Uncertainty Visualization Of Critical Points Of 2D Scalar Fields For Parametric And Nonparametric Probabilistic Models

This paper presents a novel end-to-end framework for closed-form computation and visualization of critical point uncertainty in 2D uncertain scalar fields. Critical points are fundamental topological descriptors used in the visualization and analysis of scalar fields. The uncertainty inherent in data (e.g., observational and experimental data, approximations in simulations, and compression), however, creates uncertainty regarding critical point positions. Uncertainty in critical point positions, therefore, cannot be ignored, given their impact on downstream data analysis tasks. In this work, we study uncertainty in critical points as a function of uncertainty in data modeled with probability distributions. Although Monte Carlo (MC) sampling techniques have been used in prior studies to quantify critical point uncertainty, they are often expensive and are infrequently used in production-quality visualization software. We, therefore, propose a new end-to-end framework to address these challenges that comprises a threefold contribution. First, we derive the critical point uncertainty in closed form, which is more accurate and efficient than the conventional MC sampling methods. Specifically, we provide the closed-form and semianalytical (a mix of closed-form and MC methods) solutions for parametric (e.g., uniform, Epanechnikov) and nonparametric models (e.g., histograms) with finite support. Second, we accelerate critical point probability computations using a parallel implementation with the VTK-m library, which is platform portable. Finally, we demonstrate the integration of our implementation with the ParaView software system to demonstrate near-real-time results for real datasets.

Tushar M. Athawale, Zhe Wang, David Pugmire, Kenneth Moreland, Qian Gong, Scott Klasky, Chris R. Johnson, and Paul Rosen. Uncertainty Visualization Of Critical Points Of 2D Scalar Fields For Parametric And Nonparametric Probabilistic Models. To appear in IEEE Transactions on Visualization and Computer Graphics (IEEE VIS), 2025.

@article{athawale2024uncertain,
  title = {Uncertainty Visualization of Critical Points of 2D Scalar Fields for
    Parametric and Nonparametric Probabilistic Models},
  author = {Athawale, Tushar M. and Wang, Zhe and Pugmire, David and Moreland, Kenneth
    and Gong, Qian and Klasky, Scott and Johnson, Chris R. and Rosen, Paul},
  journal = {To appear in IEEE Transactions on Visualization and Computer Graphics (IEEE
    VIS)},
  year = {2025},
  note = {textit{Presented at IEEE VIS 2024.}},
  abstract = {This paper presents a novel end-to-end framework for closed-form
    computation and visualization of critical point uncertainty in 2D uncertain scalar
    fields. Critical points are fundamental topological descriptors used in the
    visualization and analysis of scalar fields. The uncertainty inherent in data (e.g.,
    observational and experimental data, approximations in simulations, and compression),
    however, creates uncertainty regarding critical point positions. Uncertainty in critical
    point positions, therefore, cannot be ignored, given their impact on downstream data
    analysis tasks. In this work, we study uncertainty in critical points as a function of
    uncertainty in data modeled with probability distributions. Although Monte Carlo (MC)
    sampling techniques have been used in prior studies to quantify critical point
    uncertainty, they are often expensive and are infrequently used in production-quality
    visualization software. We, therefore, propose a new end-to-end framework to address
    these challenges that comprises a threefold contribution. First, we derive the critical
    point uncertainty in closed form, which is more accurate and efficient than the
    conventional MC sampling methods. Specifically, we provide the closed-form and
    semianalytical (a mix of closed-form and MC methods) solutions for parametric (e.g.,
    uniform, Epanechnikov) and nonparametric models (e.g., histograms) with finite support.
    Second, we accelerate critical point probability computations using a parallel
    implementation with the VTK-m library, which is platform portable. Finally, we
    demonstrate the integration of our implementation with the ParaView software system to
    demonstrate near-real-time results for real datasets.}
}