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Detection and Recognition of Matrix Code in Real Time
Dobrovolný, Martin ; Juránková, Markéta (referee) ; Herout, Adam (advisor)
This work is dealing with detecting and recongnizing matrix codes. It is experimenting use of PCLines algorithm. PCLines is using Hough transform and parallel coordinates for fast detection of lines. Suggested algorithm with double use PCLines detects sets of parallels and problem with image distorted by with parallel projection is solved by cross-ratio equation. We did some optimizations for realtime running and created experimental implementation. Test results shows, that use PCLines one way to detect matrix codes.
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Detection and Recognition of Matrix Code in Real Time
Dobrovolný, Martin ; Juránková, Markéta (referee) ; Herout, Adam (advisor)
This work is dealing with detecting and recongnizing matrix codes. It is experimenting use of PCLines algorithm. PCLines is using Hough transform and parallel coordinates for fast detection of lines. Suggested algorithm with double use PCLines detects sets of parallels and problem with image distorted by with parallel projection is solved by cross-ratio equation. We did some optimizations for realtime running and created experimental implementation. Test results shows, that use PCLines one way to detect matrix codes.
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Geometrochemistry vs Soft Computing of Mendeleev's Brain
Gottvald, Aleš
The role of projective geometry in nature remains somewhat enigmatic for centuries. It is very strange indeed, as the projective geometry is the mother of all geometries with more restrictive symmetry groups, as clearly recognized yet by seminal insights of Felix Klein, Arthur Cayley, Paul Dirac and other eminent scientists. We usually imagine that Euclidean geometry is primary for the geometrization of our (nonrelativistic) spaces, and the Euclidean-Pythagorean metric is natural for measuring the distances in such a space. However, how to measure distances in spaces associated with statistical thermodynamics or quantum mechanics? We show that projective geometry and associated "geometrochemistry" is manifest in nature. In particular, it offers a novel soft-computing rationale for recovering basic structure of Mendeleev's periodic table of chemical elements, and elucidates some mysteries of brain information processing, including a new understanding of Artificial Neural Networks.
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Projective Geometry and the Law of Mass Action
Gottvald, Aleš
A new law of nature asserts that chemical equilibria and chemical kinetics are governed by fundamental principles of projective geometry. The equilibrium constans of chemical reactions are the invariants of projective geometry in disguise. Chemical reactions may geometrically be represented by incidence structures, which are preserved under projective transformations. Theorems of Ceva, Menelaus, and Carnot for triangles and n-gons represent the chemical equilibria, while Routh's theorem represents non-equilibria. Intrinsically projective Riccati's differential equation, being also generic to many other equations of mathematical physics, governs parametric dependence of the equilibrium constants. The theory offers tangible geometrizations and generalizations to the Law of Mass Action, including a new projective-geometric approach to soft computing of very complex problems.
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Projektivní geometrie - náhled z vyšší dimenze
Gottvald, Aleš
Upon recognizing principal and ubiquitous role of projective geometry in theory and applications, we select some of its basic concepts and ideas (homogeneous coordinates, Möbius transformation, cross-ratio, Cayley's hyperbolic distance, ...), and show their first metamorphoses.
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Fyzika z teorie pravděpodobnosti
Gottvald, Aleš
Following basic ideas of information physics, probability theory features as the inner symmetries of physical laws. Consequently, we conjecture that many fundamental physical facts are already hidden in the unique logical structure of probability theory and need not be postulated. A link with statistical thermodynamics emerges via the exponential (MaxEnt) mapping between probability and entropy, whose scaling symmetry also makes a natural bridge to fractal physics and projective geometries. To facilitate links with many other symmetries and physical areas, the exponential mapping between Lie groups and Lie algebras is suggested as a generalization of the MaxEnt relationship. We point out that the natural space of probability theory is an intrinsically 6-dimensional manifold with two fundamental governing equations imposed, which gives a novel straightforward rationale for the emergence of the 4+6=10-dimensional hyperspace, particularly important in modern particle physics.
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