A multiscale model for structure-based volume rendering

A scalar volume V={(x,f(x))|x/spl isin/R} is described by a function f(x) defined over some region R of the 3D space. We present a simple technique for rendering multiscale interval sets of the form I/sub s/(a,b)={(x,f/sub s/(x))|a/spl les/g/sub s/(x)/spl les/b}, where a and b are either real numbers or infinities, and f/sub s/(x) is a smoothed version of f(x). At each scale s, the constraint a/spl les/g/sub s/(x)/spl les/b identifies a subvolume in which the most significant variations of V are found. We use a dyadic wavelet transform to construct g/sub s/(x) from f(x) and derive subvolumes with the following attractive properties: 1) the information contained in the subvolumes are sufficient for reconstructing the entire V; and 2) the shapes of the subvolumes provide a hierarchical description of the geometric structures of V. Numerically, the reconstruction in 1) is only an approximation, but it is visually accurate as errors reside at fine scales where our visual sensitivity is not so acute. We triangulate interval sets as /spl alpha/-shapes, which can be efficiently rendered as semi-transparent clouds. Because interval sets are extracted in the object space, their visual display can respond to changes of the view point or transfer function quite fast. The result is a volume rendering technique that provides faster, more effective user interaction with practically no loss of information from the original data. The hierarchical nature of multiscale interval sets also makes it easier to understand the usual complicated structures in scalar volumes.