RANGE-IMAGE-BASED CALCULATION OF 3-DIMENSIONAL CONVEX OBJECT MOMENTS

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.