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Computer Graphics and Image Processing

Subheadings:

Image processing in microscopy

Annotation:
Microscopy is one of the most important techniques used in current biomedical research. The analysis of images taken with a microscope has its own specifics, which are necessary to know in order for this analysis to be correct and effective. The candidate will get acquainted with microscopy, microscopic techniques and algorithms used in this field.

Keywords:
Image formation in microscopy; image correction; signal quantification; basic imaging techniques; colocalization; principles of multidimensional imaging; image restoration; time series analysis; motion tracking.

Basic study material:
Qiang Wu, Fatima A. Merchant, and Kenneth R. Castelman, Microscope Image Processing, Academic Press, 2008. Chapters: 1, 2, 12, 14, 15 (total 188 pages)

Examiner: prof. RNDr. Michal Kozubek, Ph.D. , doc. RNDr. Pavel Matula, Ph.D. , doc. RNDr. Petr Matula, Ph.D.

Other recommended literature:
Kenneth R. Castleman, Digital Image Processing, Upper Saddle River: Prentice Hall, 1996.
James B. Pawley (ed.), Handbook of biological confocal microscopy, 3rd edition, New York: Springer, 2006.

Connected operators

Annotation:
Connected operators are a class of operators in the field of mathematical morphology. Their main feature is that their application cannot create new contours or change the position of existing contours between regions. The candidate will get acquainted with the mathematical properties of connected operators, ways of their use for simplification and segmentation of the image and possible ways of their effective implementation.

Keywords:
Definitions and properties of continuous operators; tree structures to represent them; pruning strategies that preserve the arrangement; image reconstruction using continuous operators (levelings); hierarchical segmentation; examples of use in practice.

Basic study material:
Laurent Najman and Hugues Talbot (eds.), Mathematical morphology: From Theory to Applications, John Wiley & Sons, 2010. Chapters 1, 7, 8 and 9 (total 121 pages).

Examiner: doc. RNDr. Petr Matula, Ph.D.

Other recommended literature:
Serra J. Tutorial on Connective Morphology. IEEE Journal of Selected Topics in Signal Processing 2012; 6: 739–752.
Salembier P, Oliveras A, Garrido L. Antiextensive connected operators for image and sequence processing. IEEE Transactions on Image Processing 1998; 7: 555–70.
Salembier P, Garrido L. Binary partition tree as an efficient representation for image processing, segmentation, and information retrieval. IEEE Transactions on Image Processing 2000; 9: 561–576.

Image segmentation using active contours

Annotation:
Active contours solve image segmentation as a minimization task. The basic models include geodetic active contours and active contours without edges. The candidate will get acquainted in detail with the segmentation using these models and the basic ways of finding the minimum contour. In contrast to the master's degree, emphasis is placed on a deeper understanding of the subject.

Keywords:
Active contours without edges, geodesic active contours, level-set methods, segmentation using graph cuts.

Basic study material:
Appleton, B., & Talbot, H. (2006). Globaly Minimal Surfaces by Continuous Maximal Flows. IEEE Transactions on Pattern Analysis and Machine Intelligence, 28 (1), 106–118. Stanley Osher, Ronald Fedkiw, Level Set Methods and Dynamic Implicit Surfaces, Springer, 2002.
T. Chan and L. Vese, “An active contour model without edges,” in Scale-Space Theories in Computer Vision, 1999, pp. 141–151. 13.
C.Xuand JL Prince, “Snakes, shapes and gradient vector flow,” IEEE Transaction on Image Processing, Vol. 7, no. 3, pp. 359– 369, 1998. 34.

Examiner: doc. RNDr. Pavel Matula, Ph.D.

Image segmentation using graph theory

Annotation:
A digital image can be represented using a graph, where nodes correspond to pixels and edges to relationships between pixels. Graph theory offers many efficient algorithms for solving optimization problems (eg finding the minimum spanning tree, the shortest paths or the minimal cuts). These algorithms are increasingly being used to solve the problem of image segmentation. The candidate will get acquainted with basic segmentation models that can be effectively solved using graph theory.

Keywords:
segmentation by finding the minimum spanning trees, segmentation by finding the minimal cuts (Markov random fields), segmentation by finding the shortest paths, discussion of applicability of methods

Basic study material:
Bo Peng, Lei Zhang, David Zhang, A survey of graph theoretical approaches to image segmentation, Pattern Recognition, Volume 46, Issue 3, March 2013, Pages 1020-1038 and referenced works.

