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Multidimensional Signal and Image Analysis, 6 credits
Multidimensionell signal- och bildanalys, 6 hp
TSBB36
Main field of study
Electrical EngineeringCourse level
First cycleCourse type
Programme courseExaminer
Mårten WadenbäckDirector of studies or equivalent
Lasse AlfredssonEducation components
Preliminary scheduled hours: 0 hRecommended self-study hours: 160 h
Available for exchange students
YesECV = Elective / Compulsory / Voluntary
| Course offered for | Semester | Period | Timetable module | Language | Campus | ECV | |
|---|---|---|---|---|---|---|---|
| 6CTMA | Engineering Mathematics, Master of Science in Engineering | 5 (Autumn 2026) | 2 | 3 | Swedish/English | Linköping, Valla | C |
The course syllabus is preliminary
Main field of study
Electrical EngineeringCourse level
First cycleAdvancement level
G2FSpecific information
The course overlaps with TSBB06 Multidimensional Signal Analysis, and the two may not be part of the same degree.
Course offered for
- Master of Science in Engineering Mathematics
Prerequisites
Basic Linear Algebra: vector spaces, bases, scalar product, least squares problems, eigenvalue problems. Convolution and Fourier transform of one-variable signals. Basic skills in Matlab or Python is recommended.
Intended learning outcomes
An objective of the course is to provide a solid theoretical foundation for further studies and applications in 3D computer vision and in machine learning with images. Passing the course means that the student is able to use concepts and methods in signal and image analysis that are based on linear algebra. The student is then able to:
Goal 1: Explain and use homogeneous coordinates for geometric calculations in two and three dimensions. This includes points and lines in two dimensions, points, planes, and lines in three dimensions, homographies, camera projections, and epipolar geometry.
Goal 2: Explain and use least squares techniques to define estimation problems for different geometric objects. This includes triangulation, image filtering, and rigid transformations.
Goal 3: Explain and use bases, dual bases, and subspace bases to perform calculations for signal analysis.
Goal 4: Explain and use linear signal representations on practical problems, including: image filtering, image blending, and feature maps.
Course content
Signal spaces and signal bases, dual bases. Least squares problem, normalized convolution. Eigenvalue and singular value analysis. Principal component analysis. Feature maps. Projective spaces, homogeneous coordinates, homographies, camera projections, epipolar geometry. Representation and estimation of various types of geometric objects.
Teaching and working methods
The course has lectures that present basic concepts and theory. The course also contains lessons with a focus on calculations in order to concretise and emphasise the concepts and theory from the lectures. In a set of mandatory computer exercises, each participant must demonstrate the ability to carry out more complex calculation and answer related questions.
Examination
| TEN1 | Written Examination | 4 credits | U, 3, 4, 5 |
| LAB1 | Laboratory Work | 2 credits | U, G |
Attendance is mandatory at the computer exercises. The “use” parts of Goals 1-4 are tested during the computer exercises, and during the written examination. Deeper understanding and ability to explain are tested by the written examination.
For grade 3, a pass on the computer exercises and the exam are required. For grades 4 and 5, it is additionally required to demonstrate, on the exam, a higher ability to use methods in combination and explain and conduct deeper reasoning concerning concepts and methods in the course.
Grades for examination modules are decided in accordance with the assessment criteria presented at the start of the course.
Grades
Four-grade scale, LiU, U, 3, 4, 5Other information
Supplementary courses: 3D Computer Vision, Computer Vision for Video Analysis, Machine Learning for Computer Vision, Image and Audio Coding, Medical Image Analysis, Neural Networks and Learning Systems, Computational Photography
About teaching and examination language
The teaching language is presented in the Overview tab for each course. The examination language relates to the teaching language as follows:
- If teaching language is “Swedish”, the course as a whole could be given in Swedish, or partly in English. Examination language is Swedish, but parts of the examination can be in English.
- If teaching language is “English”, the course as a whole is taught in English. Examination language is English.
- If teaching language is “Swedish/English”, the course as a whole will be taught in English if students without prior knowledge of the Swedish language participate. Examination language is Swedish or English depending on teaching language.
Other
The course is conducted in such a way that there are equal opportunities with regard to sex, transgender identity or expression, ethnicity, religion or other belief, disability, sexual orientation and age.
