A MULTISCALE MODEL FOR STRUCTURE-BASED VOLUME RENDERING

A scalar volume V = {(x,f(x)) \ x is an element of R} is described by a function f(jr) defined over some region R of the 3D space. In this p aper, we present a simple technique for rendering multiscale interval sets of the form I-s(a, b) = {(x,f(s)(x)) \ a less than or equal to g( s)(x) less than or equal to b}, where a and b are either real numbers or infinities, and f(s)(x) is a smoothed version of f(x). At each scal e s, the constraint a less than or equal to g(s)(x) less than or equal to b identifies a subvolume in which the most significant variations of V are found. We use dyadic wavelet transform to construct g(s)(x) f rom f(x) and derive subvolumes with the following attractive propertie s: 1) the information contained in the subvolumes are sufficient for r econstructing the entire V, and 2) the shapes of the subvolumes provid e a hierarchical description of the geometric structures of V. Numeric ally, the reconstruction in 1) is only an approximation, but it is vis ually accurate as errors reside at fine scales where our visual sensit ivity is not so acute. We triangulate interval sets as alpha-shapes, w hich can be efficiently rendered as semi-transparent clouds. Because i nterval sets are extracted in the object space, their visual display c an respond to changes of the view point or transfer function quite fas t. The result is a volume rendering technique that provides faster, mo re 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 structu res in scalar volumes.