Curvature-Based Transfer Functions for Direct Volume Rendering:
Methods and Applications

Gordon Kindlmann1 Ross Whitaker1 Tolga Tasdizen1 Torsten Möller2
1  Scientific Computing and Imaging Institute, University of Utah
2  Graphics, Usability, and Visualization (GrUVi) Lab, Simon Fraser University


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.