Bc. Li et J. Shen, RANGE-IMAGE-BASED CALCULATION OF 3-DIMENSIONAL CONVEX OBJECT MOMENTS, IEEE transactions on robotics and automation, 9(4), 1993, pp. 484-490
In the paper, a novel method is proposed to calculate three-dimensiona
l (3-D) moments. First, a discrete Gaussian theorem is proposed to con
vert the summation in a 3-D volume domain to that on a 2-D plane regio
n, which decreases computational complexity from O(N3) to O(N2). Secon
d, a Pascal triangle transform, a Pascal triangle matrix, and a systol
ic structure are proposed to calculate the monomials on a 3-D object b
oundary surface, which simplifies the monomial calculation. Third, a r
ange image measurement system is used to implement the new method. Fin
ally, a comparison of our method with the known ones is provided, show
ing that our method is much simpler.