## 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 **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**- The course is taught once in two years.

The course is taught: every week.

## PA170 Digital Geometry

**Faculty of Informatics**

Autumn 2019

**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**- Thu 12:00–14:50 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****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.

## PA170 Digital Geometry

**Faculty of Informatics**

Autumn 2017

**Extent and Intensity**- 2/1. 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. Petr 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 10:00–12:50 A318
**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 23 fields of study the course is directly associated with, display
**Course objectives****Learning outcomes****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 attandance at exercises. Homework score.
**Language of instruction**- Czech
**Further Comments**- Study Materials

The course is taught once in two years.

## PA170 Digital Geometry

**Faculty of Informatics**

Autumn 2015

**Extent and Intensity**- 2/1. 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. Petr 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**- Thu 9:00–11:50 A318
**Prerequisites**- The basic knowledge of mathematics and graph theory is recommended.
**Course Enrolment Limitations****fields of study / plans the course is directly associated with**- there are 23 fields of study the course is directly associated with, display
**Course objectives****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)
- 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****Assessment methods**- Written test, oral exam. Obligatory attandance at exercises. Homework score.
**Language of instruction**- Czech
**Further Comments**- Study Materials

The course is taught once in two years.

## PA170 Digital Geometry

**Faculty of Informatics**

Autumn 2013

**Extent and Intensity**- 2/1. 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. Petr 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**- Tue 9:00–11:50 C418
**Prerequisites**- The basic knowledge of mathematics and graph theory is recommended.
**Course Enrolment Limitations****fields of study / plans the course is directly associated with**- there are 22 fields of study the course is directly associated with, display
**Course objectives****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)
- 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****Assessment methods**- Written test, oral exam. Obligatory attandance at exercises. Homework score.
**Language of instruction**- Czech
**Further Comments**- Study Materials

The course is taught once in two years.

## PA170 Digital Geometry

**Faculty of Informatics**

Autumn 2011

**Extent and Intensity****Teacher(s)**- doc. RNDr. Pavel Matula, Ph.D. (lecturer)
**Guaranteed by**- prof. Ing. Jiří Sochor, CSc.

Department of Visual Computing - Faculty of Informatics

Contact Person: doc. RNDr. Pavel Matula, Ph.D. **Timetable**- Mon 10:00–11:50 A107, Mon 12:00–13:50 A107
**Prerequisites**- The basic knowledge of mathematics and graph theory is recommended.
**Course Enrolment Limitations****fields of study / plans the course is directly associated with**- there are 25 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 an object representation using a grid of points (e.g., in the form of 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: digital image, pixel, voxel, image resolution, types of grids, grid scanning
- grid point and grid cell models: adjacency, incidence, connectedness, components, component labeling algorithms.
- Digitalization: digitization models, line digitization.
- Measurement in digital images: metrics, integer-valued metrics approximating Euclidean metric, distance transform, distance measurement between sets.
- Oriented adjacency graphs: border, boundary, border tracing algorithm, holes, combinatorial results for regular graphs (grids)
- Application of graph theory in image processing, graph-cut based image segmentation.
- Incidence pseudographs, open and closed regions, ordered labeling of multilevel images.
- Introduction to topology. Basic topological concepts. Definition of continuous as well as digital curve. Jordan Veblen theorem.
- Euclidean and simplex complexes (triangulation). Topological definition of surfaces and their classification. Combinatorial results. Regular tilings.
- Estimation and computation of geometric and topological properties of digital sets: volume, surface, area, perimeter, length, curvature, Euler characteristic, etc.
- Digital straight segment recognition, digital straightness, digital convex hull and its computation.
- Image deformations: Thinning, 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****Assessment methods**- Written test, oral exam. Obligatory attandance at exercises. Homework score.
**Language of instruction**- Czech
**Further Comments**- Study Materials

The course is taught annually.

## PA170 Digital Geometry

**Faculty of Informatics**

Autumn 2010

**Extent and Intensity****Teacher(s)**- doc. RNDr. Pavel Matula, Ph.D. (lecturer)
**Guaranteed by**- prof. Ing. Jiří Sochor, CSc.

