IEEE Trans Vis Comput Graph - Visualizing the Variability of Gradients in Uncertain 2D Scalar Fields.

Tópicos

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Resumo

In uncertain scalar fields where data values vary with a certain probability, the strength of this variability indicates the confidence in the data. It does not, however, allow inferring on the effect of uncertainty on differential quantities such as the gradient, which depend on the variability of the rate of change of the data. Analyzing the variability of gradients is nonetheless more complicated, since, unlike scalars, gradients vary in both strength and direction. This requires initially the mathematical derivation of their respective value ranges, and then the development of effective analysis techniques for these ranges. This paper takes a first step into this direction: Based on the stochastic modeling of uncertainty via multivariate random variables, we start by deriving uncertainty parameters, such as the mean and the covariance matrix, for gradients in uncertain discrete scalar fields. We do not make any assumption about the distribution of the random variables. Then, for the first time to our best knowledge, we develop a mathematical framework for computing confidence intervals for both the gradient orientation and the strength of the derivative in any prescribed direction, for instance, the mean gradient direction. While this framework generalizes to 3D uncertain scalar fields, we concentrate...

Resumo Limpo

uncertain scalar field data valu vari certain probabl strength variabl indic confid data howev allow infer effect uncertainti differenti quantiti gradient depend variabl rate chang data analyz variabl gradient nonetheless complic sinc unlik scalar gradient vari strength direct requir initi mathemat deriv respect valu rang develop effect analysi techniqu rang paper take first step direct base stochast model uncertainti via multivari random variabl start deriv uncertainti paramet mean covari matrix gradient uncertain discret scalar field make assumpt distribut random variabl first time best knowledg develop mathemat framework comput confid interv gradient orient strength deriv prescrib direct instanc mean gradient direct framework general d uncertain scalar field concentr

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