• 호남수학학술지
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• 제37권1호
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• pp.113-126
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• 2015

Recently, Liu and Wang generalized Appell's and Lauricella's hypergeometric functions. Motivated by the work of Liu and Wang, the main object of this paper is to present new generalizations of Appell's and Lauricella's hypergeometric functions. Some integral representations, transformation formulae, differential formulae and recurrence relations are obtained for these new generalized Appell's and Lauricella's functions.

• 대한기계학회논문집A
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• 제39권6호
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• pp.589-596
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• 2015

횡등방성 압전재료에 대한 모서리경사균열 문제를 해석하였다. 두 기계적 집중 면외하중과 전기적 집중 면내하중이 표면과 균열면에 각각 작용하고, 균열면은 절연균열면이다. 일반화된 변위벡터를 도입하고 Mellin 변환을 사용하여 문제를 수식화하고, 이로부터 Wiener-Hopf 식을 유도하였다. 이식을 풀므로써 폐형으로 주어지는 해를 얻었다. 임의의 균열길이나 경사각에 대해서도 적용이 되는 응력 및 전기변위 강도계수와 에너지 방출율을 구하였다. 이 해는 중첩에 의하여 임의로 분포하는 전기기계하중 문제에 대한 해를 제공하는 기본해로 사용될 수 있다.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제12권9호
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• pp.4467-4486
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• 2018

Trying to deal with the problem of low robustness of Copy-Move Forgery Detection (CMFD) under various transformation and degradation attacks, a novel CMFD method is proposed in this paper. The main advantages of proposed work include: (1) Discrete Analytical Fourier-Mellin Transform (DAFMT) and Locality Sensitive Hashing (LSH) are combined to extract the block features and detect the potential copy-move pairs; (2) The Euclidian distance is incorporated in the pixel variance to filter out the false potential copy-move pairs in the post-verification step. In addition to extracting the effective features of an image block, the DAMFT has the properties of rotation and scale invariance. Unlike the traditional lexicographic sorting method, LSH is robust to the degradations of Gaussian noise and JEPG compression. Because most of the false copy-move pairs locate closely to each other in the spatial domain or are in the homogeneous regions, the Euclidian distance and pixel variance are employed in the post-verification step. After evaluating the proposed method by the precision-recall-$F_1$ model quantitatively based on the Image Manipulation Dataset (IMD) and Copy-Move Hard Dataset (CMHD), our method outperforms Emam et al.'s and Li et al.'s works in the recall and $F_1$ aspects.

• 한국멀티미디어학회논문지
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• 제13권6호
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• pp.875-883
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• 2010

In this paper, we present a secure biometric hashing scheme for face recognition by random fusion of global and local features. The Fourier-Mellin transform and Radon transform are adopted respectively to form specialized representation of global and local features, due to their invariance to geometric operations. The final biometric hash is securely generated by random weighting sum of both feature sets. A fourfold key is involved in our algorithm to ensure the security and privacy of biometric templates. The proposed biometric hash can be revocable and replaced by using a new key. Moreover, the attacker cannot obtain any information about the original biometric template without knowing the secret key. The experimental results confirm that our scheme has a satisfactory accuracy performance in terms of EER.

• International Journal of Contents
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• 제5권2호
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• pp.26-31
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• 2009

This paper describes a new image watermarking scheme invariant to rotation, scaling and translation (RST) attacks. For obtaining the invariance properties we propose to present an image of watermark by wedges and rings to convert its rotation to shift and then utilize the shift invariance property of the Direct Fourier Transform (DFT). But in contrast to conversional schemes based on the Fourier-Mellin transform (FMT), we do not use a log-polar mapping (LPM). As a result, our scheme preserves high quality of original image since it is not underwent to LPM For withstanding against JPEG compression, noise addition and low-pass (LP) filtering attacks a low frequency watermark is embedded into middle frequencies of the original image. Experiments with various attacks show the robustness of the proposed scheme.

• 전자공학회논문지B
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• 제33B권8호
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• pp.30-41
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• 1996

This paper presents a comparative study of four pattern recognition algorithms which are invariant to translations, rotations, and scale changes of the input object; namely, object shape features (OSF), geometrica fourier mellin transform (GFMT), moment invariants (MI), and centered polar exponential transform (CPET). Pattern description is obviously one of the most important aspects of pattern recognition, which is useful to describe the object shape independently of translation, rotation, or size. We first discuss problems that arise in the conventional invariant pattern recognition algorithms, or size. We first discuss problems that arise in the coventional invariant pattern recognition algorithms, then we analyze their performance using the same criterion. Computer simulations with several distorted images show that the CPET algorithm yields better performance than the other ones.

• 호남수학학술지
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• 제45권2호
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• pp.184-197
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• 2023

For the numerous uses and significance of the Whittaker function in the diverse research areas of mathematical sciences and engineering sciences, This paper aims to introduce an extension of the Whittaker function by using a new extended confluent hypergeometric function of the first kind in terms of the Mittag-Leffler function. We also drive various valuable results like integral representation, integral transform and derivative formula. Further, we also analyze specific known results as a particular case of the main result.

• 대한기계학회논문집A
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• 제39권9호
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• pp.859-869
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• 2015

횡등방성 압전재료에 기하학적 비대칭인 쐐기균열문제를 해석하였다. 기계적 집중면외하중과 전기적 집중 면내하중이 쐐기표면 점에 작용하고 있고, 반면에 균열면 한점에는 기계적 집중하중만 작용한다. 균열면은 침투형 얇은 슬릿으로 가정하여, 전기변위의 수직성분 및 전위가 균열면을 가로질러 연속으로 두었다. Mellin 변환을 사용하여 문제를 수식화하고, Wiener-Hopf 식을 유도하였다. 이 식을 풀므로써 폐형으로 주어지는 해를 얻었다. 임의 균열길이나 경사각, 쐐기각에 대해서도 적용이 가능한 응력 및 전기변위 강도계수를 구하였다. 장의 강도계수들은 전기적 하중에는 무관하고, 전기변위강도계수는 응력강도계수만의 함수로 표현되었다. 전기장 강도계수는 영으로 계산되었다. 또한 에너지방출률을 얻었다. 이 해는 중첩에 의하여 임의로 분포하는 전기기계하중문제에 대한 해를 제공하는 기본해로 사용될 수 있다.

• Journal of Mechanical Science and Technology
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• 제18권9호
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• pp.1549-1558
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• 2004

This study is concerned with the general solution of the field intensity factors and energy release rate for a Griffith crack in a piezoelectric ceramic of finite radius under combined anti-plane mechanical and in-plane electrical loading. Both electrically continuous and impermeable crack surface conditions are considered. Employing Mellin transforms and Fourier series, the problem is reduced to dual integral forms. The solution to the resulting expressions is expressed in terms of Fredholm integral equation of the second kind. The solutions are provided to study the influence of the crack length, the crack surface boundary conditions on the intensity factors and the energy release rate.

• 호남수학학술지
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• 제36권2호
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• pp.357-385
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• 2014

Recently several authors have extended the Gamma function, Beta function, the hypergeometric function, and the confluent hypergeometric function by using their integral representations and provided many interesting properties of their extended functions. Here we aim at giving further extensions of the abovementioned extended functions and investigating various formulas for the further extended functions in a systematic manner. Moreover, our extension of the Beta function is shown to be applied to Statistics and also our extensions find some connections with other special functions and polynomials such as Laguerre polynomials, Macdonald and Whittaker functions.