Multiscale Representation of Geometry

Howard L. Resnikoff () and Raymond O. Wells ()
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Howard L. Resnikoff: Future WAVE Inc.
Raymond O. Wells: Rice University, Department of Mathematics

Chapter 11 in Wavelet Analysis, 1998, pp 266-279 from Springer

Abstract: Abstract In this chapter, we introduce a wavelet multiscale representation for geometric regions and geometric integrals in Euclidean space. The basic idea is to represent a geometric region in terms of the characteristic function of its interior. By differentiating this function, we obtain a measure supported on the boundary of the region. For instance, for an interval, this measure would consist of Dirac delta measures supported at the endpoints. By using the connection coefficients introduced in the preceding chapter, we are able to formulate a multiresolution expansion for the boundary measure and, consequently, for boundary integrals. These boundary integrals have been used extensively in the wavelet—Galerkin solution for certain types of elliptic boundary value problems as discussed in Chapter 12.

Keywords: Boundary Integral; Wavelet Representation; Daubechies Wavelet; Geometric Measure Theory; Wavelet System (search for similar items in EconPapers)
Date: 1998
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-0593-7_11

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DOI: 10.1007/978-1-4612-0593-7_11

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