Lecture 3 : Direct Volume Rendering
Bong-Soo Sohn
School of Computer Science and Engineering
Chung-Ang University
Acknowledgement : Han-Wei Shen Lecture Notes 사용
Direct Volume Rendering
• Direct : no conversion to surface geometry
• Four methods
–
–
–
–
Ray-Casting
Splatting
3D Texture-Based Method
CUDA
Data Representation
• 3D volume data are represented by a finite number of cross sectional
slices (hence a 3D raster)
• On each volume element (voxel), stores a data value (if it uses only a single
bit, then it is a binary data set. Normally, we see a gray value of 8 to 16 bits
on each voxel.)
N x 2D arraies
=
3D array
Data Representation
What is a Voxel? – Two definitions
A voxel is a cubic cell, which
has a single value cover
the entire cubic region
A voxel is a data point
at a corner of the cubic cell
The value of a point inside the
cell is determined by interpolation
Basic Idea
Based on the idea of ray tracing
• Trace from eat each pixel as a ray
into object space
• Compute color value along the ray
• Assign the value to the pixel
Transfer Function
• Maps voxel data values to optical properties
•
•
•
•
Voxel Data
Optical Properties
• Density
• Temperature
• Color
• Opacity
Color/opacity map
Emphasize or classify features of interest in the data
Piecewise linear functions, Look-up tables, 1D, 2D
GPU – simple shader functions, texture lookup tables
Viewing
Ray Casting
• Where to position the volume and image plane
• What is a ‘ray’
• How to march a ray
Viewing
E0
v0
u0
E
v
+ S0
u
S
B = [0,0,0]
S0 = [0,0,-D]
u0 = [1,0,0]
v0 = [0,1,0]
B
(0,0,0)
y
z
x
Now,
R: the rotation matrix
S=B–Dxg
U = [1,0,0] x R
V = [0,1,0] x R
Ray Casting
• Stepping through the volume: a ray is cast into the volume,
sampling the volume at certain intervals
• The sampling intervals are usually equi-distant, but don’t
have to be (e.g. importance sampling)
• At each sampling location, a sample is interpolated /
reconstructed from the grid voxels
• popular filters are: nearest neighbor (box), trilinear (tent),
Gaussian, cubic spline
• Along the ray - what are we looking for?
Basic Idea of Ray-casting Pipeline
- Data are defined at the corners
of each cell (voxel)
- The data value inside the
voxel is determined using
interpolation (e.g. tri-linear)
- Composite colors and opacities
along the ray path
c1
c2
c3
- Can use other ray-traversal schemes as well
Ray Traversal Schemes
Intensity
Max
Average
Accumulate
First
Depth
Ray Traversal -
First
Intensity
First
Depth
• First: extracts iso-surfaces (again!)
done by Tuy&Tuy ’84
Ray Traversal -
Average
Intensity
Average
Depth
• Average: produces basically an X-ray picture
Ray Traversal -
MIP
Intensity
Max
Depth
• Max: Maximum Intensity Projection
used for Magnetic Resonance Angiogram
Ray Traversal -
Accumulate
Intensity
Accumulate
Depth
• Accumulate opacity while compositing colors:
make transparent layers visible!
Levoy ‘88
Raycasting
volumetric compositing
color
opacity
1.0
object (color, opacity)
Raycasting
Interpolation
kernel
volumetric compositing
color
opacity
1.0
object (color, opacity)
Raycasting
Interpolation
kernel
volumetric compositing
color c = c s s(1 - ) + c
opacity  =  s (1 - ) + 
1.0
object (color, opacity)
Raycasting
volumetric compositing
color
opacity
1.0
object (color, opacity)
Raycasting
volumetric compositing
color
opacity
1.0
object (color, opacity)
Raycasting
volumetric compositing
color
opacity
1.0
object (color, opacity)
Raycasting
volumetric compositing
color
opacity
1.0
object (color, opacity)
Raycasting
volumetric compositing
color
opacity
object (color, opacity)
Volume Ray Marching
1.
2.
3.
4.
Raycast – once per pixel
Sample – uniform intervals along ray
Interpolate – trilinear interpolate, apply transfer function
Accumulate – integrate optical properties
Shading and Classification
- Shading: compute a color(lighting) for each data point in the
volume
- Classification: Compute color and opacity for each data point
in the volume
f(xi)
C(xi), a(xi)
-Done by table lookup (transfer function)
Shading (Local Illumination)
• Blinn-Phong Shading Model
N
ˆ
ˆ
ˆ
ˆ
I  ka  I L kd (l  n)  I L ks (h  n)
Resulting = Ambient + Diffuse + Specular
• Requires surface normal vector
– What’s the normal vector of a voxel? Gradient
– Central differences between neighboring voxels
(right  left ) (top  bottom ) ( front  back )
grad ( I )  I 
,
,
2x
2x
2x
Shading (Local Illumination)
• Compute on-the-fly within fragment shader
– Requires 6 texture fetches per calculation
• Precalculate on host and store in voxel data
– Requires 4x texture memory
– Pack into 3D RGBA texture to send to GPU
Voxel Data
3D Texture
• X Gradient
• Y Gradient
• Z Gradient
• Value
•R
•G
•B
•A
Shading (Local Illumination)
• Improve perception of depth
• Amplify surface structure
Composition (alpha blending)
Texture Based Volume Rendering
3D Texture Based Volume Rendering
• Best known practical volume rendering method for
rectlinear grid datasets
• Realtime Rendering is possible
Interpolation of Samples
•
•
•
•
Volume stored as 3D texture
Viewport-aligned slices
Blended back-to-front
Trilinear interpolation by hardware
Classification
• Density values from texture map
• Classification via lookup table
• Takes place in texture mapping stage
Shading is possible
• Principle
– Precompute Gradient plus density in texture
– Shade first  intensity (keep density!)
– Classification via 2D pixel texture
Texture Mapping
+
2D image
2D polygon
Textured-mapped
polygon
Texture Mapping for Volume Rendering
Consider ray casting …
(top view)
z
x
y
Texture based volume rendering
Use pProxy geometry for
sampling
z
y
x
•
•
•
•
Render every xz slice in the volume as a texture-mapped polygon
The proxy polygon will sample the volume data
Per-fragment RGBA (color and opacity) as classification results
The polygons are blended from back to front
Texture based volume rendering
Changing Viewing Direction
What if we change the viewing position?
y
x
That is okay, we just
change the eye position
(or rotate the polygons
and re-render),
Until …
Solution
Use Image-space axis-aligned slicing plane:
the slicing planes are always parallel to the view plane
3D Texture Based Volume Rendering
Shading
• Use per-fragment shader
–
–
–
–
–
Store the pre-computed gradient into a RGBA texture
Light 1 direction as constant color 0
Light 1 color as primary color
Light 2 direction as constant color 1
Light 2 color as secondary color
CUDA Volume Rendering
• Utilize massively parallel computing resources
• Assign each CUDA thread deal with a single ray
• CUDA
– Suitable for computing lots of independent work
(e.g. processing pixels or voxels)