# FI:PA170 Digital Geometry - Course Information

## PA170 Digital Geometry

**Faculty of Informatics**

Autumn 2021

**Extent and Intensity**- 2/1/0. 3 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: z (credit).
**Teacher(s)**- doc. RNDr. Pavel Matula, Ph.D. (lecturer)

doc. RNDr. Petr Matula, Ph.D. (assistant) **Guaranteed by**- doc. RNDr. Pavel Matula, Ph.D.

Department of Visual Computing – Faculty of Informatics

Contact Person: doc. RNDr. Pavel Matula, Ph.D.

Supplier department: Department of Visual Computing – Faculty of Informatics **Timetable**- Wed 15. 9. to Wed 8. 12. Wed 9:00–11:50 A218
**Prerequisites**- The basic knowledge of mathematics and graph theory is recommended.
**Course Enrolment Limitations**- The course is also offered to the students of the fields other than those the course is directly associated with.
**fields of study / plans the course is directly associated with**- there are 52 fields of study the course is directly associated with, display
**Course objectives**- At the end of the course students should be able to: understand and explain basic problems that arise after object digitization and object representation using a grid of points (e.g., in the form of a digital image); measure geometric and topological properties of digital objects (e.g., length, area, perimeter, volume, Euler characteristic, and the number of holes); compare digital metrics; efficiently implement the key algorithms of digital geometry (e.g., region labeling, border tracing, and distance map computation); identify the fundamentals of the discussed methods.
**Learning outcomes**- At the end of the course students should be able to: understand and explain basic problems that arise after object digitization and object representation using a grid of points (e.g., in the form of a digital image); measure geometric and topological properties of digital objects (e.g., length, area, perimeter, volume, Euler characteristic, and the number of holes); compare digital metrics; efficiently implement the key algorithms of digital geometry (e.g., region labeling, border tracing, and distance map computation); identify the fundamentals of the discussed methods.
**Syllabus**- Basic terms of digital geometry
- Component labeling algrotithms
- Object digitization
- Measurements in digital spaces
- Distance maps and their computation
- Border tracing algorithms
- Topological properties of digital spaces
- Digital geometric figure recognition (line, arc, plane)
- Estimation and computation of geometric and topological properties of digital sets (volume, surface, length, curvature, etc.)
- Digital convex hull
- Thinning and skeletons

**Literature**- KLETTE, Reinhard and Azriel ROSENFELD.
*Digital geometry: geometric methods for digital picture analysis*. Amsterdam: Elsevier, 2004, 656 pp. info

- KLETTE, Reinhard and Azriel ROSENFELD.
**Teaching methods**- Lectures followed by class exercises where we will solve practical problems by taking the advantage of lecture findings. Homework.
**Assessment methods**- Written test, oral exam. Obligatory attendance at exercises. Homework score.
**Language of instruction**- English
**Further Comments**- Study Materials

The course is taught once in two years.

- Enrolment Statistics (Autumn 2021, recent)
- Permalink: https://is.muni.cz/course/fi/autumn2021/PA170