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Curve fitting to point clouds

Curve fitting to point clouds. Reporter: Lincong Fang Oct 18, 2006. Curve fitting. The data points are ordered. Curve fitting to point clouds. The data points are unorganized. Applications. Some applications: Reverse engineering Curve design Surface reconstruction Etc.

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Curve fitting to point clouds

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  1. Curve fitting to point clouds Reporter: Lincong Fang Oct 18, 2006

  2. Curve fitting • The data points are ordered.

  3. Curve fitting to point clouds • The data points are unorganized.

  4. Applications • Some applications: • Reverse engineering • Curve design • Surface reconstruction • Etc.

  5. Approaches overview • Preprocess the point clouds • Thin the point clouds (Levin98, Lee00) • Point clusters (Lin 04) • Map into a digital image (Goshtasby00) • Mathematical model • Parameteric curves • Implicit curves • Other methods

  6. Curve Reconstruction from unorganized points In-Kwon Lee CAGD 2000

  7. Least squares

  8. Moving Least Squares

  9. Moving Least Squares

  10. Moving Least Squares

  11. Moving Least Squares

  12. The choice of H

  13. Improved Moving Least Squares Delaunay triangulation Euclidean minimum spanning tree (EMSP)

  14. Correlation

  15. Correlation

  16. Refining

  17. Compare with and without EMST

  18. Ordering points

  19. Example

  20. Approaches overview • Preprocess the point clouds • Thin the point clouds (Levin98, Lee00) • Point clusters (Lin 04) • Map into a digital image (Goshtasby00) • Mathematical model • Parameteric curves • Implicit curves • Other methods

  21. Curve reconstruction based on interval B-spline curve Hongwei Lin, Wei Chen, Guojin Wang The Visual Computer,21(6), 418-427,2005

  22. Overview

  23. Shape-based joining scheme

  24. Sequence Joining Method

  25. Boundary sequence

  26. Example

  27. Example

  28. Approaches overview • Preprocess the point clouds • Thin the point clouds (Levin98, Lee00) • Point clusters (Lin 04) • Map into a digital image (Goshtasby00) • Mathematical model • Parameteric curves • Implicit curves • Other methods

  29. Grouping and parameterizing irregularly spaced points for curve fitting Ardeshir Goshtasby ACM Transactions on Graphics, 19:185--203, 2000

  30. Minor and major ridges

  31. Map into a digital image

  32. Minor and major ridges

  33. Example

  34. Example

  35. Approaches overview • Preprocess the point clouds • Thin the point clouds (Levin98, Lee00) • Point clusters (Lin 04) • Map into a digital image (Goshtasby00) • Mathematical model • Parameteric curves • Implicit curves • Other methods

  36. Multidimensional curve fitting to unorganized data points by nonlinear minimization Lian Fang, David C Gossard CAD 95

  37. Physical analogy

  38. Error term

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