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Surface Reconstruction

Surface Reconstruction. Some figures by Turk, Curless, Amenta, et al. Two Related Problems. Given a point cloud, construct a surface Given several aligned scans (range images), construct a surface. Surface Reconstruction from Point Clouds.

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Surface Reconstruction

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  1. Surface Reconstruction Some figures by Turk, Curless, Amenta, et al.

  2. Two Related Problems • Given a point cloud, construct a surface • Given several aligned scans (range images), construct a surface

  3. Surface Reconstruction from Point Clouds • Most techniques figure out how to connect up “nearby” points • Need sufficiently dense sampling, little noise • Delaunay triangulation: connect nearest points • Officially, a triangle is in the Delaunay triangulation iff its circumcircle does not contain any points

  4. The “Crust” Algorithm • Amenta et al., 1998 • Medial axis: set of points equidistant from 2 original points • In 2D:

  5. Medial Axes in 3D • May contain surfaces as well as edges and vertices

  6. Voronoi Diagrams • Partitioning of plane according to closest point (in a discrete point set) • A subset of Voronoi vertices is an approximation to medial axis

  7. Compute Voronoi diagram Compute Delaunay triangulation of original points + Voronoi vertices The “Crust” Algorithm

  8. Voronoi Cells in 3D • Some Voronoi vertices lie neither near the surface nor near the medial axis • Keep the “poles”

  9. Crust Results • 36K vertices • 23 minutes (1998)

  10. Crust Problems • Problems with sharp corners • Medial axis touches surface • Theoretically need infinitely high sampling • In practice, heuristics to choose poles • Topological problems

  11. The Ball Pivoting Algorithm • Bernardini et al., 1999 • Roll ball around surface, connect what it hits

  12. Alpha Shapes

  13. Problems With Reconstruction fromPoint Clouds

  14. Surface Reconstruction from Range Images • Often an easier problem than reconstruction from arbitrary point clouds • Implicit information about adjacency, connectivity • Roughly uniform spacing

  15. Surface Reconstruction From Range Images • First, construct surface from each range image • Then, merge resulting surfaces • Obtain average surface in overlapping regions • Control point density

  16. Range Image Tesselation • Given a range image, connect up the neighbors

  17. Range Image Tesselation • Caveat #1: can’t be too aggressive • Introduce distance threshold for tesselation

  18. Range Image Tesselation • Caveat #2: Which way to triangulate? • Possible heuristics: • Shorter diagonal • Dihedral angle closer to 180 • Maximize smallest angle in both triangles • Always the same way (best triangle strips)

  19. Scan Merging Using Zippering • Turk & Levoy, 1994 • Erode geometry in overlapping areas • Stitch scans together along seam • Re-introduce all data • Weighted average

  20. Zippering

  21. Point Weighting • Higher weights to points facing the camera • Favor higher sampling rates

  22. Point Weighting • Lower weights(tapering to 0)near boundaries • Smooth blendsbetween views

  23. Point Weighting

  24. Consensus Geometry

  25. Zippering Example

  26. Zippering Example

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