[[https://intranet.fel.cvut.cz/cz/education/bk/predmety/46/84/p4684406.html|Annotation]]
[[https://cw.felk.cvut.cz/upload/|BRUTE]]
[[https://cw.felk.cvut.cz/forum/forum-1873.html|Forum]]
[[https://intranet.fel.cvut.cz/cz/education/rozvrhy-ng.B232/public/html/predmety/46/84/p4684406.html|Schedule]]
Students:
[[https://intranet.fel.cvut.cz/cz/education/rozvrhy-ng.B232/public/html/paralelky/P46/84/par4684406.1.html|CZ]]
[[https://intranet.fel.cvut.cz/cz/education/rozvrhy-ng.B232/public/html/paralelky/P46/84/par4684306.1.html|EN]]

===== Geometry of Computer Vision and Graphics 2024 =====

{{:courses:gvg:daliborka-2-top-h-191.png}}
{{:courses:gvg:labs:11_projection.gif|A reconstruction}}

//He who loves practice without theory is like the sailor who boards a ship without a rudder and compass and never knows where he may cast.//
— Leonardo Da Vinci (1452-1519)

//And since geometry is the right foundation of all painting, I have decided to teach its rudiments and principles to all youngsters eager for art.//
— Albrecht Durer (1471-1528)

//As for everything else, so for a mathematical theory: beauty can be perceived but not explained.//
— Arthur Cayley (1821–1895)

We will explain Euclidean, Affine, and Projective geometry basics, introduce a model of the perspective camera, and explain how images change when moving a camera. We will show how to compute camera poses and the 3D scene geometry from images. We will demonstrate the theory in practical panorama construction tasks, finding the camera pose, adding a virtual object to a real scene, and reconstructing a 3D model of a scene from its images. We will build on our previous knowledge of linear algebra and provide fundamentals of geometry for computer vision, computer graphics, augmented reality, image processing, and object recognition.

==== Lectures [Monday 11:00-12:30 KN:E-112] ====

[[courses:gvg:start#Contacts|Tomas Pajdla]], [[courses:gvg:start#Contacts|Torsten Sattler]]

