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

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3 Author(s)
Jacob, M. ; Biomed. Imaging Group, Swiss Federal Inst. of Technol., Lausanne, Switzerland ; Blu, T. ; Unser, M.

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 sinc(x)

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Pattern Analysis and Machine Intelligence, IEEE Transactions on  (Volume:23 ,  Issue: 6 )