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.

Object moments and moment invariants are widely used in image analysis and recognition. The paper describes an approach and presents explicit formulae for calculation of polyhedron volume and surface moments via coordinates of polyhedron vertices. General formulae for calculation of arbitrary order volume and surface moments for polytopes in R/sup n/ are also obtained.