An exact method for computing the area moments of wavelet and spline curves

We present a method for the exact computation of the moments of a region bo unded 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 equiva lent to applying a suitable multidimensional filter on the coefficients of the curve and thereafter computing a scalar product. The multidimensional f ilter coefficients are precomputed exactly as the solution of a two-scale r elation. To demonstrate the performance improvement of the new method, we c ompare it with existing methods such as pixel-based approaches and approxim ation of the region by a polygon. We also propose an alternate scheme when the scaling function is sinc(x).