1,107 research outputs found
Conditional vorticity budget of coherent and incoherent flow contributions in fully developed homogeneous isotropic turbulence
We investigate the conditional vorticity budget of fully developed
three-dimensional homogeneous isotropic turbulence with respect to coherent and
incoherent flow contributions. The Coherent Vorticity Extraction based on
orthogonal wavelets allows to decompose the vorticity field into coherent and
incoherent contributions, of which the latter are noise-like. The impact of the
vortex structures observed in fully developed turbulence on statistical balance
equations is quantified considering the conditional vorticity budget. The
connection between the basic structures present in the flow and their
statistical implications is thereby assessed. The results are compared to those
obtained for large- and small-scale contributions using a Fourier
decomposition, which reveals pronounced differences
Applications of wavelet-based compression to multidimensional Earth science data
A data compression algorithm involving vector quantization (VQ) and the discrete wavelet transform (DWT) is applied to two different types of multidimensional digital earth-science data. The algorithms (WVQ) is optimized for each particular application through an optimization procedure that assigns VQ parameters to the wavelet transform subbands subject to constraints on compression ratio and encoding complexity. Preliminary results of compressing global ocean model data generated on a Thinking Machines CM-200 supercomputer are presented. The WVQ scheme is used in both a predictive and nonpredictive mode. Parameters generated by the optimization algorithm are reported, as are signal-to-noise (SNR) measurements of actual quantized data. The problem of extrapolating hydrodynamic variables across the continental landmasses in order to compute the DWT on a rectangular grid is discussed. Results are also presented for compressing Landsat TM 7-band data using the WVQ scheme. The formulation of the optimization problem is presented along with SNR measurements of actual quantized data. Postprocessing applications are considered in which the seven spectral bands are clustered into 256 clusters using a k-means algorithm and analyzed using the Los Alamos multispectral data analysis program, SPECTRUM, both before and after being compressed using the WVQ program
Craya decomposition using compactly supported biorthogonal wavelets
Special Issue on Continuous Wavelet Transform in Memory of Jean Morlet, Part IIInternational audienceWe present a new local Craya--Herring decomposition of three-dimensional vector fields using compactly supported biorthogonal wavelets. Therewith vector-valued function spaces are split into two orthogonal components, i.e., curl-free and divergence-free spaces. The latter is further decomposed into toroidal and poloidal parts to decorrelate horizontal from vertical contributions which are of particular interest in geophysical turbulence. Applications are shown for isotropic, rotating and stratified turbulent flows. A comparison between isotropic and anisotropic orthogonal Craya--Herring wavelets, built in Fourier space and thus not compactly supported, is also given
On the Structure and Dynamics of Sheared and Rotating Turbulence: Direct Numerical Simulations and Wavelet Based Coherent Vortex Extraction
The influence of rotation on the structure and dynamics of sheared turbulence is investigated using a series of direct numerical simulations. Five cases are considered: turbulent shear flow without rotation, with moderate rotation, and with strong rotation, where the rotation configuration is either parallel or antiparallel. For moderate rotation rates an antiparallel configuration increases the growth of the turbulent kinetic energy, while the parallel case reduces the growth as compared to the nonrotating case. For strong rotation rates decay of the energy is observed, linear effects dominate the flow, and the vorticity probability density functions tend to become Gaussian. Visualizations of vorticity show that the inclination angle of the vortical structures depends on the rotation rate and orientation. Coherent vortex extraction, based on the orthogonal wavelet decomposition of vorticity, is applied to split the flow into coherent and incoherent parts. It was found that the coherent part preserves the vortical structures using only a few percent of the degrees of freedom. The incoherent part was found to be structureless and of mainly dissipative nature. With increasing rotation rates, the number of wavelet modes representing the coherent vortices decreases, indicating an increased coherency of the flow. Restarting the direct numerical simulation with the filtered fields confirms that the coherent component preserves the temporal dynamics of the total flow, while the incoherent component is of dissipative nature
A Generative Model of Natural Texture Surrogates
Natural images can be viewed as patchworks of different textures, where the
local image statistics is roughly stationary within a small neighborhood but
otherwise varies from region to region. In order to model this variability, we
first applied the parametric texture algorithm of Portilla and Simoncelli to
image patches of 64X64 pixels in a large database of natural images such that
each image patch is then described by 655 texture parameters which specify
certain statistics, such as variances and covariances of wavelet coefficients
or coefficient magnitudes within that patch.
