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Fast Computation of Three-Dimensional Geometric Moments Using a Discrete Divergence Theorem and a Generalization to Higher Dimensions by Luren Yang; Fritz Albregtsen; Torfinn Taxt is a Computer Science article available to read on EtoBox.

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three-dimensional Cartesian geometric moment (for short 3-D moment) of order p ϩ q ϩ r of a 3-D object is defined The three-dimensional Cartesian geometric moments (for short 3-D moments) are important features for 3-D object recogas [2] nition and shape description. To calculate the moments of objects in a 3-D image by a straightforward method requires m pqr ϭ ͵ ͵ ͵ R x p y q z r g(x, y, z) dz dy dx, (2) large number of computing operations. Some authors have proposed fast algorithms to compute the 3-D moments. However, the problem of computation has not been well solved since where R is a 3-D region. In a binary 3-D image, the moment all known methods require computations of order N 3 , assuming that the object is represented by an N ؋ N ؋ N voxel image. of a 3-D homogeneous object represented by voxels (vol-In this paper, we present a discrete divergence theorem which ume elements) is often evaluated as [3] can be used to compute the sum of a function over an ndimensional discrete region by a summation over the discrete m pqr ϭ R x p y q z r (3) surface enclosing the region. As its corollaries, we give a discrete Gauss's theorem for 3-D discrete objects and a discrete Green's th

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Author

Luren Yang; Fritz Albregtsen; Torfinn Taxt

Publisher

Elsevier Science; Elsevier - Academic Press; Academic Press; Elsevier BV (ISSN 1077-3169)

Published

1997

Language

EN

Field

Computer Science (Physical Sciences)