Efficient Computation of Three-dimensional Geometric Moments Based on Object Partition
Humberto Sossa, Héctor Benítez‐Pérez · LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas) · 2005
We present a method for computing the three-dimensional moments of an object. The method is based on the idea that the object of interest is first decomposed in a set of cubes under d . This decomposition is known to form a partition. The required moments are computed as a sum of the moments of the elements of the partition. The moments of each cube can be calculated in terms of a set of very simple formula using the center of the cube and its radio. The method provides integral accuracy by applying the exact definition of moments. The desired partition is obtained both by morphological erosions and the distance transformation of the image. Both variants are compared, showing that the one using the distance transform is much faster, making it comparable to other traditional sequential approaches. Another interesting feature of the proposed idea to compute the geometric moments of a 3-D object is that once the partition is obtained, moment computation is much faster than earlier methods. Its complexity is in fact of O(N).