Course Information

PA170 Digital Geometry

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. Martin Maška, Ph.D. (lecturer)

Guaranteed by

doc. RNDr. Martin Maška, 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

Mon 14:00–16:50 B204

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 22 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.

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

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

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)

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

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 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

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 annually.

PA170 Digital Geometry

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)

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

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 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

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 annually.

PA170 Digital Geometry

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)

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

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 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

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

The course is taught annually.

PA170 Digital Geometry

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)

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

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 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.
• Estimation and computation of geometric and topological properties of digital sets: volume, surface, area, perimeter, length, curvature, Euler characteristic, 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

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

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. (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

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 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.
• Estimation and computation of geometric and topological properties of digital sets: volume, surface, area, perimeter, length, curvature, Euler characteristic, 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

Assessment methods (in Czech)

Přenášky v češtině. Povinná účast na cvičeních, domácí úkoly. Písemná zkouška.

Language of instruction

Czech

Follow-Up Courses

• PA166 Advanced Methods of Digital Image Processing
• PA173 Mathematical Morphology

Further Comments

Study Materials
The course is taught annually.

Teacher's information

http://cbia.fi.muni.cz

PA170 Digital Geometry

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. (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

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

• 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.
• Estimation and computation of geometric and topological properties of digital sets: volume, surface, area, perimeter, length, curvature, Euler characteristic, 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

Assessment methods (in Czech)

Přenášky v češtině. Povinná účast na cvičeních, domácí úkoly. Písemná zkouška.

Language of instruction

Czech

Follow-Up Courses

• PA166 Advanced Methods of Digital Image Processing
• PA173 Mathematical Morphology

Further Comments

The course is taught annually.

Teacher's information

http://lom.fi.muni.cz

PA170 Digital Geometry

The course is not taught in Autumn 2024

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).
In-person direct teaching

Teacher(s)

doc. RNDr. Martin Maška, Ph.D. (lecturer)

Guaranteed by

doc. RNDr. Martin Maška, 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 28 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

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

The course is not taught in Autumn 2022

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

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

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

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

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

The course is not taught in Autumn 2018

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

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

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

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

The course is taught once in two years.
The course is taught: every week.

PA170 Digital Geometry

The course is not taught in Autumn 2016

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

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

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

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

The course is taught once in two years.
The course is taught: every week.

PA170 Digital Geometry

The course is not taught in Autumn 2014

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

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 22 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.

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

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

The course is taught once in two years.
The course is taught: every week.

PA170 Digital Geometry

The course is not taught in Autumn 2012

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)

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

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 22 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

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.

• Enrolment Statistics (recent)