1. Real-Time Volume Graphics [06] Local Volume Illumination

2. Volume Illumination Types of Volume Illumination
Up until now: Light was emitted by the volume
Now: Illumination from external light sources
Types of Volume Illumination
Single scattering, no attenuation.
Light reaches every point unimpededly
Light is scattered once before it reaches the eye
Not physically plausible
Multiple scattering
Light is scattered multiple times before it reaches the eye (Global illumination)
Single scattering with attenuation.
Light is attenuated along ist way through the volume (Volumetric shadows)
Light is scattered once before it reaches the eye

3. Single Scattering Local illumination, similar to surface lighting
Lambertian reflection (light is reflected equally in all directions)
Perfect mirror reflection (light is reflected in exactly one direction)
Specular reflection (light is reflected scattered around the direction of perfect reflection)

4. Blinn/Phong Illumination
Diffuse Term (Lambertian reflection) n l

5. Phong Illumination
Specular Term (view-dependent) n r l v

6. Blinn/Phong Illumination
Specular Term (view-dependent) n h r l v

7. Blinn/Phong Illumination
Ambient Term (constant illumination) lightens up the shadows, also decreases the contrast!
Consider using a fill light instead of ambient light!
Example images taken from Jeremy Birn: Digital Lighting & Rendering,New Riders Publishing, 2000

8. Local Illumination Surface lighting: Light is reflected at surfaces
Volume lighting: Light is scattered at isosurfaces
Isosurfaces
Isosurface extraction not required!
We only need the normal vector
Normal vector of isosurface is equal to (normalized) gradient vector

9. Gradient Estimation
The gradient vector is the first-order derivative of the scalar field
We can estimate the gradient vector using finite differencing schemes
partial derivative in x-direction
partial derivative in y-direction
partial derivative in z-direction

10. Finite Differences Taylor expansion: Forward Difference:
Backward Difference:

11. Finite Differences Central Difference:
Gradient Approximation using Central Differences:

12. Ray Traversal Schemes
Intensity
Max
Average
Accumulate
First
Depth

13. Ray Traversal - First Intensity First Depth
First: extracts iso-surfaces (again!) done by Tuy&Tuy ’84

14. Ray Traversal - Average
Intensity
Average
Depth
Average: produces basically an X-ray picture

15. Ray Traversal - MIP Intensity Max Depth
Max: Maximum Intensity Projection used for Magnetic Resonance Angiogram

16. Ray Traversal - Accumulate
Intensity
Accumulate
Depth
Accumulate opacity while compositing colors: make transparent layers visible! Levoy ‘88

17. 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
Can use other ray-traversal schemes as well c1 c2 c3

18. Raycasting volumetric compositing color opacity
1.0
object (color, opacity)

19. Raycasting Interpolation kernel volumetric compositing color opacity
1.0
object (color, opacity)

20. Raycasting Interpolation kernel volumetric compositing
color c = c s s(1 - ) + c
opacity  =  s (1 - ) + 
1.0
object (color, opacity)

21. Raycasting volumetric compositing color opacity
1.0
object (color, opacity)

22. Raycasting volumetric compositing color opacity
1.0
object (color, opacity)

23. Raycasting volumetric compositing color opacity
1.0
object (color, opacity)

24. Raycasting volumetric compositing color opacity
1.0
object (color, opacity)

25. Raycasting volumetric compositing color opacity
object (color, opacity)

26. Brute-Force Algorithm
Basic Routines Used:
First: accept a ray index and returns the object-space coordinates of the points where the ray enters the data;
Last: accept a ray index and returns the object-space coordinates of the points where the ray leaves the data;
Object: convert to object-space coordinates from image-space coordinates;
Image: convert to image-space coordinates from object-space coordinates; and
Sample: accepts a 3D array of colors or opacities and the object-space coordinates of a point, and returns an approximation to the color or opacity at that point by trilinearly interpolating from the eight surrounding voxels.

27. Brute-Force Algorithm

28. Volume Rendering Pipeline
Acquired values
Data preparation
Prepared values
shading
classification
Voxel colors
Voxel opacities
Ray-tracing / resampling
Ray-tracing / resampling
Sample colors
Sample opacities
compositing
Image Pixels

29. FIN DU COURS

30. Pre-computed Gradients
Calculate the gradient for each voxel
Store the normalized gradient in an additional texture : values between -1 and +1. Then add 1 and divide by 2 to get values in [0,1]
Example: Use an RGB texture:
Example: Use an RGBA texture: