Abstract

SOSSA-AZUELA, H.; CUEVAS, F.J.; AGUILAR-IBANEZ, C.  and  BENITEZ-MUNOZ, H.. 3-D Cartesian Geometric Moment Computation using Morphological Operations and its Application to Object Classification. Ing. invest. y tecnol. [online]. 2007, vol.8, n.2, pp.111-123. ISSN 2594-0732.

Three-dimensional Cartesian geometric moments are important features for 3-D object recognition and shape description. Computing these features in the 3-D case by a straight for ward method requires a large number of operations. Several authors have proposed fast methods to compute the 3-D moments. Most of them require computations of order N³ , assuming that the object is represented by a NxNxN voxel image. Recently, Yang et al. (1996) presented a method requiring computation of O(N²) by using a discrete divergence theorem that allows to compute the sum of a function over an -dimensional discrete region by a summation over the discrete surface enclosing the object. In this paper, we present a new method to compute 3-D moments. For this, we first de compose the region into a set of balls (cubes) under d_∞ This decomposition forms a partition. Triple summations used in the computation of the moments are replaced by the sum of the moments of each cube of the partition. The moments of each cube can be computed in terms of a set of very simple expressions using the center of the cube and its radio. We show that once the partition is obtained, moment computation using the proposed approach is much faster than earlier methods; its complex ity is in fact of O(N). We also show several experiments where the de rived moments can be used to compute invariants useful in the recognition of three-dimensional objects.

Keywords : 2-D geometric moments; 3-D geometric moments; mathematical morphology; metric spaces.

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