Department of Visual Computing - Faculty of Informatics

Contact Person: doc. RNDr. Pavel Matula, Ph.D. **Timetable**- Mon 10:00–11:50 C525, Mon 12:00–13:50 C525
**Prerequisites**- The basic knowledge of mathematics and graph theory is recommended.
**Course Enrolment Limitations****fields of study / plans the course is directly associated with**- there are 24 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 an object representation using a grid of points (e.g., in the form of 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: digital image, pixel, voxel, image resolution, types of grids, grid scanning
- grid point and grid cell models: adjacency, incidence, connectedness, components, component labeling algorithms.
- Digitalization: digitization models, line digitization.
- Measurement in digital images: metrics, integer-valued metrics approximating Euclidean metric, distance transform, distance measurement between sets.
- Oriented adjacency graphs: border, boundary, border tracing algorithm, holes, combinatorial results for regular graphs (grids)
- Application of graph theory in image processing, graph-cut based image segmentation.
- Incidence pseudographs, open and closed regions, ordered labeling of multilevel images.
- Introduction to topology. Basic topological concepts. Definition of continuous as well as digital curve. Jordan Veblen theorem.
- Euclidean and simplex complexes (triangulation). Topological definition of surfaces and their classification. Combinatorial results. Regular tilings.
- Estimation and computation of geometric and topological properties of digital sets: volume, surface, area, perimeter, length, curvature, Euler characteristic, etc.
- Digital straight segment recognition, digital straightness, digital convex hull and its computation.
- Image deformations: Thinning, 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****Assessment methods**- Written test, oral exam. Obligatory attandance at exercises. Homework score.
**Language of instruction**- Czech
**Further Comments**- Study Materials

The course is taught annually.

## PA170 Digital Geometry

**Faculty of Informatics**

Autumn 2009

**Extent and Intensity****Teacher(s)**- doc. RNDr. Pavel Matula, Ph.D. (lecturer)
**Guaranteed by**- prof. Ing. Jiří Sochor, CSc.

Department of Visual Computing - Faculty of Informatics

Contact Person: doc. RNDr. Pavel Matula, Ph.D. **Timetable**- Fri 10:00–11:50 C525, Fri 12:00–13:50 C525
**Prerequisites**- The basic knowledge of mathematics and graph theory is recommended.
**Course Enrolment Limitations****fields of study / plans the course is directly associated with**- there are 24 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 an object representation using a grid of points (e.g., in the form of 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: digital image, pixel, voxel, image resolution, types of grids, grid scanning
- grid point and grid cell models: adjacency, incidence, connectedness, components, component labeling algorithms.
- Digitalization: digitization models, line digitization.
- Measurement in digital images: metrics, integer-valued metrics approximating Euclidean metric, distance transform, distance measurement between sets.
- Oriented adjacency graphs: border, boundary, border tracing algorithm, holes, combinatorial results for regular graphs (grids)
- Application of graph theory in image processing, graph-cut based image segmentation.
- Incidence pseudographs, open and closed regions, ordered labeling of multilevel images.
- Introduction to topology. Basic topological concepts. Definition of continuous as well as digital curve. Jordan Veblen theorem.
- Euclidean and simplex complexes (triangulation). Topological definition of surfaces and their classification. Combinatorial results. Regular tilings.
- Estimation and computation of geometric and topological properties of digital sets: volume, surface, area, perimeter, length, curvature, Euler characteristic, etc.
- Digital straight segment recognition, digital straightness, digital convex hull and its computation.
- Image deformations: Thinning, 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****Assessment methods**- Written test, oral exam. Obligatory attandance at exercises. Homework score.
**Language of instruction**- Czech
**Further Comments**- The course is taught annually.

## PA170 Digital Geometry

**Faculty of Informatics**

Autumn 2008

**Extent and Intensity****Teacher(s)**- doc. RNDr. Pavel Matula, Ph.D. (lecturer)
**Guaranteed by**- prof. Ing. Jiří Sochor, CSc.

Department of Visual Computing - Faculty of Informatics

Contact Person: doc. RNDr. Pavel Matula, Ph.D. **Timetable**- Fri 12:00–13:50 B411, Fri 14:00–14:50 B411
**Prerequisites**- The basic knowledge of mathematics and graph theory is recommended.
**Course Enrolment Limitations****fields of study / plans the course is directly associated with**- there are 17 fields of study the course is directly associated with, display
**Course objectives**- The course brings the basic overview of digital geometry. We will discuss problems that arise from object digitalization and their representation by the set of points on a grid (e.g, digital image). Especially, we will define the basic terms (adjacency, connectedness, boundary, etc.) and show how to measure geometric as well as topologic properties of digital sets (distance, length, volume, etc.).
**Syllabus**- Digital image, pixel, voxel, image resolution
- Types of grids, grid point and grid cell models, adjacency vs. incidence, switch adjacency
- Connectedness and components, component labeling
- Digitalization
- Measurement in digital images: metrics, integer-valued metrics, regular metric, approximation to Euclidean metric, chamfer distance
- Distance transform
- Distance measurement between sets
- Digital sets: digital line, digital circle, etc.
- Boundary and border and their computation

**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.
**Assessment methods**- optional homework, written test and then oral exam
**Language of instruction**- Czech
**Further Comments**- Study Materials

The course is taught annually.

