We present a new method of magnification for textured images featuring scale invariance properties. This work is originally motivated by an application to astronomical images. One goal is to propose a method to quantitatively predict statistical and visual properties of images taken by a forthcoming higher resolution telescope from older images at lower resolution. This is done by performing a virtual super resolution using a family of scale invariant stochastic processes, namely compound Poisson cascades, and fractional integration. The procedure preserves the visual aspect as well as the statistical properties of the initial image. An augmentation of information is performed by locally adding random small scale details below the initial pixel size. This extrapolation procedure yields a potentially infinite number of magnified versions of an image. It allows for large magnification factors (virtually infinite) and is physically conservative: zooming out to the initial resolution yields the initial image back. The (virtually) super resolved images can be used to predict the quality of future observations as well as to develop and test compression or denoising techniques. Keywords natural images • scale invariance • multifractal analysis • extrapolation • enhancement • infinitely divisible cascades
Abstract.A new generation of instruments in astrophysics or vision now provide spherical data. These spherical data may present a selfsimilarity property while no spherical analysis tool is yet available to characterize this property. In this paper we present a first numerical study of the extension of multifractal analysis onto the sphere using spherical wavelet transforms. We use a model of multifractal spherical textures as a reference to test this approach. The results of the spherical analysis appear qualitatively satisfactory but not as accurate as those of the usual 2D multifractal analysis.
The future European Extremely Large Telescope will be composed of one or two giant segmented mirrors (up to 100 m of diameter) and of several large monolithic mirrors (up to 8 m in diameter). To limit the aberrations due to misalignments and defective surface quality it is necessary to have a proper active optics system. This active optics system must include a phasing system to limit the degradation of the PSF due to misphasing of the segmented mirrors. We will present the lastest design and development of the Active Phasing Experiment that will be tested in laboratory and on-sky connected to a VLT at Paranal in Chile. It includes an active segmented mirror, a static piston plate to simulate a secondary segmented mirror and of four phasing wavefront sensors to measure the piston, tip and tilt of the segments and the aberrations of the VLT. The four phasing sensors are the Diffraction Image Phase Sensing Instrument developed by Instituto de Astrofisica de Canarias, the Pyramid Phasing Sensor developed by Arcetri Astrophysical Observatory, the Shack-Hartmann Phasing Sensor developed by the European Southern Observatory and the Zernike Unit for Segment phasing developed by Laboratoire d'Astrophysique de Marseille. A reference measurement of the segmented mirror is made by an internal metrology developed by Fogale Nanotech. The control system of Active Phasing Experiment will perform the phasing of the segments, the guiding of the VLT and the active optics of the VLT. These activities are included in the Framework Programme 6 of the European Union.
4 pagesInternational audienceWe present a new method of magnification for textured im- ages featuring scale invariance properties. The procedure pre- serves the visual aspect as well as the statistical properties of the initial image. An augmentation of information is per- formed by locally adding small scale details below the ini- tial pixel size. This is made possible thanks to a family of scale invariant stochastic processes, namely compound Pois- son cascades. This extrapolating procedure yields a poten- tially infinite number of magnified versions of an image. It allows for large magnification factors (virtually infinite) and is physically conservative: zooming out to the initial reso- lution yields the initial image back. This work is motivated by an application to images of the quiet Sun to quantitatively predict statistical and visual properties of images taken by a forthcoming high resolution telescope
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