Other DVR Algorithms and A
Comparison
Jian Huang, CS 594, Spring 2002
Papers Covered
• P. Lacroute et. al, SIGGRAPH’94 (shear-warp)
• B. Cabral et. al, VolViz’94 (3D texture mapping)
• M. Meissner et. al, VolViz’2000 (A practical
comparison of the four main volume rendering
algorithms)
Shear Warp Algorithm
• Goal – speed!!
• Approach: make viewing rays parallel to each other and
perpendicular to the image
– Achieved by a simple shear
shear
warp
Original method only works with orthogonal projection, later extended
to perspective projection but less efficient and less known.
Shear Warp Algorithm
• Stop rays in every sheared slice and use bilinear
interpolation to estimate a sample value
– only interpolate in-slice, not between slices as in usual raycasting
– cheap bilinear interpolation instead of trilinear interpolation in
raycasting
• Volume is projected onto a baseplane parallel to the volume
slices
– NOT the image plane: the resulting image is called intermediate
image
• Undo the shearing by warping the intermediate image onto
the true image plane (use M-1shear, the inverse of M-shear )
Shear Warp Algorithm
Shear Warp Algorithm
• General algorithm:
M view  P  S  M warp
• Where
– Mview = general viewing matrix
– P = permutation matrix, which transposes the coordinate system in
order to make the z-axis the principal viewing axis
– S = transforms volume into sheared object space
– Mwarp = sheared object coordinates into image coordinates
Shear Warp Algorithm
• Parallel vs. Perspective
S par
1

0

0

0

0 sx
1 sy
0 1
0
0
0

0
0

1 
S persp
1

0

0

0

shear
warp
0 sx
1 sy
0 1
0 sw
0

0
0

1 
Shear Warp Algorithm
• Three properties:
1. scanlines of pixels in the intermediate image are parallel to
scanlines of voxels in the volume data
2. (orthogonal projection only) all voxels in a given voxel
slice are scaled by the same factor
3. (orthogonal projections only) every voxel slice had the
same scale factor, and this factor can be chosen arbitrarily.
In particular, we can choose a unity scale factor so that for
a given voxel scan-line there is a one-to-one mapping
between voxels and intermediate image pixels.
Shear Warp Algorithm
• Property one leads to dynamic screen type data structure:
resample and composite
skip
skip
work
skip
work
transparent voxel run
opaque image pixel run
non-transparent voxel run
non-opaque image pixel run
Shear Warp Algorithm
• Parallel projection:
–
–
–
–
efficient reconstruction
lookup table for shading
lookup table for opacity correction (thickness)
three RLE of the actual volume (in x, y, z)
• Perspective Projection:
– similar to parallel projection
– except - voxels also need to be scaled!
– Hence more than two voxel scan-lines needed for one image scanline
Shear Warp Algorithm
• Fast classification:
–
–
–
–
–
–
classification through density and gradient of density
consider “block” of volume, that contains the scan-line
is it transparent?
Yes - if whole block is transparent
No - subdivide block
transparent blocks - lookup through summed area table
SAT
Shear Warp Algorithm
• Advantage: Very fast when opacity transfer function is kept constant
• Disadvantages:
– Need to encode the volume after each opacity transfer change
– Need 3 encoded volumes, one for each main viewing axis
– True sampling rate in z varies between [1.0, 1.72] due to shearing
• thus Nyquist theorem is almost always violated
• leads to staircasing artifacts for diagonal views (e. g., at 45°)
– Always pre- shaded, no post-shading. Blurred zoom-in views
Texture Mapping
+
2D image
2D polygon
Textured-mapped
polygon
Texture Mapping (2)
(0,1)
(0,0)
(1,1)
(0,0.5)
(0.5,0.5)
(0,0)
(0.5,0)
(1,0)
Each texel has 2D
coordinates assigned
to it.
assign the texture coordinates
to each polygon to establish
the mapping
Tex. Mapping for Volume Rendering
Remember ray casting …
y
z
Texture based volume rendering
z
y
x
• Render each xz slice in the volume as a texture-mapped polygon
• The texture contains RGBA (color and opacity)
• The polygons are drawn from back to front
Texture based volume rendering
Algorithm: (using 2D texture mapping hardware)
Turn off the z-buffer; Enable blending
For (each slice from back to front) {
- Load the 2D slice of data into texture memory
- Create a polygon corresponding to the slice
- Assign texture coordinates to four corners of
the polygon
- Render and composite the polygon (use OpenGL
alpha blending)
}
Some Considerations… (2)
What if we change the viewing position?
y
z
That is okay, we just
change the eye position
(or rotate the polygons
and re-render),
Until …
Some Considerations… (3)
Until …
You are not going to see anything
this way …
This is because the view direction now is
Parallel to the slice planes
What do we do?
y
z
Some Considerations… (4)
What do we do?
• Change the orientation of slicing planes
• Now the slice polygons are parallel to
XZ plane in the object space
• We need to reorganize the input textures
y
z
• Reorganize the textures on the fly is too
time consuming. We might want to
prepare this texture sets beforehand
Some Considerations… (5)
When do we need to change the slicing planes?
y
z
?
When the major component of view vector changes from z to y
Some Considerations… (6)
Major component of view vector?
Normalized view vector (x,y,z) -> get the maximum one
If x: then the slicing planes are parallel to yz plane
If y: then the slicing planes are parallel to xz plane
If z: then the slicing planes are parallel to xy plane
-> This is called (object-space) axis-aligned method.
Therefore, we need to keep three copies of data around
all the time!!
Problem
Object-space axis-alighed method can create artifact:
Poping Effect
y
z
V = 44.999
V = 45.0001
There is a sudden change of viewing slicing (and thus the sampling
rate) then the view vector transits from one major direction to another.
The change in the result image intensity can be quite visible
Solution
Use image-aligned slicing plane:
the slicing planes are always parallel to the image plane
3D Texture Mapping
Arbitrary slicing through the volume and texture
mapping capabilities are needed
- Arbitrary slicing polygon: this can be computed
using software in real time
This is basically polygon-volume
clipping
3D Texture Mapping
Texture mapping to the arbitrary slices
This requires 3D texture mapping harware
Input texture: volume (pre-classified and shaded)
essentially an (R,G,B,a) volume
Depending on the position of the polygon,
appropriate textures are resampled, constructed and
mapped to the polygon.
Solid (3D) Texture Mapping
Now the input texture space is 3D
(0,1,1)
(1,1,1)
Texture coordinates: (r,s,t)
(0,1,0)
(1,1,0)
(r2,s2,t2)
(0,0,0)
(r3,s3,t3)
(1,0,0)
(r0,s0,t0)
(r1,s1,t1)
Pros and Cons
Advantages:
- Fast with volume sizes that the hardware can take
e.g. 2 fps for 256 cube volumes
- No popping effect
Disadvantages: - Need to compute the slicing planes for
every view angle
- only supported on high end hardware
- low quality without per-pixel classification shading
and classification (i.e. post-classification and shading)
Both 2D or 3D hardware texture mapping methods can not compute
Shading on the fly. The input textures have to be pre-shaded.
With multi-texturing functions, per-pixel shading and classification are
becoming possible.
A Practical Comparison
• Quality is directly correlated with
– how closely the volume ray integration can be approximated
– and the quality of volume reconstruction
– post-reconstruction shading and classification are key to visual
sharpness of renderings.
• Ray-casting and image-aligned splatting are of high quality,
each is more efficient for different types of data sets
• Not considering limitations of hardware precision, 3D texture
mapping can achieve high quality as well
• Shear-warp is fast but poor quality