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Reconstruction of Power Cables from LIDAR Data Using Eigenvector Streamlines

This presentation explores a novel methodology for reconstructing power cables from LIDAR data utilizing eigenvector streamlines of the point distribution tensor field. We employ various weighting functions and integrate streamlines to visualize and analyze the tensor field derived from LIDAR point clouds. Results from the implementation demonstrate effective reconstruction of cable lengths while minimizing errors. The methodology, based on tensor analysis and streamline integration, showcases potential applications in civil engineering and resource management.

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Reconstruction of Power Cables from LIDAR Data Using Eigenvector Streamlines

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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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