Description:

This course introduces methods and algorithms for 3D geometric scene reconstruction from images. The student will understand these methods and their essence well enough to be able to build variants of simple systems for reconstruction of 3D objects from a set of images or video, for inserting virtual objects to video-signal source, or for computing ego-motion trajectory from a sequence of images. The labs will be hands-on, the student will be gradually building a small functional 3D scene reconstruction system and using it to compute a virtual 3D model of an object of his/her choice.

Contents:

1. 3D computer vision, its goals and applications, course overview
2. Basic geometry of points and lines, homography
3. Perspective camera, projection matrix decomposition, optical center
4. Optical ray, axis, plane; vanishing point, cross-ratio
5. Camera calibration from vanishing points, camera resection from 6 points, critical configurations for resection
6. The exterior orientation problem, the relative orientation problem, epipolar geometry, epipolar constraint
7. Essential matrix decomposition, 7-point algorithm for fundamental matrix estimation, 5-point algorithm for essential matrix estimation
8. Triangulation by algebraic error minimization, reprojection error, Sampson error correction
9. The golden standard triangulation method, local optimization for fundamental matrix estimation, robust error function
10. Optimization by random sampling, MH sampler, RANSAC
11. Camera system reconstruction
12. Bundle adjustment, gauge freedom in bundle adjustment, minimal representations, introduction to stereovision
13. Epipolar rectification, occlusion constraint
14. Matching table, Marroquin's WTA matching algorithm, maximum-likelihood matching algorithm, ordering constraint, stereo matching algorithm comparison

Seminar contents:

1. Introduction, term project specification, instructions on how to select an object suitable for 3D reconstruction, on image capture, and on camera calibration.
2. An introductory computer programming exercise with points and lines in a plane.
3. An exercise on the geometric description of perspective camera. Robust maximum likelihood estimation of a planar line.
4. Computing sparse correspondences by WBS matcher.
5. A computer exercise with matching and estimation of two homographies in an image pair.
6. Calibration of poses of a set of cameras.
7. Midterm test.
8. Sparse point cloud reconstruction.
9. Optimization of point and camera estimates by bundle adjustment.
10. Epipolar rectification and dense stereomatching. Dense point cloud reconstruction.
11. 3D surface reconstruction.
12. Presentation and submission of resulting models.

Recommended literature:

R. Hartley and A. Zisserman. Multiple View Geometry. 2nd ed. Cambridge University Press 2003.

Keywords:

computer vision, digital image and video processing

Abbreviations used:

Semester:

• W ... winter semester (usually October - February)
• S ... spring semester (usually March - June)
• W,S ... both semesters

Mode of completion of the course:

• A ... Assessment (no grade is given to this course but credits are awarded. You will receive only P (Passed) of F (Failed) and number of credits)
• GA ... Graded Assessment (a grade is awarded for this course)
• EX ... Examination (a grade is awarded for this course)
• A, EX ... Examination (the award of Assessment is a precondition for taking the Examination in the given subject, a grade is awarded for this course)

Weekly load (hours per week):

• P ... lecture
• C ... seminar
• L ... laboratory
• R ... proseminar
• S ... seminar