^#^Date^Lecture {{https://cw.fel.cvut.cz/wiki/_media/courses/gvg/pajdla-gvg-lecture-2021.pdf|T Pajdla. Elements of Geometry for Computer Vision and Computer Grahics}}^
|  01  | 19.2. | TP: Geometry of CV & CG {{courses:gvg:GVG-01-2023-02-20-I.pdf|S}} {{courses:gvg:gvg-01-2021-02-15-L-0.mp4?linkonly|V}}, LA [Sec. 2.1] {{courses:gvg:gvg-01-2021-02-15-1.pdf|S}} {{courses:gvg:gvg-01-2021-02-15-L-1.mp4?linkonly|V}}, Image coordinate system [Sec. 5] {{courses:gvg:gvg-01-2021-02-15-L-2.mp4?linkonly|V}} |
|  02  | 26.2. | TP: Mathematical model of the perspective camera [Sec. 6], Kronecker product [Sec. 2.5] {{courses:gvg:gvg-02-2021-02-22-1.pdf|S}} {{courses:gvg:gvg-02-2021-02-22-L-1.mp4?linkonly|V1}} {{courses:gvg:gvg-02-2021-02-22-L-2.mp4?linkonly|V2}} {{courses:gvg:gvg-02-2021-02-22-L-3.mp4?linkonly|V3}} |
|  03  | 04.3. | TP: Camera calibration and pose [Sec. 7.1] {{courses:gvg:gvg-03-2021-03-01-1.pdf|S}} {{courses:gvg:gvg-03-2021-03-01-L-1.mp4?linkonly|V1}} {{courses:gvg:gvg-03-2021-03-01-L-2.mp4?linkonly|V2}} |
|  04  | 11.3. | TP: Calibrated camera pose computation [Sec. 7.2, 7.3], Vector product [Sec. 2.2, 2.3] {{courses:gvg:gvg-04-2021-03-08-1.pdf|S}} {{courses:gvg:gvg-04-2021-03-08-L.mp4?linkonly|V}} |
|  05  | 18.3. | VK: Homography [Sec. 8.1-8.5] {{courses:gvg:gvg-05-2021-03-15-1.pdf|S}} {{courses:gvg:gvg-05-2021-03-15-L-1.mp4?linkonly|V1}}  {{courses:gvg:gvg-05-2021-03-15-L-2.mp4?linkonly|V2}} |
|  06  | 25.3. | TS: Image based camera localization {{courses:gvg:GVG-06-2022-03-21-image_based_localization.pdf|S}} {{courses:gvg:gvg-06-2021-03-22-L-1.mp4?linkonly|V1}} {{courses:gvg:gvg-06-2021-03-22-L-2.mp4?linkonly|V2}} {{courses:gvg:gvg-06-2021-03-22-L-3.mp4?linkonly|V3}} |
|  ---  | 01.4. | // Easter Monday // |
|  07  | 08.4. | TS: Projective plane [Sec. 9.1-9.2] {{courses:gvg:gvg-07-2022-03-28-projective_plane.pdf|S}} {{courses:gvg:gvg-07-2021-03-29-L.mp4?linkonly|V}} |
|  08   | 15.4. | TP: Vanishing points & line [Sec. 9.4, 9.5] projective space [Sec. 10] camera autocalibration [Sec. 11] {{courses:gvg:gvg-08-2021-04-12-1.pdf|S}} {{courses:gvg:gvg-08-2021-04-12-L.mp4?linkonly|V}} |
|  09  |  22.4. | TP: Dual space [Sec. 2.4] lines under homography [Sec. 9.3] {{courses:gvg:gvg-09-2021-04-19-0.pdf|S0}} {{courses:gvg:gvg-09-2021-04-19-1.pdf|S1}} {{https://cw.fel.cvut.cz/wiki/_media/courses/gvg/gvg-09-2021-04-19-L.mp4?linkonly|V}} |
|  10   | 29.4 | TP: Epipolar geometry [Sec. 12.1-12.2] {{courses:gvg:gvg-10-2022-04-25-epipolar_geometry.pdf|Slides}} {{courses:gvg:gvg-10-2021-04-26-0.pdf|S0}} {{courses:gvg:gvg-09-2020-05-04-1_annotated.pdf|S1}} {{courses:gvg:gvg-10-2021-04-26-L.mp4?linkonly|V}} | 
|  11   | 06.5 | TP: 3D reconstruction with a calibrated camera [Sec. 12.3, 12.4] {{courses:gvg:gvg-11-2021-05-03-0.pdf|S0}}, {{courses:gvg:gvg-11-2021-05-03-1.pdf|S1}}, {{https://cw.fel.cvut.cz/wiki/_media/courses/gvg/gvg-11-2021-05-03-L.mp4?linkonly|V}} |
|  12   | 13.5. | TP: Calibrated camera motion computation [Sec. 12.5] {{courses:gvg:gvg-12-2021-05-10-1.pdf|S0}}, {{courses:gvg:gvg-12-2021-05-10-2.pdf|S1}}, {{https://cw.fel.cvut.cz/wiki/_media/courses/gvg/gvg-12-2021-05-10-L.mp4?linkonly|V}} |
|  13   | 20.5. | TS: 3D Reconstruction pipelines {{courses:gvg:gvg-13-2022-05-16-3d_reconstruction.pdf|S}}{{https://cw.fel.cvut.cz/wiki/_media/courses/gvg/gvg-13-2021-05-17-L.mp4?linkonly|V}} |

==== Labs [Monday 12:45-14:15, 14:30-16:00 KN:E-230] ====
[[courses:gvg:start#Contacts|Martin Matoušek]], [[courses:gvg:start#Contacts|Viktor Korotynskiy]] , [[courses:gvg:start#Contacts|Vojtěch Pánek]]

See [[courses:gvg:labs:start|Labs]] for more details.


==== Exam ====
The exam consists of a written and an oral part. It is required to achieve at least 50% of points from the written exam to be admitted to the oral exam. The grade depends on the exam (40%), tests (30%), and homework (30%). You may skip the oral exam if you are satisfied with the result after the written exam.

Exam content:

  - Linear algebra [4,5,6,7]: linear space, basis, coordinates, linear dependence/independence, matrices, rank, determinant, eigenvalues, and eigenvectors, solving systems of linear equations, Frobenius theorem and linear independence, linear function, affine function, linear mapping, and its matrix, computing roots of a polynomial via eigenvalues of its companion matrix, dual space, dual basis, change of the dual basis corresponding to a change of a basis, vector product and derived linear mappings, SVD, dual space, and dual basis.
  - ** {{https://cw.fel.cvut.cz/wiki/_media/courses/gvg/pajdla-gvg-lecture-2021.pdf|Course material}} **

Written exam terms

  - **27.5.2024 11:00-14:00 KN:E-112 **
  - ??.?.2024 11:00-14:00 KN:E-112
 
Written exam organization:

  -  The written exam is in person in room KN:E-112.

Oral exam organization:

  - You may skip the oral exam if you are satisfied with the result after the written exam.
  - The oral face-to-face exam will be done online via MS Teams and will take about 30 mins. 


