# FI:PA170 Digital Geometry - Course Information

## PA170 Digital Geometry

**Faculty of Informatics**

Autumn 2011

**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

- 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 annually.

- Enrolment Statistics (Autumn 2011, recent)
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