## PA170 Digital Geometry

Faculty of Informatics
Autumn 2007
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
• 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