==== Grade ====
  - All homework must be submitted via [[https://cw.felk.cvut.cz/upload/|BRUTE]] and accepted.  
  - At least 50% of points in total for the homework.
  - At least 50% of points in total from the tests.


==== Rules ====
  - **Lecture:** It is very **difficult** to pass the course without attending the lectures.
  - **Labs:** It is **impossible** to pass the course without attending the labs.
  - **Homework:** Homework is assigned at a lab where it can be discussed with teaching assistants. Students work out homework **individually** ({{http://cw.felk.cvut.cz/doku.php/help/common/plagiarism_cheating|rules}}{{http://cw.felk.cvut.cz/doku.php/help/common/plagiaty_opisovani|in Czech}}). The deadline for submitting homework via [[https://cw.felk.cvut.cz/upload/|BRUTE]] is on Monday at 6:00 in the morning two weeks after the assignment. Late submissions are penalized (10% for each commenced **day** of delay but not more than 50% of points).
  - **Assessment:** see above.
  - **Tests:** Students take tests **individually**. 

==== Literature ====
  - T Pajdla {{https://cw.fel.cvut.cz/wiki/_media/courses/gvg/pajdla-gvg-lecture-2021.pdf|Elements of Geometry for Computer Vision}}
  - R Hartley, A Zisserman {{http://www.robots.ox.ac.uk/~vgg/hzbook/index.html|Multiple View Geometry in Computer Vision}} Cambridge University Press, 2003
  - K Daniilidis, J Shi. {{https://www.coursera.org/lecture/robotics-perception/introduction-3lIVo|Robotics: Perception - Coursera Online Course}}
  - G Sanderson {{https://youtu.be/fNk_zzaMoSs|Essence of Linear Algebra}} from 3Blue1Brown
  - J Strom, K Astrom, T Akenine-Moller {{http://immersivemath.com/ila/index.html|Interactive Linear Algebra Course}}
  - P Olšák {{http://petr.olsak.net/linal.html|Úvod do algebry, zejména lineární}} ČVUT 2007
  - P Pták {{http://ucebnice.heureka.cz/introduction-to-linear-algebra-pavel-ptak|Introduction to Linear Algebra}} ČVUT 2007
  - Maple {{http://math.feld.cvut.cz/nemecek/matvmap.html|A0B01MVM Matematika v Maple}} {{http://math.feld.cvut.cz/nemecek/pas.html|Installation}}


==== Contacts ====

|[[https://people.ciirc.cvut.cz/~pajdla/|Tomas Pajdla]]|[[https://scholar.google.com/citations?user=jzx6_ZIAAAAJ|Torsten Sattler]]|[[https://people.ciirc.cvut.cz/~xmatousm|Martin Matousek]]|[[https://people.ciirc.cvut.cz/~korotvik|Viktor Korotynskiy]]|[[https://people.ciirc.cvut.cz/~panekvo1|Vojtech Panek]]|
|  [[pajdla@cvut.cz|email]]  |  [[torsten.sattler@cvut.cz|email]]  |  [[martin.matousek@cvut.cz|email]]  |  [[viktor.korotynskiy@cvut.cz|email]]  |    [[vojtech.panek@cvut.cz|email]]  |  
|  [[http://aag.ciirc.cvut.cz/contact|CIIRC B-638]]  |  [[http://aag.ciirc.cvut.cz/contact|CIIRC B-609]]  |  [[http://aag.ciirc.cvut.cz/contact|CIIRC B-606B]]  |  [[http://aag.ciirc.cvut.cz/contact|CIIRC B-640A]]  |  [[http://aag.ciirc.cvut.cz/contact|CIIRC B-634A]]  |
|  |  |  [[https://teams.microsoft.com/l/meetup-join/19%3ab0a8d9a0638c474892ab358f1e45c043%40thread.tacv2/1600776448022?context=%7b%22Tid%22%3a%22f345c406-5268-43b0-b19f-5862fa6833f8%22%2c%22Oid%22%3a%227b127957-1abe-4c2e-9a41-b1782621d23a%22%7d|MS Teams]]  | | |
|  [[https://people.ciirc.cvut.cz/~pajdla|{{:courses:pro:pajdla.png?130}}]]  |  [[https://scholar.google.com/citations?user=jzx6_ZIAAAAJ|{{:courses:gvg:torstensattler.png?130}}]]  |  [[https://people.ciirc.cvut.cz/~xmatousm|{{:courses:gvg:martin_matousek.jpg?110|}}]]  |  [[https://people.ciirc.cvut.cz/~korotvik|{{:courses:gvg:korotynskiy.jpeg?135}}]]  |  [[https://people.ciirc.cvut.cz/~panekvo1|{{:courses:gvg:vojtechpanek.jpg?138x150}}]] |