Filtering Volumetric Data

The display of volumetric data is a problem of increasing importance. The display of this data is being studied in texture mapping and volume rendering applications. The goal of texture mapping is to add variation to the surfaces that is not caused by the geometric models of the objects. The goal of volume rendering is to display the data so that the study of this data is made easier. Three-dimensional texture mapping requires the use of ltering not only to reduce aliasing artifacts but also to compute the texture value which is to be used for the display. Study of two-dimensional texture map ltering techniques led to a number of techniques which were extended to three dimensions: namely clamping, elliptical weighted average (EWA) lters, and a pyramidal scheme known as NIL maps; (NIL stands for nodus in largo, the rough translation of which is knot large). The use of three-dimensional textures is not a straightforward extension of the use of two-dimensional textures. Where two-dimensional textures are usually discrete arrays of texture samples which are applied to the surface of objects, three-dimensional textures are usually procedural textures which can be applied on the surface of an object, throughout the object, or in volumes near the object. We studied the three-dimensional extensions of clamping, EWA lters, and NIL maps for ltering these textures. In addition to these three techniques a direct evaluation technique based on quadrature methods is presented. The performance of these four techniques is compared using a variety of criteria, and recommendations are made regarding their use. There are several techniques for volume rendering which can be formulated as ltering operations. By altering these display lters di erent views of the data can be generated. We modi ed the NIL map ltering technique for use as a lter-prototyping tool. This extension incorporated transfer functions into the NIL map technique. This allows the manipulation of the transfer functions without requiring the re-computation of the NIL maps. The use of NIL maps as a lter-prototyping tool is illustrated with a series of examples.