Build Your Own 3D Scanner: The Mathematics of 3D Triangulation

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Build Your Own 3D Scanner:
The Mathematics of 3D Triangulation

http://mesh.brown.edu/byo3d/

SIGGRAPH 2009 Courses
Douglas Lanman and Gabriel Taubin

This course provides a beginner with the necessary mathematics, software, and practical details to leverage projector-camera systems in their own 3D scanning projects. An example-driven approach is used throughout; each new concept is illustrated using a practical scanner implemented with off-the-shelf parts. The course concludes by detailing how these new approaches are used in rapid prototyping, entertainment, cultural heritage, and web-based applications.

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  • Build Your Own 3D Scanner 2/18/2009 These sections will be completed if the course is accepted. Preliminary versions of the source materials for these sections can be found on the websites for the semester-long courses in 3D Photography previously taught by the submission authors at Brown University: 3D Photography and Geometry Processing (ENGN 2911-I) http://mesh.brown.edu/3DPGP-2007/ http://mesh.brown.edu/3DPGP-2009/ For the submission round we have included a preview of the notes only for the second session.
  • Build Your Own 3D Scanner 2/18/2009 These sections will be completed if the course is accepted. Preliminary versions of the source materials for these sections can be found on the websites for the semester-long courses in 3D Photography previously taught by the submission authors at Brown University: 3D Photography and Geometry Processing (ENGN 2911-I) http://mesh.brown.edu/3DPGP-2007/ http://mesh.brown.edu/3DPGP-2009/ For the submission round we have included a preview of the notes only for the second session.
  • Build Your Own 3D Scanner 2/18/2009 These sections will be completed if the course is accepted. Preliminary versions of the source materials for these sections can be found on the websites for the semester-long courses in 3D Photography previously taught by the submission authors at Brown University: 3D Photography and Geometry Processing (ENGN 2911-I) http://mesh.brown.edu/3DPGP-2007/ http://mesh.brown.edu/3DPGP-2009/ For the submission round we have included a preview of the notes only for the second session.
  • Build Your Own 3D Scanner 2/18/2009 These sections will be completed if the course is accepted. Preliminary versions of the source materials for these sections can be found on the websites for the semester-long courses in 3D Photography previously taught by the submission authors at Brown University: 3D Photography and Geometry Processing (ENGN 2911-I) http://mesh.brown.edu/3DPGP-2007/ http://mesh.brown.edu/3DPGP-2009/ For the submission round we have included a preview of the notes only for the second session.
  • Build Your Own 3D Scanner 2/18/2009 These sections will be completed if the course is accepted. Preliminary versions of the source materials for these sections can be found on the websites for the semester-long courses in 3D Photography previously taught by the submission authors at Brown University: 3D Photography and Geometry Processing (ENGN 2911-I) http://mesh.brown.edu/3DPGP-2007/ http://mesh.brown.edu/3DPGP-2009/ For the submission round we have included a preview of the notes only for the second session.
  • Build Your Own 3D Scanner 2/18/2009 These sections will be completed if the course is accepted. Preliminary versions of the source materials for these sections can be found on the websites for the semester-long courses in 3D Photography previously taught by the submission authors at Brown University: 3D Photography and Geometry Processing (ENGN 2911-I) http://mesh.brown.edu/3DPGP-2007/ http://mesh.brown.edu/3DPGP-2009/ For the submission round we have included a preview of the notes only for the second session.
  • Build Your Own 3D Scanner 2/18/2009 These sections will be completed if the course is accepted. Preliminary versions of the source materials for these sections can be found on the websites for the semester-long courses in 3D Photography previously taught by the submission authors at Brown University: 3D Photography and Geometry Processing (ENGN 2911-I) http://mesh.brown.edu/3DPGP-2007/ http://mesh.brown.edu/3DPGP-2009/ For the submission round we have included a preview of the notes only for the second session.
  • Build Your Own 3D Scanner 2/18/2009 These sections will be completed if the course is accepted. Preliminary versions of the source materials for these sections can be found on the websites for the semester-long courses in 3D Photography previously taught by the submission authors at Brown University: 3D Photography and Geometry Processing (ENGN 2911-I) http://mesh.brown.edu/3DPGP-2007/ http://mesh.brown.edu/3DPGP-2009/ For the submission round we have included a preview of the notes only for the second session.
  • Build Your Own 3D Scanner 2/18/2009 These sections will be completed if the course is accepted. Preliminary versions of the source materials for these sections can be found on the websites for the semester-long courses in 3D Photography previously taught by the submission authors at Brown University: 3D Photography and Geometry Processing (ENGN 2911-I) http://mesh.brown.edu/3DPGP-2007/ http://mesh.brown.edu/3DPGP-2009/ For the submission round we have included a preview of the notes only for the second session.
  • Build Your Own 3D Scanner 2/18/2009 These sections will be completed if the course is accepted. Preliminary versions of the source materials for these sections can be found on the websites for the semester-long courses in 3D Photography previously taught by the submission authors at Brown University: 3D Photography and Geometry Processing (ENGN 2911-I) http://mesh.brown.edu/3DPGP-2007/ http://mesh.brown.edu/3DPGP-2009/ For the submission round we have included a preview of the notes only for the second session.
  • Build Your Own 3D Scanner 2/18/2009 These sections will be completed if the course is accepted. Preliminary versions of the source materials for these sections can be found on the websites for the semester-long courses in 3D Photography previously taught by the submission authors at Brown University: 3D Photography and Geometry Processing (ENGN 2911-I) http://mesh.brown.edu/3DPGP-2007/ http://mesh.brown.edu/3DPGP-2009/ For the submission round we have included a preview of the notes only for the second session.
  • Build Your Own 3D Scanner 2/18/2009
  • Build Your Own 3D Scanner 2/18/2009 These sections will be completed if the course is accepted. Preliminary versions of the source materials for these sections can be found on the websites for the semester-long courses in 3D Photography previously taught by the submission authors at Brown University: 3D Photography and Geometry Processing (ENGN 2911-I) http://mesh.brown.edu/3DPGP-2007/ http://mesh.brown.edu/3DPGP-2009/ For the submission round we have included a preview of the notes only for the second session.
  • These sections will be completed if the course is accepted. Preliminary versions of the source materials for these sections can be found on the websites for the semester-long courses in 3D Photography previously taught by the submission authors at Brown University: 3D Photography and Geometry Processing (ENGN 2911-I) http://mesh.brown.edu/3DPGP-2007/ http://mesh.brown.edu/3DPGP-2009/ For the submission round we have included a preview of the notes only for the second session.
  • Build Your Own 3D Scanner: The Mathematics of 3D Triangulation

