Fast Recursive Computation of Krawtchouk Polynomials

Abdulhussain, Sadiq H.; Ramli, Abd Rahman; Al-Haddad, S. A. R.; Mahmmod, Basheera M.; Jassim, Wissam A.

doi:10.1007/s10851-017-0758-9

Cited by 40 publications

(38 citation statements)

References 22 publications

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“…Obviously, in the proposed method, the average execution time to generate DKPCs is less than existing methods. This achievement is due to: (1) the proposed method computed only 12.5% of the DKPCs, and (2) a reduced complexity forms of the existing recurrence relations are introduced (Equations (11) and (13)). To affirm the results of the proposed algorithm, the improvement ratio of the execution time is measured.…”

Section: Performance Evaluation Of the Proposed Methodsmentioning

confidence: 99%

“…The proposed method is also evaluated in terms of maximum size can be generated and compared to that of the existing methods. For each method, the maximum size is found using the procedure presented in [13]…”

Section: Performance Evaluation Of the Proposed Methodsmentioning

confidence: 99%

“…The coefficients in the range Figure 4) are computed using the following symmetry relation [13]: The steps of the method are depicted in Figure 5 and can be summarized as follows:…”

Section: Proposed Recurrence Algorithmmentioning

confidence: 99%

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On Computational Aspects of Krawtchouk Polynomials for High Orders

et al. 2020

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Discrete Krawtchouk polynomials are widely utilized in different fields for their remarkable characteristics, specifically, the localization property. Discrete orthogonal moments are utilized as a feature descriptor for images and video frames in computer vision applications. In this paper, we present a new method for computing discrete Krawtchouk polynomial coefficients swiftly and efficiently. The presented method proposes a new initial value that does not tend to be zero as the polynomial size increases. In addition, a combination of the existing recurrence relations is presented which are in the n- and x-directions. The utilized recurrence relations are developed to reduce the computational cost. The proposed method computes approximately 12.5% of the polynomial coefficients, and then symmetry relations are employed to compute the rest of the polynomial coefficients. The proposed method is evaluated against existing methods in terms of computational cost and maximum size can be generated. In addition, a reconstruction error analysis for image is performed using the proposed method for large signal sizes. The evaluation shows that the proposed method outperforms other existing methods.

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Section: Performance Evaluation Of the Proposed Methodsmentioning

confidence: 99%

Section: Performance Evaluation Of the Proposed Methodsmentioning

confidence: 99%

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On Computational Aspects of Krawtchouk Polynomials for High Orders

et al. 2020

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“…Different TTR algorithms have been proposed [11], [16]. In this study, the TTR algorithm, which was proposed by [15], is used. In this TTR algorithm, the KP plane is divided into four triangular parts bounded by primary and secondary diagonals, as shown in FIGURE 1.…”

Section: B Krawtchouk Orthogonal Polynomialmentioning

confidence: 99%

A New Separable Moments Based on Tchebichef-Krawtchouk Polynomials

2020

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Orthogonal moments are beneficial tools for analyzing and representing images and objects. Different hybrid forms, which are first and second levels of combination, have been created from the Tchebichef and Krawtchouk polynomials. In this study, all the hybrid forms, including the first and second levels of combination that satisfy the localization and energy compaction (EC) properties, are investigated. A new hybrid polynomial termed as squared Tchebichef-Krawtchouk polynomial (STKP) is also proposed. The mathematical and theoretical expressions of STKP are introduced, and the performance of the STKP is evaluated and compared with other hybrid forms. Results show that the STKP outperforms the existing hybrid polynomials in terms of EC and localization properties. Image reconstruction analysis is performed to demonstrate the ability of STKP in actual images; a comparative evaluation is also applied with Charlier and Meixner polynomials in terms of normalized mean square error. Moreover, an object recognition task is performed to verify the promising abilities of STKP as a feature extraction tool. A correct recognition percentage shows the robustness of the proposed polynomial in object recognition by providing a reliable feature vector for the classification process.

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“…The difference between transforms is determined by the type of the transform (polynomial) basis function. Basis functions are used to extract significant features of signals [ 114 ]. For example, DFT uses a set of complex and natural harmonically related exponential functions, whereas DCT is based on a cosine function with real values from

to 1.…”

Section: Sbd Approachesmentioning

confidence: 99%

Methods and Challenges in Shot Boundary Detection: A Review

Abdulhussain

Ramli

Saripan

et al. 2018

Entropy

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Abstract:The recent increase in the number of videos available in cyberspace is due to the availability of multimedia devices, highly developed communication technologies, and low-cost storage devices. These videos are simply stored in databases through text annotation. Content-based video browsing and retrieval are inefficient due to the method used to store videos in databases. Video databases are large in size and contain voluminous information, and these characteristics emphasize the need for automated video structure analyses. Shot boundary detection (SBD) is considered a substantial process of video browsing and retrieval. SBD aims to detect transition and their boundaries between consecutive shots; hence, shots with rich information are used in the content-based video indexing and retrieval. This paper presents a review of an extensive set for SBD approaches and their development. The advantages and disadvantages of each approach are comprehensively explored. The developed algorithms are discussed, and challenges and recommendations are presented.

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Fast Recursive Computation of Krawtchouk Polynomials

Cited by 40 publications

References 22 publications

On Computational Aspects of Krawtchouk Polynomials for High Orders

On Computational Aspects of Krawtchouk Polynomials for High Orders

A New Separable Moments Based on Tchebichef-Krawtchouk Polynomials

Methods and Challenges in Shot Boundary Detection: A Review

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