An Exact Method for Computing the Area Moments of Wavelet and Spline Curves

  • Authors:

  • Mathews Jacob;Thierry Blu;Michael Unser

  • Affiliations:

  • Swiss Federal Institute of Technology, Lausanne, Switzerland;Swiss Federal Institute of Technology, Lausanne, Switzerland;Swiss Federal Institute of Technology, Lausanne, Switzerland

  • Venue:
  • IEEE Transactions on Pattern Analysis and Machine Intelligence
  • Year:
  • 2001

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Abstract

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 ${\rm sinc}(x)$.