Curvature-based transfer functions for direct volume rendering: methods and applications

Abstract

Figure 1: Volume renderings of a 64 3 synthetic volume with four different curvature measures. Left to right: first principal curvature κ 1 , second principal curvature κ 2 , mean curvature (κ 1 + κ 2 )/2, and Gaussian curvature κ 1 κ 2 . Magenta indicates negative curvature, green indicates positive. Iso-curvature contours are in black, except for zero curvature in blue. AbstractDirect 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: nonphotorealistic volume rendering, surface smoothing via anisotropic diffusion, and visualization of isosurface uncertainty.

Shape Modeling and Analysis with Entropy-Based Particle Systems

“…In general, label mask segmentations are also not directly useful because they are not suitable representations for finite numerical calculations of surface geometry and features, which assume the image is a sampling of a smooth function. However, a related surface representation, the signed distance transform of the label mask, does satisfy this criterion [67]. A distance transform is a graded, membership function, or fuzzy classification of the pixels within an object, with a surface implicitly defined as the zero level set [67].…”

“…However, a related surface representation, the signed distance transform of the label mask, does satisfy this criterion [67]. A distance transform is a graded, membership function, or fuzzy classification of the pixels within an object, with a surface implicitly defined as the zero level set [67]. In particular, distance transforms are useful for constructing particle-based representations of surfaces, which is discussed further in Section 2.1.4.…”

“…When properly constructed, a distance transform has nice properties for finite numerical methods for computing surface features and geometry [67]. Several wellknown algorithms have been proposed for constructing smooth distance transforms from label masks.…”

“…The tangent-plane projection is followed by iterative reprojection of the particle onto the nearest root of F by the method of Newton-Raphson. Principal curvatures are computed analytically from the implicit function, as described in [67].…”

Biomedical Visualization

“…SCI Institute researchers have done substantial new research in volume rendering [6][7][8][9][10][11][12][13][14][15]. For example, Kindlmann and Kniss [15] have recently developed a method for the semi-automatic generation of transfer functions.…”