On the Mathematical Properties of the Zernike Polynomials

Kintner, Eric C.

doi:10.1080/713819334

Cited by 91 publications

(60 citation statements)

References 3 publications

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“…This makes it impractical for many applications. This limitation has prompted considerable study of algorithms for the fast evaluation of Zernike moments [3,29,36]. Several algorithms have been proposed to speed up the computation.…”

Section: Methods 3: Region Of Interest Image Classification Using a Zementioning

confidence: 99%

“…Belkasim et al [3] introduced a fast algorithm based on the series expansion of radial polynomials. Parta et al [36] and Kintner [29] have proposed recurrence relations for fast computation of radial polynomials of Zernike moments. Chong et al [7] modified Kintners method so that it would be applicable for all cases.…”

Section: Methods 3: Region Of Interest Image Classification Using a Zementioning

confidence: 99%

See 1 more Smart Citation

Region Of Interest Based Image Classification: A Study in MRI Brain Scan Categorization

Elsayed¹

2012

Data Mining Applications in Engineering and Medicine

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Section: Methods 3: Region Of Interest Image Classification Using a Zementioning

confidence: 99%

Section: Methods 3: Region Of Interest Image Classification Using a Zementioning

confidence: 99%

Region Of Interest Based Image Classification: A Study in MRI Brain Scan Categorization

Elsayed¹

2012

Data Mining Applications in Engineering and Medicine

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“…As orthogonal frequently appears in conjunction with Bessel functions it is also called the Neumann factor (Kintner, 1976). The product of the angular and radial parts establishes the orthogonality of the Zernike functions with respect to both indices if integrated over the unit disk Eq.…”

Section: Methodsmentioning

confidence: 99%

Automatic Palmprint Identification based on High Order Zernike Moment

S.¹

2012

American Journal of Applied Sciences

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Problem statement: Hand geometry contains relatively invariant features of an individual. Palmprint recognition is an efficient biometric solution for authentication system. The existence of several hand-based authentication commercial systems indicates the effectiveness of this type of biometric. Approach: We proposed a palmprint verification system using high order Zernike moment that was robust to rotation, translation and occlusion. Zernike moment was an efficient algorithm for representing the shape features of an image. The design consists of feature extraction and matching of image using high order Zernike moment. Zernike moments at high orders was calculated from the image and the image was classified using K-Nearest Neighborhood (KNN). The reason for using Zernike moment was that it was the best algorithm due to its orthogonality and rotation invariance property. Results and Conclusion: Computational cost can be reduced by detecting the common term of Zernike moment. Experiments and classifications have been performed using Hong Kong PolyU palm print database with 125 individuals' left hand palm images; every person has 5 samples, totaling up to 625. We then get every person's palm images as a template (totaling 125). The remaining 500 are used as the training samples. The proposed palmprint authentication system achieves a recognition accuracy of 98% and interesting working point with False Acceptance Rate (FAR) of = 1.062% and False Rejection Rate (FRR) of = 0%. Experimental evaluation demonstrates the efficient recognition performance of the proposed algorithm compared with conventional palmprint recognition algorithms.

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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.

show abstract

On the Mathematical Properties of the Zernike Polynomials

Cited by 91 publications

References 3 publications

Region Of Interest Based Image Classification: A Study in MRI Brain Scan Categorization

Region Of Interest Based Image Classification: A Study in MRI Brain Scan Categorization

Automatic Palmprint Identification based on High Order Zernike Moment

Sorting of rice grains using Zernike moments

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