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Scaling Function (scaling + function)
Selected AbstractsShrinkability Maps for Content-Aware Video ResizingCOMPUTER GRAPHICS FORUM, Issue 7 2008Yi-Fei Zhang Abstract A novel method is given for content-aware video resizing, i.e. targeting video to a new resolution (which may involve aspect ratio change) from the original. We precompute a per-pixel cumulative shrinkability map which takes into account both the importance of each pixel and the need for continuity in the resized result. (If both x and y resizing are required, two separate shrinkability maps are used, otherwise one suffices). A random walk model is used for efficient offline computation of the shrinkability maps. The latter are stored with the video to create a multi-sized video, which permits arbitrary-sized new versions of the video to be later very efficiently created in real-time, e.g. by a video-on-demand server supplying video streams to multiple devices with different resolutions. These shrinkability maps are highly compressible, so the resulting multi-sized videos are typically less than three times the size of the original compressed video. A scaling function operates on the multi-sized video, to give the new pixel locations in the result, giving a high-quality content-aware resized video. Despite the great efficiency and low storage requirements for our method, we produce results of comparable quality to state-of-the-art methods for content-aware image and video resizing. [source] Suspended sediment load estimation and the problem of inadequate data sampling: a fractal viewEARTH SURFACE PROCESSES AND LANDFORMS, Issue 4 2006Bellie Sivakumar Abstract Suspended sediment load estimation at high resolutions is an extremely difficult task, because: (1) it depends on the availability of high-resolution water discharge and suspended sediment concentration measurements, which are often not available; (2) any errors in the measurements of these two components could significantly influence the accuracy of suspended sediment load estimation; and (3) direct measurements are very expensive. The purpose of this study is to approach this sampling problem from a new perspective of fractals (or scaling), which could provide important information on the transformation of suspended sediment load data from one scale to another. This is done by investigating the possible presence of fractal behaviour in the daily suspended sediment load data for the Mississippi River basin (at St. Louis, Missouri). The presence of fractal behaviour is investigated using five different methods, ranging from general to specific and from mono-fractal to multi-fractal: (1) autocorrelation function; (2) power spectrum; (3) probability distribution function; (4) box dimension; and (5) statistical moment scaling function. The results indicate the presence of multi-fractal behaviour in the suspended sediment load data, suggesting the possibility of transformation of data from one scale to another using a multi-dimensional model. Copyright © 2005 John Wiley & Sons, Ltd. [source] Interpretation of regional aeromagnetic data by the scaling function method: the case of Southern Apennines (Italy)GEOPHYSICAL PROSPECTING, Issue 4 2009G. Florio ABSTRACT A complex aeromagnetic anomaly in Southern Apennines (Italy) is analysed and interpreted by a multiscale method based on the scaling function. We use multiscale methods allowing analysis of a potential field along ridges, which are lines defined by the position of the extrema of the field at the considered scales. The method developed and applied in this paper is based on the study of the scaling function of the total magnetic field. It allows recovering of source parameters such as depth and structural index. The studied area includes a Pleistocene volcanic structure (Mt. Vulture) whose intense dipolar anomaly is superimposed on a longer wavelength regional anomaly. The interpretation of ridges of the modulus of the analytic signal at different altitude ranges allows recognition of at least three distinct sources between about 5 km and 20 km depth. Their interpretation is discussed in light of borehole data and other geophysical constraints. A reasonable geological model for these sources indicates the presence of intrusions, probably linked to the past activity of Mt. Vulture. [source] Topographic parameterization in continental hydrology: a study in scaleHYDROLOGICAL PROCESSES, Issue 18 2003Robert N. Armstrong Abstract Digital elevation models (DEMs) are useful and popular tools from which topographic parameters can be quickly and efficiently extracted for various hydrologic applications. DEMs coupled with automated methods for extracting topographic information provide a powerful means of parameterizing hydrologic models over a wide range of scales. However, choosing appropriate DEM scales for particular hydrologic modelling applications is limited by a lack of understanding of the effects of scale and grid resolution on land-surface representation. The scale effects of aggregation on square-grid DEMs of two continental-scale basins are examined. Base DEMs of the Mackenzie and Missouri River basins are extracted