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Volume Rendering & Shear-Warp Factorization. Joe Zadeh January 22, 2002 CS395 - Advanced Graphics. Volume Rendering (Part II). 3D Radiology Lab, Stanford. Start with Slices (usually). Stanford. Classification. What does this voxel represent? Classification via probability

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volume rendering shear warp factorization

Volume Rendering & Shear-Warp Factorization

Joe Zadeh

January 22, 2002

CS395 - Advanced Graphics

classification
Classification
  • What does this voxel represent?
  • Classification via probability
  • Assign (R,G,B,)
  • Create Isosurfaces
marching cubes
Marching Cubes

Lorensen and Cline

slide7

Watt, pg 385

OBJECT

IMAGE

image order ray casting
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!!!

the paper
The Paper
  • “Fast Volume Rendering Using a Shear-Warp Factorization of the Viewing Transform”
  • SIGGRAPH ‘94
the authors
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
history of the stanford bunny
History of the Stanford Bunny

O’Brien, Hodgins: “Animating Fracture”

image order vs object order
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
the shear warp revolution
The Shear-Warp Revolution
  • Takes the good of both Object and Image Order Algorithms
3 steps
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”
in a nutshell
In a Nutshell
  • Shear (3D)
  • Project (3D  2D)
  • Unwarp (2D)
the shear parallel
The Shear (Parallel)

Lacroute, Levoy

sheared object space
Sheared Object Space
  • Intermediate Coordinate System
  • Simple mapping from object oriented system
  • All viewing rays are parallel to the third axis
properties of sheared object space
Properties of Sheared Object Space
  • Pixel scanlines of intermediate are parallel to voxel scanlines
  • All voxels in a slice scaled by same factor.
  • (Parallel) Every voxel slice has same scale factor (voxelpixel is one-to-one)
algorithm again
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
three shear warp algorithms
Three Shear-Warp Algorithms
  • Parallel Projection
  • Perspective Projection
  • Fast Classification
  • (SW Parallel Projection first described by Cameron and Undrill, 1992)
parallel projection rendering
Parallel Projection Rendering
  • Recall: Voxel scanlines in sheared volume are aligned with Pixel scanlines in intermediate
  • Both can be traversed in scanline order
  • Simultaneously
compress voxel scanlines
Compress Voxel Scanlines
  • Run-length encoding
  • Skip transparent voxels

RTAAAASDEEEEE = RT*4A SD*5E

  • Effectiveness depends heavily on image type
compress intermediate image
Compress Intermediate Image
  • Recall: Splatting doesn’t 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 don’t have to go to deeper slices (I.e. ray termination)
for the uncompressed
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
warping
Warping
  • We now have composited intermediate image
  • Warp: Affine image warper with bilinear filter
  • We now have our image
some costs
Some Costs
  • Run-length encoded volume
    • Preprocessing created
    • View Independent
  • Three encodings (x,y,z)
    • Still less data than original volume because omits transparency
perspective projection
Perspective Projection
  • Majority of Volume Rendering Parallel (’94)
  • Perspective mostly useful in radiation beam planning
  • Viewing rays diverge, complicating sampling
perspective projection algorithm
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
fast classification algorithm
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
the algorithm
The Algorithm

Lacroute, Levoy

a bit more detail
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
further analysis
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)
pitfalls of shear warp
Pitfalls of Shear-Warp
  • Two resampling steps
    • No noticable degradation
  • Uses 2D reconstruction filter to resample the volume data
    • Not really applicable
futher research
Futher Research
  • Algorithm is parallelizable
  • Real-Time Rendering on Shared Multiprocessors (approx 10 fps) [SGI Challenge 16 Processor multiprocessor, 256x256x223 voxel]
  • Volpack