A multiscale model for structure-based volume rendering

摘要

A scalar volume V={(x,f(x))|x∈R} is described by a functionnf(x) defined over some region R of the 3D space. We present a simplentechnique for rendering multiscale interval sets of the form Isn(a,b)={(x,fs(x))|a⩽gs(x)⩽b}, where anand b are either real numbers or infinities, and fs(x) is ansmoothed version of f(x). At each scale s, the constraint a⩽gsn(x)⩽b identifies a subvolume in which the most significantnvariations of V are found. We use a dyadic wavelet transform tonconstruct gs(x) from f(x) and derive subvolumes with thenfollowing attractive properties: 1) the information contained in thensubvolumes are sufficient for reconstructing the entire V; and 2) thenshapes of the subvolumes provide a hierarchical description of thengeometric structures of V. Numerically, the reconstruction in 1) is onlynan approximation, but it is visually accurate as errors reside at finenscales where our visual sensitivity is not so acute. We triangulateninterval sets as Α-shapes, which can be efficiently rendered asnsemi-transparent clouds. Because interval sets are extracted in thenobject space, their visual display can respond to changes of the viewnpoint or transfer function quite fast. The result is a volume renderingntechnique that provides faster, more effective user interaction withnpractically no loss of information from the original data. Thenhierarchical nature of multiscale interval sets also makes it easier tonunderstand the usual complicated structures in scalar volumes