16-822 Geometry-based Methods in Vision Go back

Instructor: Martial Hebert

University Units: 12.0

Semester Offered: Spring

Course Description

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.
Prerequisites: Computer Vision (16-721 or equivalent)
Books: The Geometry of Multiple Images. Faugeras and Long, MIT Press.

Multiple View Geometry in Computer Vision, Richard Hartley and Andrew Zisserman, Cambridge University Press, June 2000.

Topic Covered:
* Fundamentals of projective, affine, and Euclidean geometries
* Invariance and duality
* Algebraic tools
* Single view geometry: The pinhole model
* Calibration techniques
* 2-view geometry: The Fundamental matrix
* 2-view reconstruction
* 3-view geometry: The trifocal tensor
* Parameter estimation and uncertainty
* n-view reconstruction
* Self-calibration