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Title: A Fast Algorithm to Map Functions Forward
Authors: Lawton, W. 
Keywords: Approximate expansions using moments
Daubechies orthonormal wavelet basis
Image warping
Interpolation kernels and subdivision
Scattered data interpolation
Issue Date: 1997
Citation: Lawton, W. (1997). A Fast Algorithm to Map Functions Forward. Multidimensional Systems and Signal Processing 8 (1-2) : 219-227. ScholarBank@NUS Repository.
Abstract: Mapping functions forward is required in image warping and other signal processing applications. The problem is described as follows: specify an integer d ≥ 1, a compact domain D ⊂ Rd, lattices L1, L2 ⊂ Rd, and a deformation function F : D → Rd that is continuously differentiable and maps D one-to-one onto F(D). Corresponding to a function J : F(D) → R, define the function I = J ○ F. The forward mapping problem consists of estimating values of J on L2 ∩ F(D), from the values of I and F on L1 ∩ D. Forward mapping is difficult, because it involves approximation from scattered data (values of I ○ F-1 on the set F(L1 ∩ D)), whereas backward mapping (computing I from J) is much easier because it involves approximation from regular data (values of J on L2 ∩ D). We develop a fast algorithm that approximates J by an orthonormal expansion, using scaling functions related to Daubechies wavelet bases. Two techniques for approximating the expansion coefficients are described and numerical results for a one dimensional problem are used to illustrate the second technique. In contrast to conventional scattered data interpolation algorithms, the complexity of our algorithm is linear in the number of samples.
Source Title: Multidimensional Systems and Signal Processing
ISSN: 09236082
Appears in Collections:Staff Publications

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