• Communications of the Korean Mathematical Society
• /
• v.34 no.2
• /
• pp.507-522
• /
• 2019

The main aim of this present paper is to present a new extension of the fractional derivative operator by using the extension of beta function recently defined by Shadab et al. [19]. Moreover, we establish some results related to the newly defined modified fractional derivative operator such as Mellin transform and relations to extended hypergeometric and Appell's function via generating functions.

• Journal of applied mathematics & informatics
• /
• v.37 no.1_2
• /
• pp.13-21
• /
• 2019

In the present research paper, we introduce a further extension of Hurwitz-Lerch zeta function by using the generalized extended Beta function defined by Parmar et al.. We investigate its integral representations, Mellin transform, generating functions and differential formula. In view of diverse applications of the Hurwitz-Lerch Zeta functions, the results presented here may be potentially useful in some related research areas.

• Nonlinear Functional Analysis and Applications
• /
• v.29 no.1
• /
• pp.99-111
• /
• 2024

In this paper, a new seven-parameter Mittag-Leffler function of a single complex variable is proposed as a generalization of the standard Mittag-Leffler function, certain generalizations of Mittag-Leffler function, hypergeometric function and confluent hypergeometric function. Certain essential analytic properties are mainly discussed, such as radius of convergence, order, type, differentiation, Mellin-Barnes integral representation and Euler transform in the complex plane. Its relation to Fox-Wright function and H-function is also developed.

• Proceedings of the Korean Society of Broadcast Engineers Conference
• /
• 2009.01a
• /
• pp.450-455
• /
• 2009

Amplitude-only logarithmic Radon transform (ALR transform) for pattern matching is proposed. This method provides robustness for object translation, scaling, and rotation. An ALR image is invariant even if objects are translated in a picture. For the object scaling and rotation, the ALR image is merely translated. The objects are identified using a phase-only matched filter to the ALR image. The ratio of size, the difference of rotation angle, and the position between the two objects are detected. Our pattern matching procedure is described, herein, and its simulation is executed. We compare matching scores with the Fourier-Mellin transform, and the general phase-only matched filter.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.17 no.2
• /
• pp.277-284
• /
• 1993

Interfacial surface crack perpendicular to the surface, which is imbedded into bonded quarter planes under single anti-plane shear load is analyzed. The problem is formulated using Mellin transform, form which single Wiener-Hopf equation is derived. By solving the equation stress intensity factor is obtained in closed form. This solution can be used as a Green's function to generate the solutions of other problems with the same geometry but of different loading conditions.

• Kyungpook Mathematical Journal
• /
• v.56 no.4
• /
• pp.1169-1177
• /
• 2016

This paper is devoted to the study of Mellin, Laplace, Euler and Whittaker transforms involving Struve function, generalized Wright function and Fox's H-function. The main results are presented in the form of four theorems. On account of the general nature of the functions involved here in, the main results obtained here yield a large number of known and new results in terms of simpler functions as their special cases. For the sake of illustration some corollaries have been recorded here as special cases of our main findings.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
• /
• 2003.05a
• /
• pp.255-258
• /
• 2003

Recently, Digital Watermarking is used to authenticate data and to determine whether the data are distorted or not in medical images which is digitalized. The Fourier Mellin method using the Fourier Transform and the Log-Polar coordinate transform gets an invariant feature for RST distortion in images. But there are several problems in the real materialization. Interpolation of the image value should be considered according to the pixel position and so a watermark loss, original image distortion, numerical approximation is happened. Therefore there should be solved to realization of the Fourier Mellin method. Using the Look up table, there reduce the data loss caused by the conversion between Rectangular and Polar coordinate. After diagnose, medical images are transformed the Polar coordinate and taken the Discrete Fourier transform in the center of ROI region. Maintaining the symmetry in Fourier magnitude coefficient, the gaussian distributed random vectors and binary images are embedded in medical images.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.15 no.5
• /
• pp.1744-1760
• /
• 2021

Since correlation filter appeared in the field of object tracking, it plays an increasingly vital role due to its excellent performance. Although many sophisticated trackers have been successfully applied to track the object accurately, very few of them attaches importance to the scale and rotation estimation. In order to address the above limitation, we propose a novel method combined with Fourier-Mellin transform and confidence evaluation strategy for robust object tracking. In the first place, we construct a correlation filter to locate the target object precisely. Then, a log-polar technique is used in the Fourier-Mellin transform to cope with the rotation and scale changes. In order to achieve subpixel accuracy, we come up with an efficient surface fitting mechanism to obtain the optimal calculation result. In addition, we introduce a confidence evaluation strategy modeled on the output response, which can decrease the impact of image noise and perform as a criterion to evaluate the target model stability. Experimental experiments on OTB100 demonstrate that the proposed algorithm achieves superior capability in success plots and precision plots of OPE, which is 10.8% points and 8.6% points than those of KCF. Besides, our method performs favorably against the others in terms of SRE and TRE validation schemes, which shows the superiority of our proposed algorithm in scale and rotation evaluation.

• International Journal of Precision Engineering and Manufacturing
• /
• v.9 no.4
• /
• pp.45-50
• /
• 2008

The Fourier-Mellin transform is the theoretical basis for the translation, rotation, and scale invariance of an image. However, its implementation requires a log-polar map of the original image, which requires logarithmic sampling of a radial variable in that image. This means that the mapping process is accompanied by considerable loss of data. To solve this problem, we propose a dual log-polar map that uses both a forward image map and a reverse image map simultaneously. Data loss due to the forward map sub-sampling can be offset by the reverse map. This is the first step in creating an invertible log-polar map. Experimental results have demonstrated the effectiveness of the proposed scheme.

• Honam Mathematical Journal
• /
• v.38 no.4
• /
• pp.739-752
• /
• 2016

The main aim of this paper is to introduce an extension of the generalized ${\tau}$-Gauss hypergeometric function $_rF^{\tau}_s(z)$ and investigate various properties of the new function such as integral representations, derivative formulas, Laplace transform, Mellin trans-form and fractional calculus operators. Some of the interesting special cases of our main results have been discussed.