Uncertainty in Continuous Scatterplots, Continuous Parallel Coordinates, and Fibers

Fiber Uncertainty Visualization for Bivariate Data With Parametric and Nonparametric Noise Models

“…The uncertainty in multivariate data can result in ambiguity as to whether a vertex should be classified as interior or exterior. The problem of uncertain vertex classification was recently addressed by Zheng and Sadlo [69] and Sane et al [52]. Zheng and Sadlo proposed a statistical framework to compute the probability of data at point P ∈ D being in the interior of a rectangular FSCP.…”

“…The interior probability (i.e., Pr(U = (X,Y ) ∈ T )) can be computed in two steps: (1) the joint probability distribution of X and Y (i.e., pdf X,Y (x, y)) is computed, and then (2) the joint probability distribution pdf X,Y (x, y) is integrated over trait T . Mathematically, the probability of point P being in the interior of a fiber surface can be expressed as the following double integral over a rectangular trait: Zheng and Sadlo [69] proposed a closed-form computation of the double integral in Equation 1 when pdf X,Y (x, y) is Gaussian distributed. Sane et al [52] proposed confidence-feature level sets for Gaussian distributed data and rectangular FSCP for bivariate fields.…”

“…Our contributions in this paper are primarily motivated by the recent work by Zheng and Sadlo [69], who studied the positional uncertainty of fibers for uncertain bivariate fields. They proposed a closed-form uncertainty quantification framework for bivariate data fibers assuming independent/correlated Gaussian (parametric) noise models and rectangular FSCP selection (see Sect.…”

“…One of the future directions identified by Zheng and Sadlo (see Sect. 7 of [69]) included extending their work to probability distributions other than Gaussian, which we address here.…”

“…4). Note that our framework is applicable to FSCP with arbitrary shapes as opposed to being limited to rectangular FSCP [52,69]. Our derivations for parametric distributions act as building blocks for our derivations relevant to nonparametric distributions.…”