from the HYDRO1k DEM of North America. Successively coarser grids of 2, 4, 8, , 64 km were generated from the ,base' DEMs using simple linear averaging. TOPAZ (Topographic Parameterization) was applied to the base and aggregated DEMs using constant critical source area and minimum source channel length values to extract topographic variables at varying scales or resolutions. The effects of changing DEM resolution are examined by considering changes in the spatial distribution and statistical properties of selected topographic variables of hydrological importance. The effects of increasing grid size on basin and drainage network delineation, and derived topographic variables, tends to be non-linear. In particular, changes in overall basin extent and drainage network configuration make it impractical to apply a simple scaling function to estimate variable values for fine-resolution DEMs from those derived from coarse-resolution DEMs. Results also suggest the resolution to which a DEM can be reduced by aggregation and still provide useful topographic information for continental-scale hydrologic modelling is that at which the mean hydraulic slope falls to approximately 1%. In this study, that generally occurred at a resolution of about 10 km. Copyright © 2003 John Wiley & Sons, Ltd. [source] Is a chaotic multi-fractal approach for rainfall possible?HYDROLOGICAL PROCESSES, Issue 6 2001Bellie Sivakumar Abstract An Erratum has been published for this article in Hydrological Processes 15 (12) 2001, 2381,2382. Applications of the ideas gained from fractal theory to characterize rainfall have been one of the most exciting areas of research in recent times. The studies conducted thus far have nearly unanimously yielded positive evidence regarding the existence of fractal behaviour in rainfall. The studies also revealed the insufficiency of the mono-fractal approaches to characterizing the rainfall process in time and space and, hence, the necessity for multi-fractal approaches. The assumption behind multi-fractal approaches for rainfall is that the variability of the rainfall process could be directly modelled as a stochastic (or random) turbulent cascade process, since such stochastic cascade processes were found to generically yield multi-fractals. However, it has been observed recently that multi-fractal approaches might provide positive evidence of a multi-fractal nature not only in stochastic processes but also in, for example, chaotic processes. The purpose of the present study is to investigate the presence of both chaotic and fractal behaviours in the rainfall process to consider the possibility of using a chaotic multi-fractal approach for rainfall characterization. For this purpose, daily rainfall data observed at the Leaf River basin in Mississippi are studied, and only temporal analysis is carried out. The autocorrelation function, the power spectrum, the empirical probability distribution function, and the statistical moment scaling function are used as indicators to investigate the presence of fractal, whereas the presence of chaos is investigated by employing the correlation dimension method. The results from the fractal identification methods indicate that the rainfall data exhibit multi-fractal behaviour. The correlation dimension method yields a low dimension, suggesting the presence of chaotic behaviour. The existence of both multi-fractal and chaotic behaviours in the rainfall data suggests the possibility of a chaotic multi-fractal approach for rainfall characterization. Copyright © 2001 John Wiley & Sons, Ltd. [source] Modification to convolution CFS-PML for the ADI-FDTD methodMICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 2 2006Linnian Wang Abstract A new implementation of perfectly matched layer (PML) using the recursive-convolution technique is introduced for an alternating-direction implicit (ADI) finite-difference time-domain (FDTD) method. Based on a "complex frequency-shifted (CFS)" scaling function, this PML boundary condition is highly effective at absorbing low-frequency evanescent waves. The numerical results show that, compared with its previously suggested analogue, the new method improves the reflection error by 30 dB for large time-step sizes. © 2005 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 261,265, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21322 [source] Fitting atomic models into electron-microscopy mapsACTA CRYSTALLOGRAPHICA SECTION D, Issue 10 2000Michael G. Rossmann Combining X-ray crystallographically determined atomic structures of component domains or subunits with cryo-electron microscopic three-dimensional images at around 22,Å resolution can produce structural information that is accurate to about 2.2,Å resolution. In an initial step, it is necessary to determine accurately the absolute scale and absolute hand of the cryo-electron microscopy map, the former of which can be off by up to 5%. It is also necessary to determine the relative height of density by using a suitable scaling function. Difference maps can identify, for instance, sites of glycosylation, the position of which helps to fit the component structures into the EM density maps. Examples are given