Examiner: doc. RNDr. Pavel Matula, Ph.D.

Frequency analysis

Annotation:
Frequency analysis is a set of methods that help to properly process and analyze image data. Its importance is especially evident in the field of image and video compression. Frequency analysis provides a different view of commonly available image data to make it easier to detect otherwise difficult to detect significant patterns or anomalies. The candidate will get acquainted with the selected basic method, its specifics and will be able to explain how it can be optimized and how to use it to solve specific tasks in the field of image or video processing.

Keywords:
Orthogonal transformations (Fourier, Wavelet, Z-transform) and their importance in image and video processing; effective implementation of orthogonal transformations; transformations in higher dimensions; transformations in polar or spherical coordinates; mutual relations between transformations.

Basic study material:
Bracewell RN. The Fourier transform and its applications. 3rd ed. Boston: McGraw Hill, 2000. xx, 616. ISBN 0073039381
Strang G and Nguyen T. Wavelets and filter banks. Wellesley: Wellesley-Cambridge Press, 1996. xxi, 490. ISBN 0961408871
Sweldens, W. The Lifting Scheme: A Construction of Second Generation Wavelets. Journal on Mathematical Analysis. 29 (2): 511–546. 1997


Examiner: doc. RNDr. David Svoboda, Ph.D.

Geometric data structures I

Annotation:
Computational geometry data structures and algorithms are used to solve difficult problems in computer graphics. Based on them, algorithms have been developed in computer graphics that are both time and memory efficient. A wide range of data structures and algorithms will be creatively applied in solving existing and new problems associated primarily with the processing and visualization of large data.

Keywords:
Quadrant and octal trees, complexity and construction, orthogonal window and range queries, interval, segment, range and kd trees, BSP trees, complexity and construction. Distance fields, Voronoi diagrams.

Basic study material:
Elmar Langetepe, Gabriel Zachmann, Geometric Data Structures for Computer Graphics, A K Peters, Wellesley, Massachusetts, 2006. Chap. 1-6 (pp.1-146).

Examiner: prof. Ing. Jiří Sochor, CSc. , doc. RNDr. Barbora Kozlíková, Ph.D., RNDr. Jan Byška, Ph.D., Mgr. Jiří Chmelík, Ph.D.

Other recommended literature:
de Berg, M., Cheong, O., van Kreveld, M., Overmars, M., Computational Geometry: Algorithms and Applications, 3rd ed. 2008, XII, 386p.

Geometric data structures II

Annotation:
Computational geometry data structures and algorithms are used to solve difficult problems in computer graphics. Based on them, algorithms have been developed in computer graphics that are efficient in terms of time and memory. A wide range of data structures and algorithms will be creatively applied in solving existing and new problems associated primarily with the processing and visualization of large data.

Keywords:
Graphs of geometric proximity, surfaces from point clouds, intersections of point clouds, kinetic data structures, instability and robustness, dynamization of geometric data structures.

Basic study material:
Elmar Langetepe, Gabriel Zachmann, Geometric Data Structures for Computer Graphics, A K Peters, Wellesley, Massachusetts, 2006. Chap.7-10 (pp.147-314)

Examiner: prof. Ing. Jiří Sochor, CSc. , doc. RNDr. Barbora Kozlíková, Ph.D., RNDr. Jan Byška, Ph.D., Mgr. Jiří Chmelík, Ph.D.

Other recommended literature:
de Berg, M., Cheong, O., van Kreveld, M., Overmars, M., Computational Geometry: Algorithms and Applications, 3rd ed. 2008, XII, 386p.

Monte Carlo methods in computer graphics

Annotation:
Monte Carlo methods are used for solving problems from various fields, especially where analytical solution of problems associated with, for example, the evaluation of multidimensional integrals is difficult or impossible. In computer graphics, they are used mainly in solving global lighting problems, in the form of random walks and sampling according to importance.

Keywords:
Random sampling, Monte Carlo evaluation of integrals with finite dimension, random walk, integral equations, variance reduction, simulation of stochastic systems, radiance transfer, pseudorandom numbers.

Basic study material:
Kalos, MH and Whitlock, PA (2007) Monte Carlo Methods, Wiley-VCH Verlag GmbH, Weinheim, Germany, 186 p.

Examiner: prof. Ing. Jiří Sochor, CSc. , doc. RNDr. Barbora Kozlíková, Ph.D., RNDr. Jan Byška, Ph.D., Mgr. Jiří Chmelík, Ph.D.

