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| Mathews Jacob, Thierry Blu, Michael Unser, "An Exact Method for Computing the Area Moments of Wavelet and Spline Curves," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 23, no. 6, pp. 633-642, June, 2001. | |||
| BibTex | x | ||
| @article{ 10.1109/34.927463, author = {Mathews Jacob and Thierry Blu and Michael Unser}, title = {An Exact Method for Computing the Area Moments of Wavelet and Spline Curves}, journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence}, volume = {23}, number = {6}, issn = {0162-8828}, year = {2001}, pages = {633-642}, doi = {http://doi.ieeecomputersociety.org/10.1109/34.927463}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, } | |||
| RefWorks Procite/RefMan/Endnote | x | ||
| TY - JOUR JO - IEEE Transactions on Pattern Analysis and Machine Intelligence TI - An Exact Method for Computing the Area Moments of Wavelet and Spline Curves IS - 6 SN - 0162-8828 SP633 EP642 EPD - 633-642 A1 - Mathews Jacob, A1 - Thierry Blu, A1 - Michael Unser, PY - 2001 KW - Area moments KW - curves KW - splines KW - wavelets KW - Fourier KW - two-scale relation KW - box splines KW - wavelet-Galerkin integrals. VL - 23 JA - IEEE Transactions on Pattern Analysis and Machine Intelligence ER - | |||
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
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