16-822:
Geometry-based Methods in Vision

Instructor: Martial Hebert

Tuesdays and Thursdays, Noon-1:20, Wean Hall 3002

Tuesdays and Thursdays, Noon-1:20, Wean Hall 3002

Summary:

The course focuses on the geometric aspects of computer vision: the geometry of image formation and its use for 3D reconstruction and calibration. The objective of the course is to introduce the formal tools and results that are necessary for developing multi-view reconstruction algorithms. The fundamental tools introduced study affine and projective geometry, which are essential to the development of image formation models. Additional algebraic tools, such as exterior algebras are also introduced at the beginning of the course. These tools are then used to develop formal models of geometric image formation for a single view (camera model), two views (fundamental matrix), and three views (trifocal tensor); 3D reconstruction from multiple images; and auto-calibration. If time permits, we will also look at the application of these concepts to the reconstruction of smooth surfaces.

Administration:

The evaluation is based on a midterm, final exam, and projects, as well as class participation.

Books:

The material covered in this class comes primarily from two textbooks:

M. Berger. "Geometry", Springer, 1987.

L. Kadison, M. T. Kromann, "Projective Geometry and Modern Algebra", Birkhauser, 1996.

Schedule and Notes:

Announcements:

The course focuses on the geometric aspects of computer vision: the geometry of image formation and its use for 3D reconstruction and calibration. The objective of the course is to introduce the formal tools and results that are necessary for developing multi-view reconstruction algorithms. The fundamental tools introduced study affine and projective geometry, which are essential to the development of image formation models. Additional algebraic tools, such as exterior algebras are also introduced at the beginning of the course. These tools are then used to develop formal models of geometric image formation for a single view (camera model), two views (fundamental matrix), and three views (trifocal tensor); 3D reconstruction from multiple images; and auto-calibration. If time permits, we will also look at the application of these concepts to the reconstruction of smooth surfaces.

Administration:

The evaluation is based on a midterm, final exam, and projects, as well as class participation.

Books:

The material covered in this class comes primarily from two textbooks:

•R. Hartley and A. Zisserman, “Multiple View Geometry in Computer Vision”, Cambridge University Press, 2000.

O.D. Faugeras, Q.-T. Luong, and T. Papadopoulo, “The Geometry of Multiple Images”, MIT Press, 2001.

D.A. Forsyth and J. Ponce, “Computer Vision: A Modern Approach”, Prentice-Hall, 2002.

M. Berger. "Geometry", Springer, 1987.

L. Kadison, M. T. Kromann, "Projective Geometry and Modern Algebra", Birkhauser, 1996.

Schedule and Notes:

Jan. 13 | Intro | Intro Geometry Intro |

Jan. 15 | Geometry intro | |

Jan. 20 | Geometry intro | |

Jan. 22 | Geometry intro | PDF |

Jan. 27 | Geometry intro | PDF |

Jan 29 | Geometry intro | |

Feb. 3 | Geometry intro | |

Feb. 5 | Single view geometry | PDF |

Feb. 10 | Single view geometry | |

Feb. 12 | Two view geometry | |

Feb. 17 | Two view geometry | |

Feb. 19 | Two view geometry | |

Feb. 24 | Two-view geometry | PDF |

Feb. 26 | Two-view geometry | PDF |

Mar. 3 | Review | |

Mar. 5 | Midterm | |

Mar. 10 | Break | |

Mar. 12 | Break | |

Mar. 17 | Three view reconstruction | PDF |

Mar. 19 | Three view reconstruction | |

Mar. 24 | Three view geometry | |

Mar. 26 | N view geometry | PDF |

Mar. 31 | N view reconstruction | PDF |

Apr. 2 | N view reconstruction | PDF |

Apr. 7 | Autocalibration | PDF |

Apr. 9 | Autocalibration | |

Apr. 14 | Surfaces |
PDF |

Apr. 16 | ||

Apr. 21 | ||

Apr. 23 | ||

Apr. 28 | ||

Apr. 30 | ||

May 1 |

Announcements: