Range-image-based calculation of three-dimensional convex object moments

In the paper, a novel method is proposed to calculate three-dimensional (3-D) moments. First, a discrete Gaussian theorem is proposed to convert the summation in a 3-D volume domain to that on a 2-D plane region, which decreases computational complexity from O(N³) to O(N²). Second, a Pascal triangle transform, a Pascal triangle matrix, and a systolic structure are proposed to calculate the monomials on a 3-D object boundary surface, which simplifies the monomial calculation. Third, a range-image measurement system is used to implement the new method. Finally, a comparison of the authors´ method with the known ones is provided, showing that the authors´ method is much simpler