Subject description - BE4M33TDV

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BE4M33TDV Three-dimensional Computer Vision
Roles:PO Extent of teaching:2P+2C
Department:13133 Language of teaching:EN
Guarantors:Šára R. Completion:Z,ZK
Lecturers:Šára R. Credits:6
Tutors:Matoušek M., Šára R. Semester:Z


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.

Study targets:

To master conceptual and practical knowledge of the basic methods in 3D computer vision.

Course outlines:

1. 3D computer vision, its goals and applications, course overview.
2. Geometry of points and lines in plane, ideal points and lines, point and line representations, line intersection and point join, homography.
3. Perspective camera model, center of projection, principal point, optical axis, optical ray and optical plane. Vanishing point and vanishing line, cross-ratio of four colinear points and its use for camera calibration. Radial distortion models.
4. Camera resection from six points, external camera orientation from three points.
5. Epipolar geometry, its representation by the fundamental matrix, essential matrix and its decomposition.
6. The seven-point algorithm for fundamental matrix estimation and the five-point algorithm for essential matrix estimation. Triangulation of points in 3D space from image correspondences.
7. The concept of algebraic and reprojection errors and Sampson approximation for reprojection error. Sampson error for fundamental matrix estimation.
8. Local optimization of Sampson error, derivation of a robust error by marginalization of a probabilistic model.
9. Robust optimization of geometric problems in 3D vision by MCMC methods.
10. Reconstruction of a multi-camera system, the bundle adjustment method, minimal and non-minimal representations for some basic geometric objects and mappings on them.
11. Introduction to stereoscopic vision, epipolar rectification of images.
12. The uniqueness, occlusion, ordering, coherence and continuity constraints in stereo and their representation in stereoscopic matching table.
13. Marroquin's greedy algorithm and the maximum-likelihood algorithm for stereoscopic matching.
14. Photometric stereo, its calibrated and uncalibrated versions.

Exercises outline:

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.


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


Knowledge equivalent to Geometry for Computer Vision and Graphics and Computer Vision Methods. Detailed up-to-date information on the course at



computer vision, digital image and video processing

Subject is included into these academic programs:

Program Branch Role Recommended semester
MEOI5_2018 Computer Vision and Image Processing PO 3
MEOI5_2016 Computer Vision and Image Processing PO 3

Page updated 14.4.2021 05:52:57, semester: Z/2020-1, L/2021-2, L/2020-1, Z,L/2022-3, Z/2021-2, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)