2,470 research outputs found

    The Local Structure of Space-Variant Images

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    Local image structure is widely used in theories of both machine and biological vision. The form of the differential operators describing this structure for space-invariant images has been well documented (e.g. Koenderink, 1984). Although space-variant coordinates are universally used in mammalian visual systems, the form of the operators in the space-variant domain has received little attention. In this report we derive the form of the most common differential operators and surface characteristics in the space-variant domain and show examples of their use. The operators include the Laplacian, the gradient and the divergence, as well as the fundamental forms of the image treated as a surface. We illustrate the use of these results by deriving the space-variant form of corner detection and image enhancement algorithms. The latter is shown to have interesting properties in the complex log domain, implicitly encoding a variable grid-size integration of the underlying PDE, allowing rapid enhancement of large scale peripheral features while preserving high spatial frequencies in the fovea.Office of Naval Research (N00014-95-I-0409

    Real-Time Anisotropic Diffusion using Space-Variant Vision

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    Many computer and robot vision applications require multi-scale image analysis. Classically, this has been accomplished through the use of a linear scale-space, which is constructed by convolution of visual input with Gaussian kernels of varying size (scale). This has been shown to be equivalent to the solution of a linear diffusion equation on an infinite domain, as the Gaussian is the Green's function of such a system (Koenderink, 1984). Recently, much work has been focused on the use of a variable conductance function resulting in anisotropic diffusion described by a nonlinear partial differential equation (PDF). The use of anisotropic diffusion with a conductance coefficient which is a decreasing function of the gradient magnitude has been shown to enhance edges, while decreasing some types of noise (Perona and Malik, 1987). Unfortunately, the solution of the anisotropic diffusion equation requires the numerical integration of a nonlinear PDF which is a costly process when carried out on a fixed mesh such as a typical image. In this paper we show that the complex log transformation, variants of which are universally used in mammalian retino-cortical systems, allows the nonlinear diffusion equation to be integrated at exponentially enhanced rates due to the non-uniform mesh spacing inherent in the log domain. The enhanced integration rates, coupled with the intrinsic compression of the complex log transformation, yields a seed increase of between two and three orders of magnitude, providing a means of performing real-time image enhancement using anisotropic diffusion.Office of Naval Research (N00014-95-I-0409

    Chandra Spectroscopy Of The Hot Star β Crucis And The Discovery Of A Pre-Main-Sequence Companion

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    In order to test the O star wind-shock scenario for X-ray production in less luminous stars with weaker winds, we made a pointed 74-ks observation of the nearby early B giant, beta Crucis (beta Cru; B0.5 III), with the Chandra High Energy Transmission Grating Spectrometer. We find that the X-ray spectrum is quite soft, with a dominant thermal component near 3 million K, and that the emission lines are resolved but quite narrow, with half widths of 150 km s(-1). The forbidden-to-intercombination line ratios of Ne IX and Mg XI indicate that the hot plasma is distributed in the wind, rather than confined near the photosphere. It is difficult to understand the X-ray data in the context of the standard wind-shock paradigm for OB stars, primarily because of the narrow lines, but also because of the high X-ray production efficiency. A scenario in which the bulk of the outer wind is shock heated is broadly consistent with the data, but not very well motivated theoretically. It is possible that magnetic channelling could explain the X-ray properties, although no field has been detected on beta Cru. We detected periodic variability in the hard (h nu \u3e 1 keV) X-rays, modulated on the known optical period of 4.58 h, which is the period of the primary beta Cephei pulsation mode for this star. We also have detected, for the first time, an apparent companion to beta Cru at a projected separation of 4 arcsec. This companion was likely never seen in optical images because of the presumed very high contrast between it and beta Cru in the optical. However, the brightness contrast in the X-ray is only 3:1, which is consistent with the companion being an X-ray active low-mass pre-main-sequence star. The companion\u27s X-ray spectrum is relatively hard and variable, as would be expected from a post-T Tauri star. The age of the beta Cru system (between 8 and 10 Myr) is consistent with this interpretation which, if correct, would add beta Cru to the roster of Lindroos binaries - B stars with low-mass pre-main-sequence companions

    The Outer Halo of the Milky Way as Probed by RR Lyr Variables from the Palomar Transient Facility

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    RR Lyr stars are ideal massless tracers that can be used to study the total mass and dark matter content of the outer halo of the Milky Way. This is because they are easy to find in the light curve databases of large stellar surveys and their distances can be determined with only knowledge of the light curve. We present here a sample of 112 RR Lyr beyond 50 kpc in the outer halo of the Milky Way, excluding the Sgr streams, for which we have obtained moderate resolution spectra with Deimos on the Keck 2 Telescope. Four of these have distances exceeding 100 kpc. These were selected from a much larger set of 447 candidate RR Lyr which were datamined using machine learning techniques applied to the light curves of variable stars in the Palomar Transient Facility database. The observed radial velocities taken at the phase of the variable corresponding to the time of observation were converted to systemic radial velocities in the Galactic standard of rest. From our sample of 112 RR Lyr we determine the radial velocity dispersion in the outer halo of the Milky Way to be ~90 km/s at 50 kpc falling to about 65 km/s near 100 kpc once a small number of major outliers are removed. With reasonable estimates of the completeness of our sample of 447 candidates and assuming a spherical halo, we find that the stellar density in the outer halo declines as the -4 power of r.Comment: Accepted for publication in the Ap

    Parametric Evolution for a Deformed Cavity

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    We consider a classically chaotic system that is described by a Hamiltonian H(Q,P;x), where (Q,P) describes a particle moving inside a cavity, and x controls a deformation of the boundary. The quantum-eigenstates of the system are |n(x)>. We describe how the parametric kernel P(n|m) = , also known as the local density of states, evolves as a function of x-x0. We illuminate the non-unitary nature of this parametric evolution, the emergence of non-perturbative features, the final non-universal saturation, and the limitations of random-wave considerations. The parametric evolution is demonstrated numerically for two distinct representative deformation processes.Comment: 13 pages, 8 figures, improved introduction, to be published in Phys. Rev.

    Deformations and dilations of chaotic billiards, dissipation rate, and quasi-orthogonality of the boundary wavefunctions

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    We consider chaotic billiards in d dimensions, and study the matrix elements M_{nm} corresponding to general deformations of the boundary. We analyze the dependence of |M_{nm}|^2 on \omega = (E_n-E_m)/\hbar using semiclassical considerations. This relates to an estimate of the energy dissipation rate when the deformation is periodic at frequency \omega. We show that for dilations and translations of the boundary, |M_{nm}|^2 vanishes like \omega^4 as \omega -> 0, for rotations like \omega^2, whereas for generic deformations it goes to a constant. Such special cases lead to quasi-orthogonality of the eigenstates on the boundary.Comment: 4 pages, 3 figure
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