To model the statistics of these texture parameters, we then developed
suitable nonlinear transformations of the parameters that allowed us to fit
their joint statistics with a multivariate Gaussian distribution. We find that
the first 200 principal components contain more than 99% of the variance and
are sufficient to generate textures that are perceptually extremely close to
those generated with all 655 components. We demonstrate the usefulness of the
model in several ways: (1) We sample ensembles of texture patches that can be
directly compared to samples of patches from the natural image database and can
to a high degree reproduce their perceptual appearance. (2) We further
developed an image compression algorithm which generates surprisingly accurate
images at bit rates as low as 0.14 bits/pixel. Finally, (3) We demonstrate how
our approach can be used for an efficient and objective evaluation of samples
generated with probabilistic models of natural images.Comment: 34 pages, 9 figure
Generative Compression
Traditional image and video compression algorithms rely on hand-crafted
encoder/decoder pairs (codecs) that lack adaptability and are agnostic to the
data being compressed. Here we describe the concept of generative compression,
the compression of data using generative models, and suggest that it is a
direction worth pursuing to produce more accurate and visually pleasing
reconstructions at much deeper compression levels for both image and video
data. We also demonstrate that generative compression is orders-of-magnitude
more resilient to bit error rates (e.g. from noisy wireless channels) than
traditional variable-length coding schemes
Exploratory Visualization of Data Pattern Changes in Multivariate Data Streams
More and more researchers are focusing on the management, querying and pattern mining of streaming data. The visualization of streaming data, however, is still a very new topic. Streaming data is very similar to time-series data since each datapoint has a time dimension. Although the latter has been well studied in the area of information visualization, a key characteristic of streaming data, unbounded and large-scale input, is rarely investigated. Moreover, most techniques for visualizing time-series data focus on univariate data and seldom convey multidimensional relationships, which is an important requirement in many application areas. Therefore, it is necessary to develop appropriate techniques for streaming data instead of directly applying time-series visualization techniques to it.
As one of the main contributions of this dissertation, I introduce a user-driven approach for the visual analytics of multivariate data streams based on effective visualizations via a combination of windowing and sampling strategies. To help users identify and track how data patterns change over time, not only the current sliding window content but also abstractions of past data in which users are interested are displayed. Sampling is applied within each single time window to help reduce visual clutter as well as preserve data patterns. Sampling ratios scheduled for different windows reflect the degree of user interest in the content. A degree of interest (DOI) function is used to represent a user\u27s interest in different windows of the data. Users can apply two types of pre-defined DOI functions, namely RC (recent change) and PP (periodic phenomena) functions. The developed tool also allows users to interactively adjust DOI functions, in a manner similar to transfer functions in volume visualization, to enable a trial-and-error exploration process. In order to visually convey the change of multidimensional correlations, four layout strategies were designed. User studies showed that three of these are effective techniques for conveying data pattern changes compared to traditional time-series data visualization techniques. Based on this evaluation, a guide for the selection of appropriate layout strategies was derived, considering the characteristics of the targeted datasets and data analysis tasks. Case studies were used to show the effectiveness of DOI functions and the various visualization techniques.
A second contribution of this dissertation is a data-driven framework to merge and thus condense time windows having small or no changes and distort the time axis. Only significant changes are shown to users. Pattern vectors are introduced as a compact format for representing the discovered data model. Three views, juxtaposed views, pattern vector views, and pattern change views, were developed for conveying data pattern changes. The first shows more details of the data but needs more canvas space; the last two need much less canvas space via conveying only the pattern parameters, but lose many data details. The experiments showed that the proposed merge algorithms preserves more change information than an intuitive pattern-blind averaging. A user study was also conducted to confirm that the proposed techniques can help users find pattern changes more quickly than via a non-distorted time axis.
A third contribution of this dissertation is the history views with related interaction techniques were developed to work under two modes: non-merge and merge. In the former mode, the framework can use natural hierarchical time units or one defined by domain experts to represent timelines. This can help users navigate across long time periods. Grid or virtual calendar views were designed to provide a compact overview for the history data. In addition, MDS pattern starfields, distance maps, and pattern brushes were developed to enable users to quickly investigate the degree of pattern similarity among different time periods. For the merge mode, merge algorithms were applied to selected time windows to generate a merge-based hierarchy. The contiguous time windows having similar patterns are merged first. Users can choose different levels of merging with the tradeoff between more details in the data and less visual clutter in the visualizations. The usability evaluation demonstrated that most participants could understand the concepts of the history views correctly and finished assigned tasks with a high accuracy and relatively fast response time
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