Stereo image processing system for robot vision

More and more applications (path planning, collision avoidance methods) require 3D description of the surround world. This paper describes a stereo vision system that uses 2D (grayscale or color) images to extract simple 2D geometric entities (points, lines) applying a low-level feature detector. The features are matched across views with a graph matching algorithm. During the projective reconstruction the 3D description of the scene is recovered. The developed system uses uncalibrated cameras, therefore only projective 3D structure can be detected defined up to a collineation. Using the Euclidean information about a known set of predefined objects stored in database and the results of the recognition algorithm, the description can be updated to a metric one

Emission from dielectric cavities in terms of invariant sets of the chaotic ray dynamics

In this paper, the chaotic ray dynamics inside dielectric cavities is described by the properties of an invariant chaotic saddle. I show that the localization of the far field emission in specific directions is related to the filamentary pattern of the saddle's unstable manifold, along which the energy inside the cavity is distributed. For cavities with mixed phase space, the chaotic saddle is divided in hyperbolic and non-hyperbolic components, related, respectively, to the intermediate exponential (t<t_c) and the asymptotic power-law (t>t_c) decay of the energy inside the cavity. The alignment of the manifolds of the two components of the saddle explains why even if the energy concentration inside the cavity dramatically changes from tt_c, the far field emission changes only slightly. Simulations in the annular billiard confirm and illustrate the predictions.Comment: Corrected version, as published. 9 pages, 6 figure

Chaotic Explosions

We investigate chaotic dynamical systems for which the intensity of trajectories might grow unlimited in time. We show that (i) the intensity grows exponentially in time and is distributed spatially according to a fractal measure with an information dimension smaller than that of the phase space,(ii) such exploding cases can be described by an operator formalism similar to the one applied to chaotic systems with absorption (decaying intensities), but (iii) the invariant quantities characterizing explosion and absorption are typically not directly related to each other, e.g., the decay rate and fractal dimensions of absorbing maps typically differ from the ones computed in the corresponding inverse (exploding) maps. We illustrate our general results through numerical simulation in the cardioid billiard mimicking a lasing optical cavity, and through analytical calculations in the baker map.Comment: 7 pages, 5 figure

Thermodynamic interpretation of the uniformity of the phase space probability measure

Uniformity of the probability measure of phase space is considered in the framework of classical equilibrium thermodynamics. For the canonical and the grand canonical ensembles, relations are given between the phase space uniformities and thermodynamic potentials, their fluctuations and correlations. For the binary system in the vicinity of the critical point the uniformity is interpreted in terms of temperature dependent rates of phases of well defined uniformities. Examples of a liquid-gas system and the mass spectrum of nuclear fragments are presented.Comment: 11 pages, 2 figure

Bevezetés a környezeti áramlások fizikájába

A környezettudomány és azon belül a környezetfizika egyik legnagyobb jelentőségű területét a globális környezeti áramlások vizsgálata jelenti. A környezeti áramlások (akár a légkörben vagy vizekben zajlanak, akár globális vagy lokális kiterjedésűek) környezetünk alakulásának legfontosabb mozzanataihoz tartoznak. Ide sorolhatjuk még a Földünk belsejében, elsősorban a folyékony köpenyben zajló áramlási jelenségeket is, amelyek a Föld kialakulása óta eltelt évmilliárdok alatt markánsan alakították és pillanatnyilag is alakítják a felszín viszonyait. Erről a közegről azonban a későbbiekben nem lesz szó, mert tárgyunk a Nap energiája által hajtott légköri és óceáni áramlások, amelyek nem geológiai, hanem „emberi” időskálán befolyásolják környezetünket. Az áramlási jelenségeknek környezetünk szempontjából alapvetően meghatározó a jelentősége. Gondoljunk csak a napi időjárás változásainak áramlási vonatkozásaira, a Golf-áramlatra, amely lakhatóvá teszi Európa északi övezeteit, a világtengerek más, jelentős áramlataira, vagy kisebb skálán azokra a jelenségekre, amelyek a bioszféra egy-egy szegmensének benépesülését és létezését lehetővé tették és teszik. A modern világ viszonyait kétség kívül alapvetően befolyásolják az emberi társadalmak gazdasági tevékenységét kísérő nem kívánt mellékhatások, elsősorban a környezet szennyezése. Ezek a szennyezések az áramlási folyamatok során mind a légkörben, mind a vizekben távoli területekre is eljutnak. Nem kérdéses, hogy a káros hatások megelőzésének, és a károk csökkentésének előfeltétele a kapcsolódó folyamatok megismerése, megértése, és ezek után esetleges befolyásolása

Topological Entropy : A Lagrangian Measure of the State of the Free Atmosphere

Topological entropy is shown to be a useful characteristic of the state of the free atmosphere. It can be determined as the stretching rate of a line segment of tracer particles in the atmosphere over a time span of about 10 days. Besides case studies, the seasonal distribution of the average topological entropy is determined in several geographical locations. The largest topological entropies appear in the mid- and high latitudes, especially in winter, owing to the greater temperature gradient between the pole and the equator and the more intense stirring and shearing effects of cyclones. The smallest values can be found in the trade wind belt. The local value of the topological entropy is a measure of the chaoticity of the state of the atmosphere and of how rapidly pollutants and contaminants spread from a given location

Poincare recurrences and transient chaos in systems with leaks

In order to simulate observational and experimental situations, we consider a leak in the phase space of a chaotic dynamical system. We obtain an expression for the escape rate of the survival probability applying the theory of transient chaos. This expression improves previous estimates based on the properties of the closed system and explains dependencies on the position and size of the leak and on the initial ensemble. With a subtle choice of the initial ensemble, we obtain an equivalence to the classical problem of Poincare recurrences in closed systems, which is treated in the same framework. Finally, we show how our results apply to weakly chaotic systems and justify a split of the invariant saddle in hyperbolic and nonhyperbolic components, related, respectively, to the intermediate exponential and asymptotic power-law decays of the survival probability.Comment: Corrected version, as published. 12 pages, 9 figure

Reply to E.G.D. Cohen, L. Rondoni, Physica A 306 (2002) 117

In their paper Cohen and Rondoni severely question the physical relevance of studies of transport by means of multibaker maps and other classes of dynamics considering the motion of independen particles - like e.g. the Lorentz gas. We argue that this is to a large extent due to inappropriate interpretation of the models. In particular, the arguments concerning the lack of local thermodynamic equilibrium are inconsistent for the models previously worked out by ourselves.Comment: 3 pages, revtex4 -- with a 4th item addresse