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# Computer Vision II: Multiple View Geometry

## Module IN2228

This Module is offered by TUM Department of Informatics.

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

### Module version of SS 2015

There are historic module descriptions of this module. A module description is valid until replaced by a newer one.

Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.

available module versions
SS 2022SS 2015WS 2011/2

### Basic Information

IN2228 is a semester module in English language at Master’s level which is offered irregular.

This Module is included in the following catalogues within the study programs in physics.

• Catalogue of non-physics elective courses
240 h 90 h 8 CP

### Content, Learning Outcome and Preconditions

#### Content

The module is focused on the mathematical aspects of multiple view geometry. The central challenge addressed in this class is the reconstruction of 3D geometry and camera motion from multiple images. To this end, the students will get a brief review of the main concepts of linear algebra (including matrix rank, SVD, various matrix groups). Students will learn about camera motion and perspective projection, camera calibration, epipolar geometry, the epipolar constraint, the 8-point algorithm, multiview matrices, rank constraints, bundle adjustment. Finally they will learn about the reconstruction of dense geometry. The key concepts will be implemented in Matlab to provide hands-on experience.

#### Learning Outcome

Upon successful completion of the module, students understand the mathematics of image formation and are able to recover camera motion and 3D geometry from images. Moreover, the students are able to implement the basic concepts in Matlab.

#### Preconditions

MA0901 Linear Algebra for Informatics
MA0902 Analysis for Informatics

### Courses, Learning and Teaching Methods and Literature

#### Learning and Teaching Methods

The main concepts will be presented in the lecture. During the tutorial, related exercises and discussions will deepen the understanding. Besides theoretical exercises, there will be programming exercises.

#### Media

Tutor presentation, interactive problem solving, discussion

#### Literature

An Invitation to 3D Vision (Y. Ma, S. Soatto, J. Kosecka, S. Sastry)
Multiple View Geometry in Computer Vision (R. Hartley, A. Zissermann)

### Module Exam

#### Description of exams and course work

The exam takes the form of a 120 minutes written test. In the written exam students should prove that they understood the reconstruction of 3D geometry and camera motion from multiple images. The questions will focus on the key concepts which have been discussed during the lecture and the tutorials. Mathematical proofs of the central concepts and questions about the implementation in Matlab assess acquaintance with the concepts in multiple view geometry.

#### Exam Repetition

The exam may be repeated at the end of the semester.

#### Current exam dates

Currently TUMonline lists the following exam dates. In addition to the general information above please refer to the current information given during the course.

Title
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Computer Vision II: Multiple View Geometry
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