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An Uncertainty Visualization Technique Using Possibility Theory: Possibilistic Marching Cubes

This paper opens the discussion about using fuzzy measure theory for isocontour/isosurface extraction in the field of uncertainty visualization. Specifically, we propose an uncertain marching cubes algorithm in the framework of possibility theory, called possibilistic marching cubes. The proposed algorithm uses the dual measures—possibility and necessity—to represent the uncertainty in the spatial location of isocontour/isosurface, which is propagated from the uncertainty in ensemble data. In addition, a novel parametric way of constructing marginal possibility distribution is proposed so that the epistemic uncertainty due to the limited size of the ensemble is considered. The effectiveness of the proposed possibilistic marching cubes algorithm is demonstrated using 2D and 3D examples.