Dear Amr,

Attached is a publication which gives a good description for Gaussian transfer functions. I have copied some relevant text for quick view:

Gaussian Transfer Functions for Multi-Field Volume Visualization

Joe Kniss1 Simon Premozeˇ 2 Milan Ikits1 Aaron Lefohn1 Charles Hansen1 Emil Praun2

http://graphics.cs.ucdavis.edu/~lefohn/work/cachedPapers/vis03_kniss.pdf

Abstract

Volume rendering is a flexible technique for visualizing dense 3D volumetric datasets. A central element of volume rendering is the conversion between data values and observable quantities such as color and opacity. This process is usually realized through the use of transfer functions that are precomputed and stored in lookup tables. For multidimensional transfer functions applied to multivariate

data, these lookup tables become prohibitively large. We propose the direct evaluation of a particular type of transfer functions based on a sum of Gaussians. Because of their simple form (in terms of number of parameters), these functions and their analytic integrals along line segments can be evaluated efficiently on current graphics hardware, obviating the need for precomputed lookup tables. We have adopted these transfer functions because they are well suited for classification based on a unique combination of multiple data values that localize features in the transfer function domain. We apply this technique to the visualization of several multivariate datasets (CT, cryosection) that are difficult to classify and render accurately at interactive rates using traditional approaches. CR Categories: I.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism I.3.7 [Computer Graphics]: ThreeDimensional Graphics

Keywords: Volume Rendering, Transfer Functions, Multi-field

visualization

Direct volume rendering is a flexible technique for visualizing arbitrary three-dimensional scalar and multi-field datasets. Other 3D visualization techniques require the computation of an intermediate geometric representation of the data prior to rendering (e.g. creating a polygonal mesh using isosurface extraction). In contrast, direct volume rendering does not require intermediate geometry; the

data is resampled and converted to optical properties as it is being rendered. This conversion from data values to optical properties is represented using a transfer function, which is typically implemented as a lookup table. 

One advantage of direct volume rendering is its ability to visualize multiple values, or fields, simultaneously. Multi-field volume rendering has been shown to dramatically improve our ability to classify subtle features that may not be well characterized by any single input field [Laidlaw 1995]. Even scalar datasets can benefit from multi-field volume rendering techniques by adding fields for local derivative information [Kindlmann 1999]. For example, gradient magnitude characterizes the rate of change of values in some neighborhood and can help classify the input data set into homogeneous and transition regions [Kindlmann 2002]. Multiple data fields effectively place the ranges of data values representing different features at different locations in a multidimensional data space. Features may therefore be easier to classify in a multivariate dataset because ambiguities can be better resolved when different features share the same range of data values in an individual field. Although a multi-field dataset can be visualized using separate transfer functions for each field, multidimensional transfer functions

that specify the optical properties for each unique combination of data values are a more general and expressive representation [Kniss et al. 2002b; Kniss et al. 2002a]. A major limitation of multidimensional transfer functions using a lookup table is the

increased storage requirement. Each additional field in the dataset increases the size of the transfer function lookup table. For instance, a 1D transfer function for eight bit data would require 256 entries, whereas a 2D transfer function requires 2562 entries. In practice, we have found that it is not uncommon to encounter datasets that require 3D or even 4D transfer functions.

Hoping this will be helpful,

Rafik