Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  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,  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,  compare it with existing methods such as pixel-based approaches and approximation of the region by a polygon.  also propose an alternate scheme when the scaling function is sinc(x).
['Mathews Jacob', 'Thierry Blu', 'Michael Unser']
I am writing a research paper on a idea An exact method for computing the area moments of wavelet and spline curves
[{"from": "human", "value": "I am writing a research paper on a idea An exact method for computing the area moments of wavelet and spline curves"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  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,  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,  compare it with existing methods such as pixel-based approaches and approximation of the region by a polygon.  also propose an alternate scheme when the scaling function is sinc(x)."}]