16-822: Geometry-based Methods in Vision

Instructor: Martial Hebert

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

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.

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

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 PDF
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 PDF
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  PDF
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
Apr. 16
Apr. 21

Apr. 23

Apr. 28

Apr. 30

May  1