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.

What May Visualization Processes Optimize?

“…This holistic nature of information-theoretic reasoning has enabled many applications in visualization, including light source placement by Gumhold [33], view selection in mesh rendering by Vázquez et al [64] and Feixas et al [22], view selection in volume rendering by Bordoloi and Shen [5], and Takahashi and Takeshima [56], focus of attention in volume rendering by Viola et al [66], multi-resolution volume visualization by Wang and Shen [68], feature highlighting in unsteady multi-field visualization by Jänicke and Scheuermann [35,37], feature highlighting in time-varying volume visualization by Wang et al [70], transfer function design by Bruckner and Möller [10], and by Ruiz et al [8,49], multimodal data fusion by Bramon et al [6], evaluating isosurfaces [74], measuring of observation capacity [7], measuring information content in multivariate data [23], and confirming the mathematical feasibility of visual multiplexing [15].…”

A Bounded Measure for Estimating the Benefit of Visualization (Part I): Theoretical Discourse and Conceptual Evaluation

“…Information theory has been used extensively in visualization [ 8 ]. It has enabled many applications in visualization, including scene and shape complexity analysis by Feixas et al [ 9 ] and Rigau et al [ 10 ], light source placement by Gumhold [ 11 ], view selection in mesh rendering by Vázquez et al [ 12 ] and Feixas et al [ 13 ], attribute selection by Ng and Martin [ 14 ], view selection in volume rendering by Bordoloi and Shen [ 15 ], and Takahashi and Takeshima [ 16 ], multi-resolution volume visualization by Wang and Shen [ 17 ], focus of attention in volume rendering by Viola et al [ 18 ], feature highlighting by Jänicke and Scheuermann [ 19 , 20 ], and Wang et al [ 21 ], transfer function design by Bruckner and Möller [ 22 ], and Ruiz et al [ 23 , 24 ], multi-modal data fusion by Bramon et al [ 25 ], isosurface evaluation by Wei et al [ 26 ], measuring observation capacity by Bramon et al [ 27 ], measuring information content by Biswas et al [ 28 ], proving the correctness of “overview first, zoom, details-on-demand” by Chen and Jänicke [ 29 ] and Chen et al [ 8 ], and confirming visual multiplexing by Chen et al [ 30 ].…”

Multivariate Pointwise Information-Driven Data Sampling and Visualization

“…For scalar datasets, Bruckner et al [ 40 ] used MI to identify the isosurface similarities. Wei et al [ 41 ] used MI to compute representativeness of isosurfaces via a level-sets for volumetric data. Bramon et al [ 42 ] used MI between data values and color pixels to compute information transfer.…”