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Discovering Structural Regularity in 3D Geometry

Discovering Structural Regularity in 3D Geometry. Speaker: JinliangWu Date: 25 / 9 /2008. Authors. Mark Pauly ETH Zurich Niloy J. Mitra IIT Delhi Johannes Wallner TU Graz Helmut Pottmann TU Vienna Leonidas Guibas Stanford University. Regular Structures. Regular Structures.

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Discovering Structural Regularity in 3D Geometry

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  1. Discovering Structural Regularity in 3D Geometry Speaker: JinliangWu Date: 25 / 9 /2008

  2. Authors • Mark Pauly ETH Zurich • Niloy J. Mitra IIT Delhi • Johannes Wallner TU Graz • Helmut Pottmann TU Vienna • Leonidas Guibas Stanford University

  3. Regular Structures

  4. Regular Structures

  5. completion geometric edits Motivation compression geometry synthesis Text Motivation

  6. Compression

  7. Completion

  8. Geometry Synthesis

  9. Transform Analysis Input Model Transform Clusters Model Estimation Aggregation Regular Structures Transform Generators Structure Discovery spatial domain transform domain Structure Discovery

  10. A similarity transformation T Repetitive Structures

  11. Repetitive Structures 1-parameter patterns

  12. Repetitive Structures 2-parameter commutative patterns

  13. Repetitive Structures

  14. Repetitive Structures regular structure is a transformation group acting on is a collection of n patches of a given surface S

  15. Repetitive Structures In the simplest setting, is a 1-parameter group with generating similarity transformation T . The elements of can be represented as

  16. Input Model Transform Clusters Model Estimation Aggregation Regular Structures Transform Generators Structure Discovery Transform Analysis Structure Discovery

  17. Transformation Analysis Algorithm for analyzing transformations

  18. Transformations spatial domain transformation space pairwise transformations

  19. Transformations spatial domain transformation space pairwise transformations

  20. Model Estimation origin density plot of pair-wise transformations

  21. Model Estimation cluster centers

  22. Transformation Analysis Algorithm for analyzing transformations

  23. Transformation

  24. Model Estimation Is there a Pattern?

  25. Model Estimation Yes, there is!

  26. Model Estimation Yes, there is!

  27. Model Estimation Global, non-linear optimization – simultaneously detects outliers and grid structure

  28. grid location generating vectors Model Estimation • Grid fitting – input: cluster centers – unknowns: grid generators

  29. data confidence cluster center closest grid point grid confidence grid point closest cluster center Model Estimation • Fitting terms

  30. Model Estimation • Fitting terms • Data and grid confidence terms • objective function

  31. Model Estimation Global, non-linear optimization – simultaneously detects outliers and grid structure

  32. Input Model Transform Clusters Model Estimation Aggregation Regular Structures Transform Generators Structure Discovery Transform Analysis Structure Discovery

  33. Aggregation • Region-growing to extract repetitive elements • Simultaneous registration

  34. Simultaneous Registration

  35. Input Model Transform Clusters Model Estimation Regular Structures Transform Generators Structure Discovery Transform Analysis Structure Discovery Aggregation

  36. Results and Applications

  37. Robustness

  38. Geometry Synthesis

  39. Geometry Synthesis

  40. Scan Completion

  41. Conclusions • Algorithm is fully automatic • Requires no prior information on size, shape, or location of repetitive elements • Robust, efficient, independent of dimension general tool for scientific data analysis

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