## PA170 Digital Geometry

**Faculty of Informatics**

Autumn 2007

**Extent and Intensity****Teacher(s)**- doc. RNDr. Pavel Matula, Ph.D. (lecturer)

doc. RNDr. Petr Matula, Ph.D. (lecturer) **Guaranteed by**- prof. Ing. Jiří Sochor, CSc.

Department of Visual Computing - Faculty of Informatics

Contact Person: doc. RNDr. Pavel Matula, Ph.D. **Timetable**- Mon 15:00–15:50 B204, Mon 16:00–17:50 B204
**Prerequisites**- The knowledge of mathematics fundamentals and graph theory is recommended.
**Course Enrolment Limitations****fields of study / plans the course is directly associated with**- there are 17 fields of study the course is directly associated with, display
**Course objectives**- The course brings the basic overview of digital geometry. We will discuss problems that arise from object digitalization and their representation by the set of points on a grid (e.g, digital image). Especially, we will define the basic terms (adjacency, connectedness, boundary, etc.) and show how to measure geometric as well as topologic properties of digital sets (distance, length, volume, etc.).
**Syllabus**- Basics: digital image, pixel, voxel, image resolution
- Grids: grid point and grid cell models
- Adjacency vs. incidence, switch adjacency
- Connectedness and components, component labeling
- Digitalization models
- Measurement in digital images: metrics, integer-valued metrics, regular metric, approximation to Euclidean metric, chamfer distance
- Distance transform
- Distance measurement between sets: Hausdorf metric and its computation
- Digital sets: digital line, digital circle, etc.
- Adjacency graphs and incidence pseudographs
- Boundary and border and their computation

**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.
**Assessment methods**(in Czech)- Přenášky v češtině. Povinná účast na cvičeních, domácí úkoly. Písemná zkouška.
**Language of instruction**- Czech
**Follow-Up Courses****Further Comments**- Study Materials

The course is taught annually. **Teacher's information**- http://cbia.fi.muni.cz

## PA170 Digital Geometry

**Faculty of Informatics**

Autumn 2006

**Extent and Intensity****Teacher(s)**- doc. RNDr. Pavel Matula, Ph.D. (lecturer)

doc. RNDr. Petr Matula, Ph.D. (lecturer) **Guaranteed by**- prof. Ing. Jiří Sochor, CSc.

Department of Visual Computing - Faculty of Informatics

Contact Person: doc. RNDr. Pavel Matula, Ph.D. **Timetable**- Mon 17:00–17:50 B011, Tue 17:00–18:50 B204
**Prerequisites**- The knowledge of mathematics fundamentals and graph theory is recommended.
**Course Enrolment Limitations****fields of study / plans the course is directly associated with**- Applied Informatics (programme FI, N-AP)
- Informatics (programme FI, N-IN)
- Upper Secondary School Teacher Training in Informatics (programme FI, N-SS) (2)

**Course objectives**- The course brings the basic overview of digital geometry. We will discuss problems that arise from object digitalization and their representation by the set of points on a grid (e.g, digital image). Especially, we will define the basic terms (adjacency, connectedness, boundary, etc.) and show how to measure geometric as well as topologic properties of digital sets (distance, length, volume, etc.).
**Syllabus**- Basics: digital image, pixel, voxel, image resolution
- Grids: grid point and grid cell models
- Adjacency vs. incidence, switch adjacency
- Connectedness and components, component labeling
- Digitalization models
- Measurement in digital images: metrics, integer-valued metrics, regular metric, approximation to Euclidean metric, chamfer distance
- Distance transform
- Distance measurement between sets: Hausdorf metric and its computation
- Digital sets: digital line, digital circle, etc.
- Adjacency graphs and incidence pseudographs
- Boundary and border and their computation

