Subject: Mathematical models in computer vision (17.0M516 )
Study programmes of the course:
| Type of studies | Title |
|---|---|
| Master Academic Studies | Mathematics in Engineering (Year: 2, Semester: Winter) |
Acquisition and understanding of basic theoretical and practical knowledge from different areas of mathematics so that students can fully master selected techniques used in image processing and analysis of objects on it, as well as appropriate applications based on shape analysis. The character of the subject is applicative; by acquiring and understanding the appropriate mathematical apparatus, through the analysis of real data from practice, students will be able to work in a team and apply the acquired knowledge in various tasks that are realized in cooperation with the industry.
The acquired knowledge is the basis for understanding image processing and analysis of objects in the image from the aspect of shape analysis. Using the acquired knowledge, the student will be fully able to abstract problems from practice, find a suitable mathematical model, and finally successfully solve or improve the solution of the problem that was the subject of study or research.
Vector, metric, normed and topological space, half-space, hyperplane. 2D and 3D transformations (isometric, affine, projective and similarity transformations). Matrices, quaternions, octonions, translation, rotation, symmetries, projections, transvection. Digital representation of images (raster images, vector images). Tools and techniques for image preprocessing and processing. Viewing in 3D: projections. Synthetic camera model. Conceptual and practical viewing, models. Networks. Image segmentation, mathematical morphology, extraction of objects in the image. Point clouds and scene graphs. Lighting and shading, texture synthesis and texture mapping, rasterization and cropping. Curves and surfaces in space (Bezier curves, splines, NURBS, rendering of curves and surfaces). Shape, fuzzy shape, describing and shape descriptors. Topological and geometric characteristics of shapes and corresponding invariants. Moments, moment invariants, numerical characterization of shape descriptors, shape measure. Shape invariants, shape feature vector and its application in tasks of classification, object registration, machine learning and computer vision.
Lectures. Consultations. Students work and pass the practical part of the material in the computer laboratory by solving mandatory tasks that are graded. Programming is implemented in the programming languages Python and Matlab. Students can do additional tasks and earn extra points there. The agreed part of the material (which makes up the methodological unit) is presented orally and submitted in written form as a seminar paper. Through study and research work, the student independently, using additional scientific and professional literature, deepens knowledge in certain areas. Part of the material that makes up the methodological unit can be taken in the form of partial exam obligations that are an integral part of the exam. Partial parts of the exam obligations are taken in written form. The oral part of the final exam as well as the practical part are eliminatory.
| Authors | Title | Year | Publisher | Language |
|---|---|---|---|---|
| 2006 | English | |||
| 2007 | English | |||
| 2012 | English | |||
| 2006 | English | |||
| 2013 | English |
| Course activity | Pre-examination | Obligations | Number of points |
|---|---|---|---|
| Exercise attendance | Yes | Yes | 5.00 |
| Practical part of the exam - tasks | No | Yes | 40.00 |
| Lecture attendance | Yes | Yes | 5.00 |
| Projektni zadatak | Yes | Yes | 20.00 |
| Oral part of the exam | No | Yes | 20.00 |
| Term paper | Yes | Yes | 10.00 |
Asst. Prof. Ilić Vladimir
Assistant Professor
Lectures
Assistant - Master Tošić Stefan
Assistant - Master
Practical classes
Faculty of Technical Sciences
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© 2024. Faculty of Technical Sciences.