Translation and scale invariants of Tchebichef moments
Pattern Recognition
Gauss-Green cubature and moment computation over arbitrary geometries
Journal of Computational and Applied Mathematics
Recursive computation of moments of 2D objects represented by elliptic Fourier descriptors
Pattern Recognition Letters
Modeling and Estimation of the Dynamics of Planar Algebraic Curves via Riccati Equations
Journal of Mathematical Imaging and Vision
3D object volume measurement using freehand ultrasound
SCIA'05 Proceedings of the 14th Scandinavian conference on Image Analysis
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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.