Efficient algorithm for fast computation of Zernike moments

Belkasim, Saeid; Ahmadi, Majid; Shridhar, M.

doi:10.1016/0016-0032(96)00017-8

Cited by 36 publications

(19 citation statements)

References 16 publications

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“…(2), there are a lot of computations (factorials) that should be carried out, if the direct method chosen for the calculation of the Zernike moments. For this reason, many researchers have introduced fast computation methods [9,[22][23][24][25][26] that eliminate the need of such time consumptive calculations. Among these, the wellknown q-recursive method [9] is considered to be the most efficient and is used in this paper.…”

Section: Recursive Computationmentioning

confidence: 99%

“…They are used, after making them invariant to scale and translation, as object descriptors in pattern recognition applications [3][4][5][17][18][19] and in image retrieval tasks [20,21] with considerable results. Recently, due to their popularity, many methods for accelerating their computation time have been proposed [9,[22][23][24][25][26] in order to make them more useful, especially in real time applications, where time is a critical factor.…”

Section: Zernike Momentsmentioning

confidence: 99%

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Numerical error analysis in Zernike moments computation

Papakostas

Boutalis

Papaodysseus

et al. 2006

Image and Vision Computing

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Section: Recursive Computationmentioning

confidence: 99%

Section: Zernike Momentsmentioning

confidence: 99%

Numerical error analysis in Zernike moments computation

Papakostas

Boutalis

Papaodysseus

et al. 2006

Image and Vision Computing

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“…Another approach which uses the recurrence relationships between successive Zernike polynomials has also been proposed to increase the computation speed. Algorithms under this approach include Belkasim's [1], Prata's [23], Kintner's [19] and its simplified version (p-recursive) [28], and q-recursive [6] methods.…”

Section: Introductionmentioning

confidence: 99%

Sorting of rice grains using Zernike moments

Wee

Raveendran

Takeda

2009

J Real-Time Image Proc

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Two important factors that determine the efficiency and reliability of a rice sorting machine are the overall processing speed and the classification accuracy. In this paper, an efficient rice sorting process which uses a subset of Zernike moments (ZM) and a multilayer perceptron is presented. Since the falling rice grains during sorting process can be in any orientation, a rotational invariant feature set is crucial in this application. Hence, the set of ZM with its inherent rotational invariance property is chosen in this context. Nevertheless, one of the main drawbacks of ZM in real-time application is its long computation time. To overcome this, a subset of ZM is selected from its original full set of 12 orders, using the combination of fuzzy ARTMAP and genetic algorithm. To further reduce the computation time, the combination of q-recursive method and Zernike polynomials' inherent symmetry property is utilized. Hence, the processing time of the subset of ZM is significantly reduced by almost 67% while maintaining the classification accuracy as compared to computing the original full set of ZMs.

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“…To mention some, Mukandan Coefficient method [9], Prata method [11], Q-Recursive method [3], Kintner method [7], and the modified Kintner method [6], within the five methods, the radial polynomials are calculated using proposed recurrence relations. Belkasim [2], used the radial and angular expansions of Zernike polynomials in order to perform fast computation of Zernike moments.…”

Section: Introductionmentioning

confidence: 99%

Fast Zernike moments

Al-Rawi

2008

J Real-Time Image Proc

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Zernike moments are important digital image descriptors used in various applications starting from image watermarking to image recognition. Lots of fast algorithms have been proposed to speedup the computation of Zernike moments. This work provides computational complexity analysis of methods for the computation of Zernike moments, as well as a thorough study and simplification to the methods of finding Zernike moments from geometric moments. A new formula that relates Zernike moments to moments of digital filters is introduced that is very efficient and accurate. Comparisons are performed using Zernike moment via geometric moments method, the Q-recursive method, the coefficient method, and the symmetry method. Using a well defined performance metric, this work finds out that Zernike moments from geometric moments of digital filters is nearly 70 times faster than the best method known as the symmetry method.

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Efficient algorithm for fast computation of Zernike moments

Cited by 36 publications

References 16 publications

Numerical error analysis in Zernike moments computation

Numerical error analysis in Zernike moments computation

Sorting of rice grains using Zernike moments

Fast Zernike moments

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