Build Your Own 3D Scanner: The Mathematics of 3D Triangulation
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The document introduces the topics that will be covered in the course, including: 1) The mathematics of 3D triangulation using line-plane and line-line intersections to reconstruct points in 3D space from 2D images. 2) Camera and light source calibration which is needed to map between image points and 3D rays. 3) Reconstruction and visualization of 3D point clouds scanned with swept-plane light sources.
Build Your Own 3D Scanner: The Mathematics of 3D Triangulation
- 1. Session I Introduction The Mathematics of 3D Triangulation 3D Scanning with Swept-Planes Camera and Swept-Plane Light Source Calibration Reconstruction and Visualization using Point Clouds Course Schedule
- 2. 3D Triangulation: plane-ray intersection projector / ray plane intersection point coordinate systems
- 3. Representation of lines and rays line reference point vector scale parameter point ray=“1/2 line” parameter is positive
- 4. Representation of planes parametric reference point 2 vectors point reference point normal vector 1 implicit equation implicit 2 scale parameters
- 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. Triangulation by line-line intersection object being scanned camera ray projected light ray lines may not intersect !
- 7. Approximate line-line intersection Midpoint of segment joining arbitrary points in the two lines Least-squares approach Find parameters which minimize
- 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. The ideal pinhole camera camera coordinate system = world coordinate system
- 11. The general pinhole model world coordinate system camera coordinate system Ideal assumptions Image lengths = world lengths Focal length = 1 Image origin = optical center Image plane spanned by two basis vectors
- 12. The general pinhole model world coordinate system camera coordinate system
- 13. Plane defined by image line and center of projection center of projection image plane Implicit equation of line in image coordinates
- 14. Session I Introduction The Mathematics of 3D Triangulation 3D Scanning with Swept-Planes Camera and Swept-Plane Light Source Calibration Reconstruction and Visualization using Point Clouds Course Schedule
Editor's Notes
- #2: 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.
- #3: 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.
- #4: 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.
- #5: 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.
- #6: 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.
- #7: 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.
- #8: 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.
- #9: 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.
- #10: 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.
- #11: 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.
- #12: 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.
- #13: Build Your Own 3D Scanner 2/18/2009
- #14: 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.
- #15: 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.