Evaluating Isosurfaces with Level-set-based Information Maps

Abstract

While isosurfaces have been widely used for scalar data visualization, it is often difficult to determine if the selected isosurfaces for visualization are sufficient to represent the entire scalar field. In this paper, we present an information-theoretic approach to evaluate the representativeness of a given isosurface set. Our basic idea is that given two isosurfaces that enclose a subvolume, if the intermediate isosurfaces in the subvolume can be generated by smoothly morphing from one isosurface to the other, no additional isosurfaces are needed since the geometry of the true isosurfaces within the subvolume can be easily inferred. To realize this idea, given a pair of isosurfaces, to determine if such a smooth condition in the enclosed region is satisfied, we use a level-set approach to generate the intermediate surfaces. On each intermediate surface, we sample the values from the scalar field and exam the distribution. If the entropy of the distribution is low, this intermediate surface is aligned well with a true isosurface in the scalar field. For the intermediate surfaces generated by the level-set method from the boundary isosurfaces, the distributions of scalar values from the level-set surfaces form a 2D distribution, called isosurface information map. This information map can be used as an indicator of the representativeness of the boundary isosurfaces for the data in the subregion, allowing a quantitative measurement of information representable by the input isosurfaces. Based on this information-theoretic approach, this paper presents an isosurface selection algorithm that can automatically select isosurfaces for more effective visualization of scalar fields.