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Direct volume rendering of scalar fields uses a transfer function to map locally measured data properties to opacities and colors. The domain of the transfer function is typically the one-dimensional space of scalar data values. This paper advances the use of curvature information in multi-dimensional transfer functions, with a methodology for computing high-quality curvature measurements. The proposed methodology combines an implicit formulation of curvature with convolution-based reconstruction of the field. We give concrete guidelines for implementing the methodology, and illustrate the importance of choosing accurate filters for computing derivatives with convolution. Curvature-based transfer functions are shown to extend the expressivity and utility of volume rendering through contributions in three different application areas: non-photorealistic volume rendering, surface smoothing via anisotropic diffusion, and visualization of isosurface uncertainty.

With respect to uncertainty visualization, this paper uses flowline curvature as a measure of uncertainty of material boundaries in isosurface extraction. Flowline curvature is a measure of the curvature of the path of the flow, viewed from above. This corresponds to the degree in which an isosurface changes orientation as a function of small changes in isovalue. Thus, areas with high flowline curvature the material boundary is probably represented poorly by the isosurface. Thus, colormapping flow curvature onto volume rendered surfaces can visually indicate areas of surface shape uncertainty.

volume rendering, implicit surface curvature, convolution-based differentiation, non-photorealistic rendering, surface processing, uncertainty visualization, flowline curvature

color mapping, transfer function

@InProceedings{	kindlmann:2003:CBTF,
author =	"Gordon Kindlmann and Ross Whitaker and Tolga Tasdizen and Torsten Moller",
title =	"Curvature-Based Transfer Functions for Direct Volume Rendering: Methods and Applications",
booktitle =	"Proceedings of the 14th IEEE Visualization 2003 (VIS'03)",
pages =	"67--74",
year =	"2004",
}