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<p><b>Abstract</b>—We present a method for the exact computation of the moments of a region bounded by a curve represented by a scaling function or wavelet basis. Using Green's Theorem, we show that the computation of the area moments is equivalent to applying a suitable multidimensional filter on the coefficients of the curve and thereafter computing a scalar product. The multidimensional filter coefficients are precomputed exactly as the solution of a two-scale relation. To demonstrate the performance improvement of the new method, we compare it with existing methods such as pixel-based approaches and approximation of the region by a polygon. We also propose an alternate scheme when the scaling function is <tmath>${\rm sinc}(x)$</tmath>.</p>
Area moments, curves, splines, wavelets, Fourier, two-scale relation, box splines, wavelet-Galerkin integrals.

M. Jacob, T. Blu and M. Unser, "An Exact Method for Computing the Area Moments of Wavelet and Spline Curves," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 23, no. , pp. 633-642, 2001.
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