Geometry-based Methods in Vision

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. 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; auto-calibration; and learning based methods. In particular, this course will cover topics including -

• Fundamentals of projective, affine, and Euclidean geometries		• Projective Transforms in 2D and 3D
• Single view geometry: The pinhole model		• 2-view geometry: The Fundamental matrix
• 2-view reconstruction		• N-view reconstruction
• Self-calibration		• Learning-based SfM and SLAM

Format and Prerequisites

The course will be lecture-based, and the grades will be determined by assignments (40%), problem sets (15%), a final project (40%) and class participation (5%). The course will require as background good coding skills, and an understanding of basics in Computer Vision (e.g. image formation, ray optics) and Linear Algebra (e.g. Vector Spaces, Matrix Factorization).