Feature Preserving Sketching of Volume Data

1. Feature Preserving Sketchingof Volume Data Jens Kerber, Michael Wand, Martin Bokeloh, Jens Krüger, Hans-Peter Seidel Saarland University and MPI Informatik

2. Goals • Task • Reduce visual complexity • Extract crease lines • Faithfully reproduce/illustrate geometry • Robust to noise • Preserving connectivity/topology • Point based features in volumes • Too many • Not expressive enough • Abstraction to line features necessary Jens Kerber, Saarland University and MPI Informatik

3. Overview • Key ingredient: • Iteratively reweighted least squares approximation Jens Kerber, Saarland University and MPI Informatik

4. Local Fitting 2D Example • Approximate local neighborhood • Fit quadratic curve • Weight influence of pixels bilaterally • Refine iteratively Jens Kerber, Saarland University and MPI Informatik

5. Local Fitting 3D Example • Approximate local neighborhood • Fit quadratic function 3D -> 3D • Iso surface • Weight influence of voxels bilaterally • Refine iteratively Behavior at an edge Behavior at a corner Jens Kerber, Saarland University and MPI Informatik

6. Mathematical Description • Resulting function • best describes local conditions • least square sense Normal Hessian Matrix Jens Kerber, Saarland University and MPI Informatik

7. Descriptor • For all voxels • Orthonormal basis (vectors) • normal, first and second principal curvature direction • Local coordinates (values) • gradient and bendings G Kmin n kmin Kmax kmax Jens Kerber, Saarland University and MPI Informatik

8. Areas of Interest • Selecting voxels by thresholding • High gradient • Iso-surface transitions • High tangent • Edges and corners • Colorcoded by kmin Jens Kerber, Saarland University and MPI Informatik

9. Projection • Shrink the spatial extension • Similar to Mean-Shift-Filtering • Continuous shift • Gradient decent • Restricted to move in one plane • slice perpendicular to the tangential direction • Preserves connectivity • Bilateral weights for all neighbors • depending of deviations in orientation Jens Kerber, Saarland University and MPI Informatik

10. Projection Jens Kerber, Saarland University and MPI Informatik

11. Projection Jens Kerber, Saarland University and MPI Informatik

12. Projection Jens Kerber, Saarland University and MPI Informatik

13. Projection Jens Kerber, Saarland University and MPI Informatik

14. Projection Jens Kerber, Saarland University and MPI Informatik

15. Projection Jens Kerber, Saarland University and MPI Informatik

16. Projection Jens Kerber, Saarland University and MPI Informatik

17. Projection Jens Kerber, Saarland University and MPI Informatik

18. Projection Jens Kerber, Saarland University and MPI Informatik

19. Without restriction Jens Kerber, Saarland University and MPI Informatik

20. Projection Jens Kerber, Saarland University and MPI Informatik

21. Clustering • Region growing • collect all neighbors with similar orientation Jens Kerber, Saarland University and MPI Informatik

22. Visualization • Inflate for rendering • Thin tubes around each line • Implicit distance function • Marching cubes based meshing • Ambient occlusion • Environment map • Impression of depth order and overlaps • Highlight intersections and corners • Locations where clusters of differing orientations meet Jens Kerber, Saarland University and MPI Informatik

23. Visualization Jens Kerber, Saarland University and MPI Informatik

24. WithandWithoutRestriction Jens Kerber, Saarland University and MPI Informatik

25. Video Jens Kerber, Saarland University and MPI Informatik

26. Visualization Jens Kerber, Saarland University and MPI Informatik

27. Video Jens Kerber, Saarland University and MPI Informatik

28. Outlook: Symmetries Jens Kerber, Saarland University and MPI Informatik

29. Thank you for your attention! • Questions? Jens Kerber, Saarland University and MPI Informatik