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Moment Computation for Objects with Spline Curve Boundary
October 2003 (vol. 25 no. 10)
pp. 1317-1322

Abstract—A new approach is proposed for computation of area and geometric moments for a plane object with a spline curve boundary. The explicit formulae are obtained for area and low order moment calculation. The complexity of calculation depends on the moment order, spline degree, and the number of control points used in spline representation. The formulae proposed use the advantage that the sequence of spline control points is cyclic. It allowed us to reduce substantially the number of summands in them. The formulae might be useful in different applications where it is necessary to perform measurements for shapes with a smooth boundary.

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Index Terms:
Area, moment, parametric curve, spline, explicit formulae.
Stanislav Sheynin, Alexander Tuzikov, "Moment Computation for Objects with Spline Curve Boundary," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 25, no. 10, pp. 1317-1322, Oct. 2003, doi:10.1109/TPAMI.2003.1233905
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