Jacob, MathewsMathewsJacobTHIERRY BLUUnser, MichaelMichaelUnser2024-03-082024-03-082001-06-0101628828https://scholars.lib.ntu.edu.tw/handle/123456789/640671We 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 sinc(x).Area moments | Box splines | Curves | Fourier | Splines | Two-scale relation | Wavelet-Galerkin integrals | Waveletsjournal article10.1109/34.9274632-s2.0-0035364932https://api.elsevier.com/content/abstract/scopus_id/0035364932