Other recommended literature:
DEKnuth. The Art of Computer Programming, Vol.2: Semi-numerical Algorithms, Addison-Wesley, Reading, Massachusetts, 1969.

Global lighting

Annotation:
Algorithms for calculating global illumination are constantly evolving and enriching themselves with new physically based models of light propagation in various environments. Their study is a basic prerequisite for the development of new effective methods of realistic scene rendering.

Keywords:
Physical models of light transmission, Monte Carlo methods, light transmission calculations, stochastic path tracking.

Basic study material:
P.Dutré, K. Bala, P. Bekaert. Advanced Global Illumination. A K Peters, Wellesley, Massachusetts, 2nd ed., 2006. Chap. 1-5 (pp. 1-150)

Examiner: prof. Ing. Jiří Sochor, CSc. , doc. RNDr. Barbora Kozlíková, Ph.D., RNDr. Jan Byška, Ph.D., Mgr. Jiří Chmelík, Ph.D.

Other recommended literature:
A.Glassner: Principles of Digital Image Synthesis, Vol.I, II. Morgan Kaufmann, San Francisco, California, 1995.

Volumetric graphics

Annotation:
Volumetric data, which come from various areas and are obtained by measurements, calculations, simulations, often contain essential and interesting information that needs to be uncovered. Volume data graphics deals with the segmentation and visualization of this information, which can be presented as solids and surfaces, or light-differentiated spatial areas.

Keywords:
Physical model of light transmission, integral equations of volume rendering, methods of rendering using GPU, transfer functions, local lighting, global lighting.

Basic study material:
Engel, Klaus; Hadwiger, Markus; Kniss, Joe; Rezk-Salama, Christof; Weiskopf, Daniel. Real-Time Volume Graphics; A K Peters, Ltd .; 497 pages, 2006. ISBN 1-56881-266-3. Chap.1-6 (pp.1-162)

Examiner: prof. Ing. Jiří Sochor, CSc. , doc. RNDr. Barbora Kozlíková, Ph.D., RNDr. Jan Byška, Ph.D., Mgr. Jiří Chmelík, Ph.D.

Other recommended literature:
P.Dutré, K. Bala, P. Bekaert. Advanced Global Illumination. A K Peters, Wellesley, Massachusetts, 2nd ed., 2006.

Numerical mathematics

Annotation:
Numerical methods are key to solving many mathematical problems on a computer. An understanding of their principles and a detailed knowledge of their limitations and accuracy are necessary for their proper use. The aim of the module is to enable the candidate to study parts of numerical mathematics according to their own focus beyond the scope of regular master's courses. Emphasis will be placed on theoretical mastery of the studied topic.

Keywords:
The subject of the exam will be the study of numerical mathematics topics beyond the framework of regular master's courses (especially courses PřF: M4180 and PřF: M5180) in agreement with the examiner. Suitable topics include: solving linear/nonlinear systems of equations, methods of numerical integration/derivation, approximation and interpolation of functions, methods of calculating eigenvalues and vectors, or numerical solution of differential equations.

Basic study material:
It will be specified according to the chosen topic and focus of the student after discussion with the examiner.

Examiner: prof. RNDr. Ivanka Horová, CSc. , Mgr. Jiří Zelinka, Dr.

Virtual Reality

Annotation:
Virtual Reality (VR), sometimes referred to as immersive multimedia, is a computer-simulated environment that can simulate physical presence in places in the real world or imagined worlds. Virtual reality can recreate sensory experiences, which include virtual taste, sight, smell, sound, and touch. Virtual Reality technologies have advanced to the point that it is possible to develop and deploy meaningful, productive applications. The focus remains squarely on the application of VR and the many issues that arise in the application design and implementation, including hardware requirements, system integration, interaction techniques, and usability. This topic also includes both exaggerated claims for VR and the view that would reduce it to entertainment, citing dozens of real-world examples from many different fields and presenting four in-depth application case studies.

Outline:
Virtual reality, augmented reality, user interfaces, displays, rendering, immersion, future of virtual reality.

The basic study material:
William R. Sherman, Alan B. Craig, Understanding Virtual Reality: Interface, Application, and Design, The Morgan Kaufmann Series in Computer Graphics, September 18, 2002. (ISBN-13: 978-1558603530)

Examiners: doc. RNDr. Barbora Kozlíková, Ph.D., RNDr. Jan Byška, Ph.D., Mgr. Jiří Chmelík, Ph.D.