Multidimensional transfer functions for interactive volume rendering

Abstract

Most direct volume renderings produced today employ one-dimensional transfer functions which assign color and opacity to the volume based solely on the single scalar quantity which comprises the data set. Though they have not received widespread attention, multidimensional transfer functions are a very effective way to extract materials and their boundaries for both scalar and multivariate data. However, identifying good transfer functions is difficult enough in one dimension, let alone two or three dimensions. This paper demonstrates an important class of three-dimensional transfer functions for scalar data, and describes the application of multidimensional transfer functions to multivariate data. We present a set of direct manipulation widgets that make specifying such transfer functions intuitive and convenient. We also describe how to use modern graphics hardware to both interactively render with multidimensional transfer functions and to provide interactive shadows for volumes. The transfer functions, widgets, and hardware combine to form a powerful system for interactive volume exploration.

Context-aware volume navigation

“…However, a multitude of parameters can affect the opacity at each sampling point: Transfer functions, segmentation data, clipping, other modalities, derived data. Additionally, transfer functions have to be differentiated further since multiple types exist (e.g., 1D intensity, 2D intensity-gradient, 2D LH [22], 3D [14]) and different segments may also have different transfer functions assigned to them. Incorporating all these parameters within the navigation algorithm would not be a trivial task, and if possible at all it would likely lead to code duplications, which would need to be updated to incorporate additional data sets or formats, new transfer function types, additional rendering parameters, etc.…”

Feature selection of 3D volume data through multi-dimensional transfer functions

“…The Kindlmann's survey [7] explains many kinds of transfer functions, but only a few multidimensional transfer functions have been developed. As transfer function domains are extended to two and three dimensions, the function yields more power in feature selection [9] [10]. For the same reason, it is difficult to set values manually.…”

“…For the same reason, it is difficult to set values manually. Nevertheless Kniss et al [10] suggested a convenient user interface widgets for setting three-dimensional (3D) transfer functions. Users, however, still needed to decide voxel transparencies from the displayed information of the two-dimensional (2D) histogram of v and g, while selecting interesting regions.…”

“…Similarly, thinner boundaries can be generated using the concave functions with larger n's. The three distance functions are represented as following: (10) and (11) where 0 < d c ≤ d max , 0 ≤ a ≤ 1, and n > 1. Eq.…”

“…The 2D transfer functions of v and g are more powerful than the 1D functions of v [9] [10]. However, as the transfer function domain is extended to 2D space, it makes it more difficult to search and locate features.…”