from the analysis of alphaviruses, rhinovirus,receptor interactions and poliovirus,receptor interactions. [source] Changes in variance and correlation of soil properties with scale and location: analysis using an adapted maximal overlap discrete wavelet transformEUROPEAN JOURNAL OF SOIL SCIENCE, Issue 4 2001R. M. Lark Summary The magnitude of variation in soil properties can change from place to place, and this lack of stationarity can preclude conventional geostatistical and spectral analysis. In contrast, wavelets and their scaling functions, which take non-zero values only over short intervals and are therefore local, enable us to handle such variation. Wavelets can be used to analyse scale-dependence and spatial changes in the correlation of two variables where the linear model of coregionalization is inadmissible. We have adapted wavelet methods to analyse soil properties with non-stationary variation and covariation in fairly small sets of data, such as we can expect in soil survey, and we have applied them to measurements of pH and the contents of clay and calcium carbonate on a 3-km transect in Central England. Places on the transect where significant changes in the variance of the soil properties occur were identified. The scale-dependence of the correlations of soil properties was investigated by calculating wavelet correlations for each spatial scale. We identified where the covariance of the properties appeared to change and then computed the wavelet correlations on each side of the change point and compared them. The correlation of topsoil and subsoil clay content was found to be uniform along the transect at one important scale, although there were significant changes in the variance. In contrast, carbonate content and pH of the topsoil were correlated only in parts of the transect. [source] Wavelet Galerkin method in multi-scale homogenization of heterogeneous mediaINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2006Shafigh Mehraeen Abstract The hierarchical properties of scaling functions and wavelets can be utilized as effective means for multi-scale homogenization of heterogeneous materials under Galerkin framework. It is shown in this work, however, when the scaling functions are used as the shape functions in the multi-scale wavelet Galerkin approximation, the linear dependency in the scaling functions renders improper zero energy modes in the discrete differential operator (stiffness matrix) if integration by parts is invoked in the Galerkin weak form. An effort is made to obtain the analytical expression of the improper zero energy modes in the wavelet Galerkin differential operator, and the improper nullity of the discrete differential operator is then removed by an eigenvalue shifting approach. A unique property of multi-scale wavelet Galerkin approximation is that the discrete differential operator at any scale can be effectively obtained. This property is particularly useful in problems where the multi-scale solution cannot be obtained simply by a wavelet projection of the finest scale solution without utilizing the multi-scale discrete differential operator, for example, the multi-scale analysis of an eigenvalue problem with oscillating coefficients. Copyright © 2005 John Wiley & Sons, Ltd. [source] Morphological and fractal studies of polypropylene/poly(ethene-1-octene) blends during melt mixing using scanning electron microscopyPOLYMER INTERNATIONAL, Issue 3 2008Xinhua Xu Abstract BACKGROUND: Polymer blending creates new materials with enhanced mechanical, chemical or optical properties, with the exact properties being determined by the type of morphology and the phase dimension of the blend. In order to control blend properties, morphology development during processing needs to be understood. The formation and evolution of polypropylene/poly(ethylene-1-octene) (PP/POE) blend morphology during blending are qualitatively represented by a series of time-dependent scanning electron microscopy (SEM) patterns. The area diameter and its distribution of dispersed phase domains are discussed in detail. In order to characterize the formation and evolution of phase morphology quantitatively, two fractal dimensions, Ds and Dd, and their corresponding scaling functions are introduced to analyze the SEM patterns. RESULTS: The evolution of the area diameter indicates that the major reduction in phase domain size occurs during the initial stage of melt mixing, and the domain sizes show an increasing trend due to coalescence with increasing mixing times. The distribution in dispersed phase dimension obeys a log-normal distribution, and the two fractal dimensions are effective to describe the phase morphology: Ds for dispersed phase dimension and Dd for the distribution in it. CONCLUSIONS: The fractal dimensions Ds and Dd can be used quantitatively to characterize the evolutional self-similarity of phase morphology and the competition of breakup and coalescence of dispersed phase domains. It is shown that the fractal dimensions and scaling laws are useful to describe the phase morphology development at various mixing times to a certain extent. Copyright © 2007 Society of Chemical Industry [source] | |||||||||||||