Interactive GPU-based Segmentation Of Large Volume Data With Level Sets

1. Interactive GPU-based Segmentation Of Large Volume Data With Level Sets Veronika Solteszova (presenting Oliver Klar’s master thesis) VRVis Research Center www.vrvis.at

2. Overview • Introduction • Level set method • Math and theoretical background • GPU Data structure for large volumes • Solution on GPU • Rendering and user interaction • Results and future work Interactive GPU-based Segmentation with Level Sets

3. Introduction • Level set main idea • Deformable implicit surface • Evolve simple surface intotarget object shape • Short demo Interactive GPU-based Segmentation with Level Sets

4. Introduction • Problem statement & motivation • Segmentation of large volumetric data is expensive • GPU allows direct rendering • Overcome GPU memory restrictions Interactive GPU-based Segmentation with Level Sets

5. Overview • Introduction • Level set Method • Math and theoretical background • GPU Data structure for large volumes • Solution on GPU • Rendering and user interaction • Results and future work Interactive GPU-based Segmentation with Level Sets

6. LS Method: Math • A level set definition • Curve represented as a set of roots of an implicit function • Contour lines = level sets • C = 0.2 ↔ 0.2 level set • Contours, iso-surfaces also level sets Φ > 0.2 Φ > 0.2 Φ < 0.2 Φ = 0.2 Interactive GPU-based Segmentation with Level Sets

7. LS Method: Math (cont.) • Advantages of such curve representation • No problems with topology changes • Gradient & curvature computation easy • Evolution described by partial differential equation (PDE) • In this approach • Φ: f(x, y, z, t) = 0.5 • Embedding 2D contour (surface) into 3D space, 4th dim = time • Discretization: values of Φ in a 3D texture • Evolution • 3D texture changes → level set moves Interactive GPU-based Segmentation with Level Sets

8. LS Method (cont.) • Convection partial differential equation (PDE), solved for each point of the grid (discrete volume data) • . • ∆t → time step, • F → gradient magnitude • F → speed function, determines deformation Interactive GPU-based Segmentation with Level Sets

9. LS Method (cont.) • Speed function F: • Density (D) and mean curvature (κ) influence • Only curvature (κ) driven • Only density factor (D) driven t α 0.3 1.0 0.0 Interactive GPU-based Segmentation with Level Sets

10. LS Method (cont.) • Density factor: • T: target density • I : volume density Interactive GPU-based Segmentation with Level Sets

11. Overview • Introduction • Level set Method • Math and theoretical background • GPU Data structure for large volumes • Solution on GPU • Rendering and user interaction • Results and future work Interactive GPU-based Segmentation with Level Sets

12. GPU Data Structure • Level set calculation only where necessary • Avoid GPU memory restrictions • Volume subdivision into bricks • Neighbors in cache≠ Neighbors in virtual volume • Bricks packed into cache texture Interactive GPU-based Segmentation with Level Sets

13. Cache Layout (cont.) • Volume subdivision into bricks (34x34x34) • Brick 32x32x32 + 1vox border (filtering) Interactive GPU-based Segmentation with Level Sets

14. Overview • Introduction • Level set Method • Math and theoretical background • GPU Data structure for large volumes • Solution on GPU • Rendering and user interaction • Results and future work Interactive GPU-based Segmentation with Level Sets

15. LS Solver • 1. Setup • Signed distance field • Values clamped to: • 0.0 (exterior) • 1.0 (interior) • Narrow band within [0.0, 1.0] Interactive GPU-based Segmentation with Level Sets

16. Narrow Band Culling • Interior: Min = Max = 1.0 • Exterior: Min = Max = 0.0 0.5 LS Narrow band width Interactive GPU-based Segmentation with Level Sets

17. LS Solver (cont.) • 2. Calculation on HW • PDE solved in fragment programs • Discretization (with time step ∆t) Interactive GPU-based Segmentation with Level Sets

18. LS Solver (cont.) • 3. Sparse volume update • GPU – CPU memory request • For each brick: min/max determination • GPU Neighbor activation & encode • CPU – GPU memory allocation • Decode & CPU neighbor activation Interactive GPU-based Segmentation with Level Sets

19. Neighbor Activation • The level set front may leak out • Activate the bricks touched by the front Interactive GPU-based Segmentation with Level Sets

20. Neighbor Activation • For each brick • 6 faces ↔ 6 bits state (active/inactive) • State decoded on CPU • Activation on full 26-neighborhood • Flagged face → activate brick • 2 adjacent bricks → edge brick • 3 adjacent bricks → corner brick Interactive GPU-based Segmentation with Level Sets

21. Overview • Introduction • Level set Method • Math and theoretical background • Data structure • Solution on GPU • Rendering and user interaction • Results and future work Interactive GPU-based Segmentation with Level Sets

22. Rendering DVR ISO • Rendering 2 different volumes simultaneously • Combination of DVR and ISO rendering DVR Interactive GPU-based Segmentation with Level Sets

23. Overview • Introduction • Level set Method • Math and theoretical background • Data structure • Solution on GPU • Rendering and user interaction • Results and future work Interactive GPU-based Segmentation with Level Sets

24. Results’ Gallery Interactive GPU-based Segmentation with Level Sets

25. Performance • Results of presented level set solver: Tests performed for 1 iteration on GeForce 8800 GTX Interactive GPU-based Segmentation with Level Sets

26. Demo • Short demo: brain segmentation process Interactive GPU-based Segmentation with Level Sets

27. Future work • Other speed functions • Further optimization of LS computation: • On neighbor look-ups • Determining the active region in the cache cross section Interactive GPU-based Segmentation with Level Sets

28. Agfa, AKH, Kplus Thank You for Your attention! Acknowledgements: Oliver Klar, Markus Hadwiger, Katja Bühler www.vrvis.at

29. /*todo*/ performance • How many iterations for brain2 • How much time does it take • Why is seg. with LS better than tresholding? (proves, illustrations) • Why is the cache by hydrogen 2x bigger as a hydrogen data set? • Segmentation mask export possible with this framework?? Interactive GPU-based Segmentation with Level Sets

30. Brick-to-tile Mapping • Address translation requires mapping • Case 1: a tile has no mapping • Case 2: a tile maps to a brick • Case 3: a brick has no mapping Case 1 Brick Tile Brick cache Case 2 Virtual volume Case 3 Interactive GPU-based Segmentation with Level Sets

31. Rendering • Hit point refinement Interactive GPU-based Segmentation with Level Sets