The planning and implementation of a course should correspond to the course syllabus. The course evaluation should therefore be conducted with the course syllabus as a starting point.
The course is campus-based at the location specified for the course, unless otherwise stated under “Teaching and working methods”. Please note, in a campus-based course occasional remote sessions could be included.
Department
Institutionen för systemteknikCourse literature
Compendia
- Prerequisites for studies at advanced level in Image Science at Linköping University
In addition to the compendium, the course is based on excerpts from books and articles, which are made available at the start of the course. - Klas Nordberg, Introduction to Representations and Estimation in Geometry
Covers the geometry part of the course.
| Code | Name | Scope | Grading scale |
|---|---|---|---|
| TEN1 | Written Examination | 4 credits | U, 3, 4, 5 |
| LAB1 | Laboratory Work | 2 credits | U, G |
Attendance is mandatory at the computer exercises. The “use” parts of Goals 1-4 are tested during the computer exercises, and during the written examination. Deeper understanding and ability to explain are tested by the written examination.
For grade 3, a pass on the computer exercises and the exam are required. For grades 4 and 5, it is additionally required to demonstrate, on the exam, a higher ability to use methods in combination and explain and conduct deeper reasoning concerning concepts and methods in the course.
Grades for examination modules are decided in accordance with the assessment criteria presented at the start of the course.
Compendia
Prerequisites for studies at advanced level in Image Science at Linköping University
In addition to the compendium, the course is based on excerpts from books and articles, which are made available at the start of the course.
Klas Nordberg, Introduction to Representations and Estimation in Geometry
Covers the geometry part of the course.
Note: The course matrix might contain more information in Swedish.
I = Introduce, U = Teach, A = Utilize
| I | U | A | Modules | Comment | ||
|---|---|---|---|---|---|---|
| 1. DISCIPLINARY KNOWLEDGE AND REASONING | ||||||
| 1.1 Knowledge of underlying mathematics and science (G1X level) |
X
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X
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X
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TEN1
LAB1
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| 1.2 Fundamental engineering knowledge (G1X level) |
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X
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| 1.3 Further knowledge, methods, and tools in one or several subjects in engineering or natural science (G2X level) |
X
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X
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X
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TEN1
LAB1
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| 1.4 Advanced knowledge, methods, and tools in one or several subjects in engineering or natural sciences (A1X level) |
X
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X
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X
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TEN1
LAB1
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| 1.5 Insight into current research and development work |
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| 2. PERSONAL AND PROFESSIONAL SKILLS AND ATTRIBUTES | ||||||
| 2.1 Analytical reasoning and problem solving |
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X
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LAB1
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| 2.2 Experimentation, investigation, and knowledge discovery |
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X
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X
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LAB1
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Experimentation to complete the laboratory exercises |
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| 2.3 System thinking |
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| 2.4 Attitudes, thought, and learning |
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| 2.5 Ethics, equity, and other responsibilities |
X
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X
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To find and read scientific articles |
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| 3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION | ||||||
| 3.1 Teamwork |
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| 3.2 Communications |
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| 3.3 Communication in foreign languages |
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| 4. CONCEIVING, DESIGNING, IMPLEMENTING AND OPERATING SYSTEMS IN THE ENTERPRISE, SOCIETAL AND ENVIRONMENTAL CONTEXT | ||||||
| 4.1 External, societal, and environmental context |
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| 4.2 Enterprise and business context |
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| 4.3 Conceiving, system engineering and management |
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| 4.4 Designing |
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| 4.5 Implementing |
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| 4.6 Operating |
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| 5. PLANNING, EXECUTION AND PRESENTATION OF RESEARCH DEVELOPMENT PROJECTS WITH RESPECT TO SCIENTIFIC AND SOCIETAL NEEDS AND REQUIREMENTS | ||||||
| 5.1 Societal conditions, including economic, social, and ecological aspects of sustainable development for knowledge development |
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| 5.2 Economic conditions for knowledge development |
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| 5.3 Identification of needs, structuring and planning of research or development projects |
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| 5.4 Execution of research or development projects |
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| 5.5 Presentation and evaluation of research or development projects |
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