Sparse Filter Banks for Binary Subdivision Schemes
نویسنده
چکیده
Schemes Joe Warren Rice University Abstract Multi-resolution analysis (MRA) produces a hierarchical basis for representing functions. This basis can be used to improve the e ciency of many algorithms for computing with those functions. Traditionally, these basis functions are translates and dilates of a single function. In this paper, we outline a generalization of MRA to those functions de ned by binary subdivision schemes. Although the mathematical underpinnings of MRA are somewhat involved, the resulting algorithms are quite simple. We start with a brief intuitive description of how the method can be applied to decompose the polyhedral object shown in Figure 1(a). The main idea behind MRA is the decomposition of an object, in this case a polyhedron, into a low resolution part and a \detail" part. The low resolution part of the polyhedron in Figure 1(a) is shown in Figure 1(b). The vertices in (b) are computed as certain weighted averages of the vertices in (a). These weighted averages essentially implement a low pass lter denoted as A. The detail part consists of a collection of fairly abstract coe cients, called wavelet coe cients, that are also computed as weighted averages of the ... A A A
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