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      Efficient Legendre moment computation for grey level images

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          Abstract

          Legendre orthogonal moments have been widely used in the field of image analysis. Because their computation by a direct method is very time expensive, recent efforts have been devoted to the reduction of computational complexity. Nevertheless, the existing algorithms are mainly focused on binary images. We propose here a new fast method for computing the Legendre moments, which is not only suitable for binary images but also for grey levels. We first set up the recurrence formula of one-dimensional (1D) Legendre moments by using the recursive property of Legendre polynomials. As a result, the 1D Legendre moments of order p, Lp = Lp(0), can be expressed as a linear combination of Lp-1(1) and Lp-2(0). Based on this relationship, the 1D Legendre moments Lp(0) is thus obtained from the array of L1(a) and L0(a) where a is an integer number less than p. To further decrease the computation complexity, an algorithm, in which no multiplication is required, is used to compute these quantities. The method is then extended to the calculation of the two-dimensional Legendre moments Lpq. We show that the proposed method is more efficient than the direct method.

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          Author and article information

          Journal
          12 March 2014
          Article
          10.1016/j.patcog.2005.08.008
          1403.3022
          a88e35f0-d654-4126-a65e-15334a8827db

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

          History
          Custom metadata
          Pattern Recognition 39, 1 (2006) 74-80
          cs.CV math.NA
          ccsd

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