocessor, 256x256x223 voxel
• Volpack

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Hardware Implementation