Modelling a large traffic system

The research involves modelling of large traffic systems, classification of transportation by means of clustering in density-intensity level and analysis and simulation of traffic micro-area, traffic data identification and prediction which yield the decision for traffic operators. Information about a real system (urban traffic micro-area, motorway system, railway network) is obtained by identifying measured data. The traffic model is based on optimal control methods, and it is carried out using Bayesian statistical methods.

Surveillance, intelligent vehicle and object recognition

The project deals with data acquisition and processing of parallel data from a moving car. The main objective of the study is to create a driver assistance system in an intelligent car, which identifies and recognises barriers, pedestrians and traffic signs in a real traffic scene.

A prototype of an automated navigation system for parking utilizing cameras in-built into the fifth car door (trunk) was developed in cooperation with Škoda Auto, a.s.

Approximation, higher transcendental function for DSP and digital filter design

The non-stationary nature of signals is a feature of all systems that are used to analyse speech, EEG or ECG signals, or that attempt to analyse the behaviour of human beings while driving a car, or to analyse the health of humans in medical applications.

Algebraic algorithms for Zolotarev polynomials, originally used to approximate finite impulse response (FIR) filters,  form the basis for a non-conventional transform for analysing non-stationary signals that outperforms both the fast Fourier transform, and the wavelet transform. All these types of time-frequency transforms are highly sensitive to the selection of window functions or base functions, and their results therefore do not provide comparable information about spectrum and time intervals.

History of mathematics

This research project aims to extend students’ interest in mathematics in a non-traditional way, to demonstrate the historical relations between mathematics and engineering, and to cultivate students’ technological thinking.

Geometry for Mobile Applications

The application of computer graphics in a mobile environment is a quite new phenomenon in the area of information technologies. The existing solutions usually do not go beyond adapting 3D viewers for a mobile environment, or adapting the common methods for handling 3D graphics for larger mobile devices (such as Tablet PC). Realistic interpretation of geometric scenes implies high demands for the level of geometric details within the displayed model, including the textures covering the surface of individual objects. Image-Based Rendering tries to eliminate this problem by displaying the scenes on the basis of previously taken photographs. Commonly-used techniques for simplifying 3D scenes are based on so-called billboards and impostors. The problem of rendering scenes based on image information is still popular within the computer graphics community, mainly in the area of computer entertainment and displaying large scenes.

Formal methods and critical applications

Formal methods bring an exact description of different aspects of railway transportation in a natural language and, in the formal way, with use of a number of mathematically exact algorithms. Descriptions of the railway networks (railway stations, lines), their dynamic behaviour (control of switches and signal devices for example), railway time-tables and railway traffic, resources planning (time, rolling stock, workers, maintenance), and proposals of railway security technique were developed. The research goal is to demonstrate that, with the help of mathematically exact specification formal techniques, it is possible to describe and understand a large system with strongly linked processes which undoubtedly is represented by every railway system