1. REAL-TIME VOLUME GRAPHICS Christof Rezk Salama Computer Graphics and Multimedia Group, University of Siegen, Germany Eurographics 2006 Real-Time Volume Graphics [06] Local Volume Illumination

2. REAL-TIME VOLUME GRAPHICS Christof Rezk Salama Computer Graphics and Multimedia Group, University of Siegen, Germany Eurographics 2006 Single scattering with attenuation. Light is attenuated along ist way through the volume (Volumetric shadows) Light is scattered once before it reaches the eye Multiple scattering Light is scattered multiple times before it reaches the eye (Global illumination) Single scattering, no attenuation. Light reaches every point unimpededly Light is scattered once before it reaches the eye Not physically plausible Volume Illumination Up until now: Light was emitted by the volume Now: Illumination from external light sources Types of Volume Illumination

3. REAL-TIME VOLUME GRAPHICS Christof Rezk Salama Computer Graphics and Multimedia Group, University of Siegen, Germany Eurographics 2006 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. REAL-TIME VOLUME GRAPHICS Christof Rezk Salama Computer Graphics and Multimedia Group, University of Siegen, Germany Eurographics 2006 l Diffuse Term (Lambertian reflection) Blinn/Phong Illumination n

5. REAL-TIME VOLUME GRAPHICS Christof Rezk Salama Computer Graphics and Multimedia Group, University of Siegen, Germany Eurographics 2006 l Phong Illumination n r v Specular Term (view-dependent)

6. REAL-TIME VOLUME GRAPHICS Christof Rezk Salama Computer Graphics and Multimedia Group, University of Siegen, Germany Eurographics 2006 l Blinn/Phong Illumination n h v Specular Term (view-dependent) r Phong Illumination

7. REAL-TIME VOLUME GRAPHICS Christof Rezk Salama Computer Graphics and Multimedia Group, University of Siegen, Germany Eurographics 2006 Blinn/Phong Illumination Ambient Term (constant illumination) lightens up the shadows, also decreases the contrast! Example images taken from Jeremy Birn: Digital Lighting & Rendering,New Riders Publishing, 2000 Consider using a fill light instead of ambient light!

8. REAL-TIME VOLUME GRAPHICS Christof Rezk Salama Computer Graphics and Multimedia Group, University of Siegen, Germany Eurographics 2006 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. REAL-TIME VOLUME GRAPHICS Christof Rezk Salama Computer Graphics and Multimedia Group, University of Siegen, Germany Eurographics 2006 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. REAL-TIME VOLUME GRAPHICS Christof Rezk Salama Computer Graphics and Multimedia Group, University of Siegen, Germany Eurographics 2006 Finite Differences Taylor expansion: Backward Difference: Forward Difference:

11. REAL-TIME VOLUME GRAPHICS Christof Rezk Salama Computer Graphics and Multimedia Group, University of Siegen, Germany Eurographics 2006 Finite Differences Central Difference: Gradient Approximation using Central Differences:

12. REAL-TIME VOLUME GRAPHICS Christof Rezk Salama Computer Graphics and Multimedia Group, University of Siegen, Germany Eurographics 2006 Example: Use an RGBA texture: Pre-computed Gradients Calculate the gradient for each voxel Store the normalized gradient in an additional texture. Example: Use an RGB texture:

13. REAL-TIME VOLUME GRAPHICS Christof Rezk Salama Computer Graphics and Multimedia Group, University of Siegen, Germany Eurographics 2006 13 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

14. REAL-TIME VOLUME GRAPHICS Christof Rezk Salama Computer Graphics and Multimedia Group, University of Siegen, Germany Eurographics 2006 14 Ray Traversal Schemes Depth Intensity Max Average Accumulate First

15. REAL-TIME VOLUME GRAPHICS Christof Rezk Salama Computer Graphics and Multimedia Group, University of Siegen, Germany Eurographics 2006 15 Ray Traversal - First Depth Intensity First First: extracts iso-surfaces (again!) done by Tuy&Tuy ’84

16. REAL-TIME VOLUME GRAPHICS Christof Rezk Salama Computer Graphics and Multimedia Group, University of Siegen, Germany Eurographics 2006 16 Ray Traversal - Average Depth Intensity Average Average: produces basically an X-ray picture

17. REAL-TIME VOLUME GRAPHICS Christof Rezk Salama Computer Graphics and Multimedia Group, University of Siegen, Germany Eurographics 2006 17 Ray Traversal - MIP Depth Intensity Max Max: Maximum Intensity Projection used for Magnetic Resonance Angiogram

18. REAL-TIME VOLUME GRAPHICS Christof Rezk Salama Computer Graphics and Multimedia Group, University of Siegen, Germany Eurographics 2006 18 Ray Traversal - Accumulate Depth Intensity Accumulate Accumulate opacity while compositing colors: make transparent layers visible! Levoy ‘88

19. REAL-TIME VOLUME GRAPHICS Christof Rezk Salama Computer Graphics and Multimedia Group, University of Siegen, Germany Eurographics 2006 19 Raycasting color opacity 1.0 volumetric compositing object (color, opacity)

20. REAL-TIME VOLUME GRAPHICS Christof Rezk Salama Computer Graphics and Multimedia Group, University of Siegen, Germany Eurographics 2006 20 Raycasting color opacity Interpolation kernel 1.0 object (color, opacity) volumetric compositing

21. REAL-TIME VOLUME GRAPHICS Christof Rezk Salama Computer Graphics and Multimedia Group, University of Siegen, Germany Eurographics 2006 21 Raycasting color c = c s  s (1 -  ) + c opacity  =  s (1 -  ) +  1.0 object (color, opacity) volumetric compositing Interpolation kernel

22. REAL-TIME VOLUME GRAPHICS Christof Rezk Salama Computer Graphics and Multimedia Group, University of Siegen, Germany Eurographics 2006 22 Raycasting color opacity 1.0 object (color, opacity) volumetric compositing

23. REAL-TIME VOLUME GRAPHICS Christof Rezk Salama Computer Graphics and Multimedia Group, University of Siegen, Germany Eurographics 2006 23 Raycasting color opacity 1.0 object (color, opacity) volumetric compositing

24. REAL-TIME VOLUME GRAPHICS Christof Rezk Salama Computer Graphics and Multimedia Group, University of Siegen, Germany Eurographics 2006 24 Raycasting color opacity 1.0 object (color, opacity) volumetric compositing

25. REAL-TIME VOLUME GRAPHICS Christof Rezk Salama Computer Graphics and Multimedia Group, University of Siegen, Germany Eurographics 2006 25 Raycasting color opacity 1.0 object (color, opacity) volumetric compositing

26. REAL-TIME VOLUME GRAPHICS Christof Rezk Salama Computer Graphics and Multimedia Group, University of Siegen, Germany Eurographics 2006 26 Raycasting color opacity object (color, opacity) volumetric compositing

27. REAL-TIME VOLUME GRAPHICS Christof Rezk Salama Computer Graphics and Multimedia Group, University of Siegen, Germany Eurographics 2006 Brute-Force Algorithm

28. REAL-TIME VOLUME GRAPHICS Christof Rezk Salama Computer Graphics and Multimedia Group, University of Siegen, Germany Eurographics 2006 28 Volume Rendering Pipeline Acquired values Data preparation Prepared values classificationshading Voxel colors Ray-tracing / resampling Sample colors compositing Voxel opacities Sample opacities Image Pixels