Magic: Marching Cubes Isosurface Uncertainty Visualization For Gaussian Uncertain Data With Spatial Correlation

In this paper, we study the propagation of data uncertainty through the marching cubes algorithm for isosurface visualization for correlated uncertain data. Consideration of correlation has been shown paramount for avoiding errors in uncertainty quantification and visualization in multiple prior studies. Although the problem of isosurface uncertainty with spatial data correlation has been previously addressed, there are two major limitations to prior treatments. First, there are no analytical formulations for uncertainty quantification of isosurfaces when the data uncertainty is characterized by a Gaussian distribution with spatial correlation. Second, as a consequence of the lack of analytical formulations, existing techniques resort to a Monte Carlo sampling approach, which is expensive and difficult to integrate into visualization tools. To address these limitations, we present a closed-form framework to efficiently derive uncertainty in marching cubes level-sets for Gaussian uncertain data with spatial correlation (MAGIC). To derive closed-form solutions, we leverage the Hinkley’s derivation on the ratio of Gaussian distributions. With our analytical framework, we achieve a significant speed-up and enhanced accuracy of uncertainty quantification over classical Monte Carlo methods. We further accelerate our analytical solutions using many-core processors to achieve speed-ups up to 585x and integrability with production visualization tools for broader impact. We demonstrate the effectiveness of our correlation-aware uncertainty framework through experiments on meteorology, urban flow, and astrophysics simulation datasets.

Tushar M. Athawale, Kenneth Moreland, David Pugmire, Chris R. Johnson, Paul Rosen, Matthew Norman, Antigoni Georgiadou, and Alireza Entezari. Magic: Marching Cubes Isosurface Uncertainty Visualization For Gaussian Uncertain Data With Spatial Correlation. IEEE Transactions on Computer Graphics and Visualization, 2026.

@article{athawale2026magic,
  title = {MAGIC: Marching Cubes Isosurface Uncertainty Visualization for Gaussian
    Uncertain Data with Spatial Correlation},
  author = {Athawale, Tushar M. and Moreland, Kenneth and Pugmire, David and Johnson,
    Chris R. and Rosen, Paul and Norman, Matthew and Georgiadou, Antigoni and Entezari,
    Alireza},
  journal = {IEEE Transactions on Computer Graphics and Visualization},
  year = {2026},
  abstract = {In this paper, we study the propagation of data uncertainty through the
    marching cubes algorithm for isosurface visualization for correlated uncertain data.
    Consideration of correlation has been shown paramount for avoiding errors in uncertainty
    quantification and visualization in multiple prior studies. Although the problem of
    isosurface uncertainty with spatial data correlation has been previously addressed,
    there are two major limitations to prior treatments. First, there are no analytical
    formulations for uncertainty quantification of isosurfaces when the data uncertainty is
    characterized by a Gaussian distribution with spatial correlation. Second, as a
    consequence of the lack of analytical formulations, existing techniques resort to a
    Monte Carlo sampling approach, which is expensive and difficult to integrate into
    visualization tools. To address these limitations, we present a closed-form framework to
    efficiently derive uncertainty in marching cubes level-sets for Gaussian uncertain data
    with spatial correlation (MAGIC). To derive closed-form solutions, we leverage the
    Hinkley’s derivation on the ratio of Gaussian distributions. With our analytical
    framework, we achieve a significant speed-up and enhanced accuracy of uncertainty
    quantification over classical Monte Carlo methods. We further accelerate our analytical
    solutions using many-core processors to achieve speed-ups up to 585x and integrability
    with production visualization tools for broader impact. We demonstrate the effectiveness
    of our correlation-aware uncertainty framework through experiments on meteorology, urban
    flow, and astrophysics simulation datasets.}
}