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:
•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:
|
|
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| Jan. 15 |
Intro |
pdf |
| Jan. 17 |
Geometry intro |
pdf |
| Jan. 22 |
Geometry intro |
pdf
scribe
|
| Jan. 24 |
Geometry intro |
pdf
|
| Jan. 29 |
Geometry intro |
scribe2
|
| Jan 31 |
Geometry intro |
pdf |
| Feb. 5 |
Geometry intro |
pdf |
| Feb. 7 |
Single view geometry |
pdf
|
| Feb. 12 |
Single view geometry |
pdf
scribe3
|
| Feb. 14 |
Planes and homography |
|
| Feb. 19 |
Guest lecture |
|
| Feb. 21 |
Single view geometry |
pdf
scribe4 |
| Feb. 26 |
Two-view geometry |
pdf
|
| Feb. 28 |
Two-view geometry
|
pdf
scribe6 |
| Mar. 4 |
Review |
|
| Mar. 6 |
Midterm |
|
| Mar. 11 |
Break |
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| Mar. 13 |
Break |
|
| Mar. 18 |
Two view reconstruction |
pdf
|
| Mar. 20 |
Two view reconstruction and estimation |
pdf |
| Mar. 25 |
Three view geometry |
pdf |
| Mar. 27 |
Three view geometry |
|
| Apr. 1 |
N view geometry |
pdf
|
| Apr. 3 |
N view geometry |
pdf |
| Apr. 8 |
|
|
| Apr. 10 |
Calibration review |
pdf
|
| Apr. 15 |
N view reconstruction |
pdf
|
| Apr. 17 |
|
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| Apr. 22 |
N view reconstruction |
pdf |
| Apr. 24 |
Auto calibration |
pdf |
| Apr. 29 |
Auto calibration |
pdf |
| May 1 |
Projections of smooth surfaces |
pdf |
Announcements:
Possible projects