Anisotropic Ambient Volume Shading
(The paper is linked to from Marco Ament’s page; be sure to watch the movie)
The authors describe how to generate anisotropic shading in direct volume rendering that shows ridge and tubular structures more clearly. While this method is not an obvious instance of algebraic visualization design, there are two aspects that can be described in algebraic terms.
In this work, the real thing of interest to be visualized is the 3D shape of the surfaces within the volume image, in particular tubular structures and ridges on surfaces. In algebraic vis terminology, these structures are the data, while the regular grid of voxel values (what one might normally call the data) is actually just the representation.
Anisotropic shading creates long specular highlights that clearly indicate the presence, location, and shape of volume structures. This increases visual-data correspondence: moving or changing such a structure will move or change the corresponding highlight in a way more visible and obvious than without anisotropic shading.
Also, the method of estimating the local structure, based on random sampling of a neighborhood, achieves representation invariance by removing potential hallucinators associated with the volume sampling grid spacing and orientation (the representation). Instead, the method highlights forms that exist at a scale much larger than a single voxel, which is not possible with previous curvature-based shading.