**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.
**Assessment methods**(in Czech)- Přenášky v češtině. Povinná účast na cvičeních, domácí úkoly. Písemná zkouška.
**Language of instruction**- Czech
**Follow-Up Courses****Further Comments**- The course is taught annually.
**Teacher's information**- http://lom.fi.muni.cz

## PA170 Digital Geometry

**Faculty of Informatics**

Autumn 2020

The course is not taught in Autumn 2020

**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 **Prerequisites**- The basic knowledge of mathematics and graph theory is recommended.
**Course Enrolment Limitations****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****Learning outcomes****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)
- 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****Assessment methods**- Written test, oral exam. Obligatory attendance at exercises. Homework score.
**Language of instruction**- English
**Further Comments**- The course is taught once in two years.

The course is taught: every week.

## PA170 Digital Geometry

**Faculty of Informatics**

Autumn 2018

The course is not taught in Autumn 2018

**Extent and Intensity****Teacher(s)**- doc. RNDr. Pavel Matula, Ph.D. (lecturer)

doc. RNDr. Petr Matula, Ph.D. (assistant) **Guaranteed by**- doc. RNDr. Petr 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 **Prerequisites**- The basic knowledge of mathematics and graph theory is recommended.
**Course Enrolment Limitations****fields of study / plans the course is directly associated with**- there are 23 fields of study the course is directly associated with, display
**Course objectives****Learning outcomes****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)
- 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****Assessment methods**- Written test, oral exam. Obligatory attandance at exercises. Homework score.
**Language of instruction**- Czech
**Further Comments**- The course is taught once in two years.

The course is taught: every week.

## PA170 Digital Geometry

**Faculty of Informatics**

Autumn 2016

The course is not taught in Autumn 2016

**Extent and Intensity****Teacher(s)**- doc. RNDr. Pavel Matula, Ph.D. (lecturer)

doc. RNDr. Petr Matula, Ph.D. (assistant) **Guaranteed by**- doc. RNDr. Petr 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 **Prerequisites**- The basic knowledge of mathematics and graph theory is recommended.
**Course Enrolment Limitations****fields of study / plans the course is directly associated with**- there are 23 fields of study the course is directly associated with, display
**Course objectives****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)
- 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****Assessment methods**- Written test, oral exam. Obligatory attandance at exercises. Homework score.
**Language of instruction**- Czech
**Further Comments**- The course is taught once in two years.

The course is taught: every week.

## PA170 Digital Geometry

**Faculty of Informatics**

Autumn 2014

The course is not taught in Autumn 2014

**Extent and Intensity****Teacher(s)**- doc. RNDr. Pavel Matula, Ph.D. (lecturer)

doc. RNDr. Petr Matula, Ph.D. (assistant) **Guaranteed by**- doc. RNDr. Petr 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 **Prerequisites**- The basic knowledge of mathematics and graph theory is recommended.
**Course Enrolment Limitations****fields of study / plans the course is directly associated with**- there are 22 fields of study the course is directly associated with, display
**Course objectives****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)
- 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****Assessment methods**- Written test, oral exam. Obligatory attandance at exercises. Homework score.
**Language of instruction**- Czech
**Further Comments**- The course is taught once in two years.

The course is taught: every week.

## PA170 Digital Geometry

**Faculty of Informatics**

Autumn 2012

The course is not taught in Autumn 2012

**Extent and Intensity****Teacher(s)**- doc. RNDr. Pavel Matula, Ph.D. (lecturer)
**Guaranteed by**- prof. Ing. Jiří Sochor, CSc.

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**- Fri 10:00–11:50 C525, Fri 12:00–12:50 B311
**Prerequisites**- The basic knowledge of mathematics and graph theory is recommended.
**Course Enrolment Limitations****fields of study / plans the course is directly associated with**- there are 22 fields of study the course is directly associated with, display
**Course objectives****Syllabus**- Basic terms: digital image, pixel, voxel, image resolution, types of grids, grid scanning
- Digitalization: digitization models, line digitization.
- Application of graph theory in image processing, graph-cut based image segmentation.
- Incidence pseudographs, open and closed regions, ordered labeling of multilevel images.
- Digital straight segment recognition, digital straightness, digital convex hull and its computation.
- Image deformations: Thinning, 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****Assessment methods**- Written test, oral exam. Obligatory attandance at exercises. Homework score.
**Language of instruction**- Czech
**Further Comments**- Study Materials

The course is taught once in two years.

- Enrolment Statistics (recent)