Three-dimensional Computer Vision

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Code Completion Credits Range Language
BE4M33TDV Z,ZK 6 2P+2C English
The course cannot be taken simultaneously with:
3D Computer Vision (A4M33TDV)
Three-dimensional Computer Vision (B4M33TDV)
The course is a substitute for:
Three-dimensional Computer Vision (B4M33TDV)
Radim Šára (guarantor)
Radim Šára (guarantor), Martin Matoušek, Jaroslav Moravec
Department of Cybernetics

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.


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 https://cw.fel.cvut.cz/wiki/courses/tdv/start

Syllabus of lectures:

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

Syllabus of tutorials:

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.

Study Objective:

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

Study materials:

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

Further information:
Time-table for winter semester 2021/2022:
Šára R.
(lecture parallel1)
Karlovo nám.
Cvičebna Vyčichlova
Matoušek M.
Moravec J.

(lecture parallel1
parallel nr.101)

Karlovo nám.
Lab K311
Time-table for summer semester 2021/2022:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2022-08-08
For updated information see http://bilakniha.cvut.cz/en/predmet4685306.html