PA170 Digital Geometry

Faculty of Informatics
Autumn 2023
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.
The course is also listed under the following terms Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2013, Autumn 2015, Autumn 2017, Autumn 2019, Autumn 2021.
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