Subject description - B4M33TDV

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B4M33TDV Three-dimensional Computer Vision
Roles:PO, PV Extent of teaching:2P+2C
Department:13133 Language of teaching:CS
Guarantors:Šára R. Completion:Z,ZK
Lecturers:Šára R. Credits:6
Tutors:Matoušek M., Moravec J., Šára R. Semester:Z

Web page:


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. 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

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.


Basics of geometry in 2D and 3D, vector algebra, linear algebra, elementary methods of continuous function optimization, Bayesian modelling basics, elementary competence in Python or Matlab programming. Detailed up-to-date information on the course, including details about the requirements, are available at


computer vision, digital image and video processing

Subject is included into these academic programs:

Program Branch Role Recommended semester
MPOI5_2018 Computer Vision and Image Processing PO 3
MPKYR_2021 Common courses PV 1

Page updated 20.6.2024 05:51:16, semester: Z/2024-5, Z,L/2023-4, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)