Volume Rendering & Shear-Warp Factorization

Joe ZadehJanuary 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

• Assign (R,G,B,)• Create Isosurfaces

Marching Cubes

Lorensen and Cline

Watt, pg 385

IMAGE OBJECT

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!!!

Image Order: Casting Image

Watt, pg 386

Image Order: Compositing with Resampling

Watt, pg 387

Image Order: Resampling (Shear) then Compositing

Watt, pg 388

Object Order: Voxel Projection

• Splatting

Watt, pg 389

The Paper

• “Fast Volume Rendering Using a Shear-Warp Factorization of the Viewing Transform”

• SIGGRAPH ‘94

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 O’Brien, Hodgins:

“Animating Fracture”

Input Data

Input Data

Output Data

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

• Takes the good of both Object and Image Order Algorithms

Lacroute, Levoy

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

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

The Shear (Parallel)

Lacroute, Levoy

The Shear (Perspective)

Lacroute, Levoy

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

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 (voxelpixel is one-to-one)

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

• Parallel Projection• Perspective Projection• Fast Classification

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

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

• Run-length encoding• Skip transparent voxels

RTAAAASDEEEEE = RT*4A SD*5E

• Effectiveness depends heavily on image type

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)

Lacroute, Levoy

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

• We now have composited intermediate image

• Warp: Affine image warper with bilinear filter

• We now have our image

Some Costs

• Run-length encoded volume– Preprocessing created– View Independent

• Three encodings (x,y,z)– Still less data than original volume

because omits transparency

Lacroute, Levoy

256x256x225 on SGI Indigo R4000 Lacroute, Levoy

Perspective Projection

• Majority of Volume Rendering Parallel (’94)

• Perspective mostly useful in radiation beam planning

• Viewing rays diverge, complicating sampling

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

• Recall: Previous two algorithms require intense preprocessing classification step

• Not acceptable when experimenting with different opacities

• Solution: Classification opacity via scalar function

The Algorithm

Lacroute, Levoy

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

• 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

• Two resampling steps– No noticable degradation

• Uses 2D reconstruction filter to resample the volume data – Not really applicable

Futher Research

• Algorithm is parallelizable• Real-Time Rendering on Shared

Multiprocessors (approx 10 fps) [SGI Challenge 16 Processor multiprocessor, 256x256x223 voxel]

• Volpack

Hardware Implementation