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WSCG2012 Plzen , Czech Rep., 26.6. 2012

Reconstructing Power Cables From LIDAR Data Using Eigenvector Streamlines of the Point Distribution Tensor Field Marcel Ritter (speaker), Werner Benger. m arcel.ritter@uibk.ac.at. WSCG2012 Plzen , Czech Rep., 26.6. 2012. ASTRO@UIBK. Center for Computation and Technology . Overview.

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WSCG2012 Plzen , Czech Rep., 26.6. 2012

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  1. Reconstructing Power Cables FromLIDAR DataUsing Eigenvector Streamlines of thePoint Distribution Tensor FieldMarcel Ritter (speaker), Werner Benger marcel.ritter@uibk.ac.at WSCG2012 Plzen, Czech Rep., 26.6. 2012 ASTRO@UIBK Center for Computation and Technology

  2. Overview • Motivation • Methodology • The Point Distribution Tensor • Weighting Functions • Eigenvector Streamlines • Implementation and Verification • Comparison Meshfree/Uniform Grid • Test Cases • Application • Conclusion and Future Work

  3. Motivation • Arose from an airborne light detection and ranging (LIDAR) application • Earth surface scanned by laser pulses  point cloud

  4. Motivation • LIDAR point cloud:

  5. Motivation

  6. Motivation • Based on previous work • Direct visualization of the point distribution tensor • Streamline integration • Inspired by diffusion tensor fiber tracking Point Distribution Tensor Field Streamlines [RBBPML12]

  7. Methodology • Computing the point distribution tensor

  8. Methodology • Tensor analysis: • Shape factors by [Westin97] • S(Pi) is a 3x3 symmetric tensor and positive definite • 3 Eigen-Values: • Shape factors: [BBHKS06]

  9. Methodology • Tensor visualization: • Ellipsoids representing the shape factors • Tensor Splats [BengerHege04] -> barycentric [BBHKS06]

  10. Methodology • Tensor Splats of a rectangular point distribution Points Tensor Splats

  11. Distribution tensor of airborne LIDAR data Methodology

  12. Methodology • Weighting functions: • 7 different weighting functions were implemented

  13. Methodology • Weighting functions:

  14. Methodology • Influence of weighting on the resulting tensor 2 1 • Distribution tensor and its linearity of a rectangular point distribution

  15. Methodology • Influence of weighting on the resulting tensor 4 3 • Distribution tensor and its linearity of a rectangular point distribution

  16. Methodology • Influence of weighting on the resulting tensor 6 5 • Distribution tensor and its linearity of a rectangular point distribution

  17. Methodology • Influence of weighting on the resulting tensor 7 • Distribution tensor and its linearity of a rectangularpoint distribution

  18. Methodology • Streamlines • Common tool for flow visualization • Curve q on Manifold M with s the curve parameter • Vector field v with Tp(M) an element of the tangential space at point P on M • Streamline as curve tangential to the vector field

  19. Methodology • Eigen-Streamlines • Must be able to follow against the vector field Tensor Streamline Valid major eigenvectors Eigen-Streamline

  20. Implementation and Verification

  21. Implementation and Verification

  22. Implementation and Verification • Verification of Meshfree Approach • Eigenvector field of MRI brain scan, [BBHKS06] • Converted uniform grid data to meshfree grid • Compare streamlines computed on both grids

  23. Implementation and Verification • Verification of Meshfree Approach • Trilinear interpolation on uniform grid • ω2 slinear interpolation on meshless grid • 81% of 144 short streamlines coincide well Meshfree Uniform Grid

  24. Implementation and Verification • Circle Integration • Tested numerical integration schemes DOP853 (Runge-Rutta order 8) Explicit Euler • Explicit Euler

  25. Implementation and Verification • Rectangle Integration • Tested different weighting functions for vector interpolation • Horizontal distance of integration start to endpoint as error measure

  26. Implementation and Verification • Error of rectangle reconstruction integration

  27. Application • LIDAR cable reconstruction

  28. Application • LIDAR cable reconstruction

  29. Application • LIDAR cable reconstruction • Manual seeding position and direction • Tested 41 different combinations of different weighting functions and neighborhood radii • Tensor computation (r = 0.5, 1.0, 2.0 [m]) • Vector interpolation (r = 0.25, 0.5, 1.0, 2.0, 3.0 [m]) • Tensor computation with 3 ,r=2.0, and interpolation with 7 , r=3.0, worked best in this scenario • Reconstructed 280m of cable with an error of 80cm

  30. Application • LIDAR cable reconstruction Tensor 1,r=2, DOP853 Eigen-streamlines 3,r=1 Tensor 3,r=2, DOP853 Eigen-streamlines 7,r=1

  31. Conclusion

  32. Future Work

  33. References

  34. Thank you Marcel Ritter 1)Werner Benger2,3) 1) Institute for Basic Sciences in Civil Engineering, University of Innsbruck, Austria 2) Center for Computation & Technology, Louisiana State University, Baton Rouge, USA 3) Institute for Astro- and Particle Physics, University of Innsbruck, Austria

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