1. Tutorial 7 Real-Time Volume Graphics
Klaus Engel
Markus Hadwiger
Christof Rezk Salama

2. Real-Time Volume Graphics [01] Introduction and Theory

3. Appliations: Medicine
CT Human Head: Visible Human Project, US National Library of Medicine, Maryland, USA
CT Angiography: Dept. of Neuroradiology University of Erlangen, Germany

4. Applications: Geology
Deformed Plasticine Model, Applied Geology, University of Erlangen
Muschelkalk: Paläontologie, Virtual Reality Group, University of Erlangen

5. Applications: Archeology
Hellenic Statue of Isis 3rd century B.C. ARTIS, University of Erlangen-Nuremberg, Germany
Sotades Pygmaios Statue, 5th century B.C ARTIS, University of Erlangen-Nuremberg, Germany

6. Applications: Biology Material Science, Quality Control
Micro CT, Compound Material, Material Science Department, University of Erlangen
biological sample of the soil, CT, Virtual Reality Group, University if Erlangen

7. Applications
Computational Science and Engineering

8. Applications: Computer Science
Visualization of Pseudo Random Numbers
Entropy of Pseudo Random Numbers, Dan Kaminsky, Doxpara Research, USA,

9. Outline in real-time on commodity graphics hardware Data Set
3D Rendering
Classification
in real-time on commodity graphics hardware

10. Physical Model of Radiative Transfer
Increase
true emission
in-scattering
Decrease
true absorption
out-scattering

11. Absorption along the ray segment s0 - s
Ray Integration
How do we determine the radiant energy along the ray?
Physical model: emission and absorption, no scattering
viewing ray
Absorption along the ray segment s0 - s
Extinction τ Absorption к
Initial intensity at s0
Without absorption all
the initial radiant energy
would reach the point s.

12. Ray Integration How do we determine the radiant energy along the ray?
Physical model: emission and absorption, no scattering
viewing ray
Every point along the
viewing ray emits additional
radiant energy
One point along the
viewing ray emits additional
radiant energy.
Absorption along the distance s - s ~
Active emission at point s ~

13. Ray Casting Software Solution Numerical Integration Resampling
Image Plane
Eye
Data Set
Numerical Integration
Resampling
High Computational Load

14. Numerical Solution
Extinction:
Approximate Integral by Riemann sum:

15. Numerical Solution
Now we introduce opacity:

16. Numerical Solution
Now we introduce opacity:

17. Numerical Solution can be computed recursively
Radiant energy observed at position i
Radiant energy emitted at position i
Absorption at position i
Radiant energy observed at position i–1

18. Numerical Solution Early Ray Termination: Stop the calculation when
Back-to-front compositing
can be computed recursively
Front-to-back compositing

19. Summary Emission Absorption Model Numerical Solutions
true absorption
true emission
Back-to-front iteration
Front-to-back iteration