    1. 1. <ul><li>Session I </li></ul><ul><li>Introduction </li></ul><ul><li>The Mathematics of 3D Triangulation </li></ul><ul><li>3D Scanning with Swept-Planes </li></ul><ul><li>Camera and Swept-Plane Light Source Calibration </li></ul><ul><li>Reconstruction and Visualization using Point Clouds </li></ul>Course Schedule
    2. 2. 3D Triangulation: plane-ray intersection projector / ray plane intersection point coordinate systems
    3. 3. Representation of lines and rays line reference point vector scale parameter point ray=“1/2 line” parameter is positive
    4. 4. Representation of planes parametric reference point 2 vectors point reference point normal vector 1 implicit equation implicit 2 scale parameters
    5. 5. Triangulation by line-plane intersection object being scanned projected light plane illuminated point on object camera ray intersection of light plane with object same coordinate system
    6. 6. Triangulation by line-line intersection object being scanned camera ray projected light ray lines may not intersect !
    7. 7. Approximate line-line intersection Midpoint of segment joining arbitrary points in the two lines Least-squares approach Find parameters which minimize
    8. 8. Approximate line-line intersection
    9. 9. Perspective projection under the pinhole model center of projection image point image plane 3D point light direction for a projector light direction for a camera Calibration: mapping from image points to rays
    10. 10. The ideal pinhole camera camera coordinate system = world coordinate system
    11. 11. The general pinhole model world coordinate system camera coordinate system <ul><li>Ideal assumptions </li></ul><ul><li>Image lengths = world lengths </li></ul><ul><li>Focal length = 1 </li></ul><ul><li>Image origin = optical center </li></ul><ul><li>Image plane spanned by two basis vectors </li></ul>
    12. 12. The general pinhole model world coordinate system camera coordinate system
    13. 13. Plane defined by image line and center of projection center of projection image plane Implicit equation of line in image coordinates
    14. 14. <ul><li>Session I </li></ul><ul><li>Introduction </li></ul><ul><li>The Mathematics of 3D Triangulation </li></ul><ul><li>3D Scanning with Swept-Planes </li></ul><ul><li>Camera and Swept-Plane Light Source Calibration </li></ul><ul><li>Reconstruction and Visualization using Point Clouds </li></ul>Course Schedule

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