Algorithms for fast computation of Zernike moments and their numerical stability

  • Authors:

  • Chandan Singh;Ekta Walia

  • Affiliations:

  • Department of Computer Science, Punjabi University, Patiala, 147002, India;Department of Information Technology, M.M.University, Mullana, Ambala, 133203, India

  • Venue:
  • Image and Vision Computing
  • Year:
  • 2011

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Abstract

Accuracy, speed and numerical stability are among the major factors restricting the use of Zernike moments (ZMs) in numerous commercial applications where they are a tool of significant utility. Often these factors are conflicting in nature. The direct formulation of ZMs is prone to numerical integration error while in the recent past many fast algorithms are developed for its computation. On the other hand, the relationship between geometric moments (GMs) and ZMs reduces numerical integration error but it is observed to be computation intensive. We propose fast algorithms for both the formulations. In the proposed method, the order of time complexity for GMs-to-ZMs formulation is reduced and further enhancement in speed is achieved by using quasi-symmetry property of GMs. The existing q-recursive method for direct formulation is further modified by incorporating the recursive steps for the computation of trigonometric functions. We also observe that q-recursive method provides numerical stability caused by finite precision arithmetic at high orders of moment which is hitherto not reported in the literature. Experimental results on images of different sizes support our claim.