1. Interactive Point-based Isosurface Exploration and High-quality Rendering Haitao Zhang Arie Kaufman Stony Brook University V I SV I S 2 0 0 62 0 0 6

2. Isosurface Exploration Isosurface extraction Isosurface rendering Interactive rate Changing view Change isovalue High quality rendering

3. Existing Methods Marching Cubes [Lorensen & Cline 87] Huge number of triangles within 1-pixel size Point-based methods Projection-based method [Co et al. 03,04] Accurate point position with expensive projection operator Active cell center [Rymon-Lipinski et al. 04] Fast but inaccurate point position Dividing Cubes [Cline et al. 88] High-quality but very expensive: O(n 3 )

4. Our Point-based Methods Active edge instead of active cell Easier to position points on the isosurface Incorporate together isosurface extraction & rendering No overhead when changing isovalue Edge splatting Efficient with accurate point position Edge kernel method View-dependent subdivision: O(n 2 )

5. Edge Splatting Send active edge info to GPU Use span-triangle for active edge query [Rymon-Lipinski et al. 04] Generate point along active edge Intersection between active edge and isosurface Surface splatting for rendering Efficient rendering

6. Edge Data Structure Span-triangle data structure for active edge query Sort by min and max value (min<max) Linear storage of edge info... Isovalue GPU Edge Info Array Base Array & Span Array

7. Point Generation Edge information Position : endpoint with min value Orientation : 6 possible directions Normal : gradient at edge center Values : min & max value Edge-Isosurface Intersection Computation:

8. Use center of active cell 26,044 active cell Edge splatting 26,042 active edge

9. Use center of active cell 368,296 active cell Edge splatting 370,122 active edge

10. Artifacts in Close View Fixed number of point (active edge) for a given isovale.

11. Edge Kernel Method Subdividing active cell: sub-cell projection < 1 pixel

12. Edge Kernel Method Subdividing active cell: sub-cell projection < 1 pixel

13. Edge Kernel Method Subdividing active cell: sub-cell projection < 1 pixel

14. Edge Kernel Method Subdividing into k 3 sub-cells At most one intersection for k sub-edges on same line along X, Y or Z direction k sub-edges 1 edge k 3 edges 3k 2 edges

15. Edge Kernel Edge kernel E(k) : 3k 2 edges c: orientation (X-, Y-, or Z-oriented) (s,t): local coordinate of edge endpoint Edge: Intersection:

16. Edge Kernel Encoding & Rendering E(k): 3k 2 edges E 1 E 2 E 3 E 4 E 5 … Store one kernel with largest possible size in VBO : E(1000) with 6MB data Rendering CPU: select kernel size k for each active cell GPU: render first 3k 2 points of the stored edge kernel with 1-pixel size

17. Edge splatting Marching Cubes Edge kernel Inside an Active Cell

18. Two Neighboring Active Cells Marching Cubes Edge kernel

19. Smooth Shading Per-pixel shading [Hadwiger et al. 05] Render point position to texture Shading from volume gradient map

20. Results 3.59GHz PC with NVIDIA Quadro FX 4500 card Volume Data Size Isovalue Range # Cell # Edge Creation Time (s) CT Head 256x256x256 (12-bit) 200-4095 5,444,366 14,831,403 6.4 Foot 128x128x128(8-bit) 0-255 658,399 1,069,804 0.4 Head MRT Angiography 416x512x112 (10-bit) 20-1023 2,063,817 2,954,384 3.5

21. Rendering of Edge Splatting Isovalue=840 (19.1 fps) 388,754 active edges 385,470 active cells Isovalue=1405 (15.2 fps) 426,749 active edges 422,244 active cells

22. Rendering of Foot (isovalue=36) Edge Splatting 19.1 fps Edge Kernel 5.2 fps

23. Rendering of Foot (isovalue=70) Edge Splatting 96 fps Edge Kernel 3.1 fps

24. Head MRT Angiography Edge Splatting 47.5 fps Edge Kernel 0.8 fps

25. Head MRT Angiography Edge Splatting 123 fpsEdge Kernel 3.1 fps

26. Head MRT Angiography Edge Splatting 86.5 fpsEdge Kernel 4.2 fps

27. Conclusion Interactive isosurface exploration system with high quality rendering: Edge splatting Accurate point position Integrating point generation in rendering Edge kernel method High quality rendering under close view 3D subdivision with complexity O(n 2 )

28. Future Work Very large volume data Design hierarchical data structure Improve edge kernel method speed GPU implementation using Geometry Shader Deal with volume with anisotropic grid

29. Thank you!