Subject: Digital Geometry (17.D0M28L )
Native organizations units: Department of Fundamentals Sciences
Study programmes of the course:
| Type of studies | Title |
|---|---|
| Doctoral Academic Studies | Mathematics in Engineering (Year: 1, Semester: Summer) |
The educational objective of the course is to introduce basic concepts of digital geometry, main topological and metric properties of digital spaces, representations and properties of discrete sets, and basics of mathematical morphology with some applications. The suggested topics may be of interest from both theoretical and practical aspects. They offer a possibility to study a mathematical theory related to digital space, nowadays forced upon us by the intensive presence of computers in our everyday life. In addition, a variety of possible applicatanios is suggested, and can be explored as well. The course is an introduction to any image processing and computer graphics course.
Understanding of digital spaces and their specificities. Theoretical knowledge about digital objects which can be both further theoretically studied and developed, and applied in various fields of computer science, in particular in image processing and computer graphics.
1. Introduction: Discretization, digitization. Tessellations and grids. Voronoi cells and Delaunay triangulation. Regular and semi-regular grids. 2. Digital spaces: Basic definitions. Interior and exterior. Neighbourhoods. Connectedness. Topological digital spaces. 3. Representations of some geometrical entities; Digitization of a continuous line. Characterization of a digital straight line segment. Digital circles. Digital set (shape) representation and description. 4. Metric properties of discrete sets; Measuring length, area, surface area, volume. Local and global approaches. Multigrid convergence. 5. Mathematical morphology; Basic morphological concepts. Binary erosion and dilation. Thinning, thickening, skeletonization, convex hull. 6. Distance transforms. Distance transforms in a square grid (path generated distance transforms, weighted distance transforms, Euclidean distance transforms). Application of distance transforms. Part of the course is organized in the form of independent study and research work in the field of discrete mathematics and digital geometry. The study and research work involves active study of primary scientific sources, organization and conduction of experiments and statistical data analysis, numerical simulations, and possibly writing a paper in the filed of mathematics.
Lectures. Consultations. The lectures are organized in combined form. The presentation of the theoretical part during the lecture classes is followed by the characteristic examples which contribute to better understanding of the subject matter. In addition to lectures there are regular consultations. Through research and study work the student will, on the bases of scientific journals and other relevant literature that has been studied independently, develop further understanding of the material covered in lectures. Working with the course teacher the student develops the ability to independently work on a scientific paper.
| Authors | Title | Year | Publisher | Language |
|---|---|---|---|---|
| razni | Odabrani stručni materijal (naučni radovi, izvodi iz predavanja i sl.) | sve | English | |
| 1998 | English | |||
| 2001 | English |
| Course activity | Pre-examination | Obligations | Number of points |
|---|---|---|---|
| Lecture attendance | Yes | Yes | 10.00 |
| Term paper | Yes | Yes | 20.00 |
| Oral part of the exam | No | Yes | 70.00 |
Prof. Čomić Lidija
Full Professor
Lectures
Prof. Čomić Lidija
Full Professor
Study research work
Faculty of Technical Sciences
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© 2024. Faculty of Technical Sciences.