Space research

The research group focuses on following areas of space research:

• Image processing

• Image analysis

• Experiment planning

• Software for imaging systems control

• Design of imaging systems

The scientific group mainly deals with applied research in the field of numerical methods of digital image analysis. Long-term cooperation (since 2007) with the team of prof. Shadia Habbal is essential for the group's work. Shadia Habbal is the leading person of the solar corona research at the Institute for Astronomy, University of Hawaii.

The task of the mathematicians from the Institute of Mathematics FME BUT in Brno is not only mathematical processing of experimental data, which are images of the solar corona obtained by space probes SDO (NASA, Solar Dynamics Observatory), SOHO (NASA, ESA Solar and Heliospheric Observatory), STEREO (NASA, Solar Terrestrial Relations Observatory) and Solar Orbiter (ESA, NASA), but also acquisition and processing of data obtained during total solar eclipses.

Together with the University of Hawaii, more than 50 scientific papers were created, some of which contain important discoveries in the field of solar physics, such as the discovery of previously unknown structures in the solar corona caused by various plasma instabilities, finding the boundary between collisional and collisionless plasma, finding that coronal cavities above the prominences are filled with hot plasma and creating the first temperature map of the solar corona based on observations of Fe and Ni ions. Newly developed mathematical methods of image processing and analysis played a crucial role in all of the above discoveries.

A world-leading position has been achieved by the team in the research of Fe and Ni forbidden lines in the solar corona in the visible and near-infrared parts of the spectrum during total solar eclipses. Numerical methods NAFE (Noise Adaptive Fuzzy Equalization, Druckmüller) and MGN (Multi-Scale Gaussian Normalization, Morgan, Druckmüller) have become standard methods for visualizing of images taken by the SDO space probe in the EUV region of the spectrum.

Analysis of movements and changes in digital images is a new area in which the team has expanded its research. The first published result is the determination of the differential rotation of the Sun based on images from the HMI detector of the SDO space probe with a time step of 45 s. This was made possible by developing a new high-precision modification of the phase correlation method.

More information:
http://www.zam.fme.vutbr.cz/~druck/Eclipse/index.htm
http://www.zam.fme.vutbr.cz/~druck/SDO/Pm-nafe/Archive.htm

Members:
Miloslav Druckmüller, Pavel Štarha, Jana Hoderová, Hana Druckmüllerová, Pavel Mikuláček

Image and spatial data analysis

Our research team actively investigates and implements standard image processing methods such as filtering and segmentation, with an emphasis on optimizing performance and accuracy. In the area of filtering, we focus on classical techniques such as Gaussian filtering, median filtering, or Laplacian operation, and explore their applications in noise removal and image enhancement. Segmentation is another important area of our interest, where we utilize methods such as thresholding, morphological operations, and edge detectors for identifying and separating individual objects or structures in the image.

As well as traditional methods, our research team is also exploring the use of artificial intelligence methods for image analysis in collaboration with the AI research group. We use deep learning and neural networks to enhance the capabilities of our systems, particularly in areas such as object detection, semantic segmentation and image classification. By combining classical techniques with the power of neural networks, we aim to develop more robust and adaptive solutions that can process diverse visual data with greater accuracy and efficiency. This hybrid approach allows us to harness the power of both traditional image processing methods and modern deep learning techniques.

Our research team also specializes in the development of advanced methods for processing 3D data from various sources such as 3D scanners, lidars, and x-rays. We use algorithms based on edge detectors, complementary image segmentation, and pattern recognition to detect objects and structures in 3D data, enabling the identification and extraction of key features from spatial data. These methods allow us to analyze and visualize 3D scenes with high accuracy, which has wide applications in various fields from industry to scientific research.

Members:
Pavel Štarha, Jana Procházková, Pavel Loučka

Artificial Intelligence

The research group focuses on various areas of artificial intelligence, including:

• Machine learning

• Computer vision

• Natural language processing

• Robotics

• Expert systems

• Game theory

• Autonomous systems

• Explainability

• Optimization

The group also compares these methods with statistical approaches in specific applications for optimization of control and calculations. Due to the group's affiliation with the Department of Mathematics, the problems they solve are mainly from the field of mechanical engineering. The group members collaborate with other departments at the faculty, as well as with the private sector, to apply their methods in real-world applications.

The group members participate in national projects (GAČR and TAČR) and international projects (COST). They publish their results in scientific journals and present them at conferences. They also contribute to the development of academic life by organizing seminars and conferences, serving on editorial boards of scientific journals, and supervising bachelor's and master's thesis.

Collaboration Opportunities:

The group is open to collaboration in all of the mentioned areas, as well as in addressing new challenges in artificial intelligence. The members of the group are able to flexibly respond to the needs of research and the market. They are strongly open to collaborating with experts in the mentioned fields, whether within the departments of the Faculty of Mechanical Engineering, other faculties or universities in the Czech Republic or abroad. Since the group is known for its practical applications, they particularly welcome the opportunity to collaborate with companies and the private sector, where basic research can be transformed into applied research with practical use. Current collaborations include those with the Department of Computer Science and Automation at FME, the University of Defence, and the ARICOMA company.

The group also offers opportunities for collaboration on student theses, which range from basic research to applied research and prototyping. These projects are either directly related to the ongoing research or are carried out in collaboration with the private sector.

Members:
Petr Vašík, Pavel Štarha, Jana Procházková, Jitka Zatočilová, Tomáš Kisela, Pavla Sehnalová, Pavel Hrabec, Hana Druckmüllerová, Ivan Eryganov, Matej Benko, Pavel Loučka, Pavel Mikuláček, Roman Byrtus, Anna Derevianko