A PUBLIC MESH WATERMARKING ALGORITHM BASED ON ADDITION PROPERTY OF FOURIER TRANSFORM

2006 ◽  
Vol 06 (01) ◽  
pp. 35-43 ◽  
Author(s):  
LI LI ◽  
ZHIGENG PAN ◽  
DAVID ZHANG
Keyword(s):  
Fourier Transform ◽  
Frequency Domain ◽  
Spatial Domain ◽  
Experimental Results ◽  
Original Image ◽  
The Fourier Transform

This paper presents a public mesh watermarking algorithm whereby the resultant watermarked image minus the original image is the watermark information. According to the addition property of the Fourier transform, a change of spatial domain will cause a change in the frequency domain. The watermark information is then scaled down and embedded in one part of the x-coordinate of the original mesh. Finally, the x-coordinate of the test mesh is amplified before extraction. Experimental results prove that our algorithm is resistant to a variety of attacks without the need for any preprocessing.

A transient technique for seismograph calibration

1962 ◽  
Vol 52 (4) ◽  
pp. 767-779
Author(s):  
A. F. Espinosa ◽  
G. H. Sutton ◽  
H. J. Miller
Keyword(s):  
Fourier Transform ◽  
Steady State ◽  
Input Pulse ◽  
Electrical Signal ◽  
Experimental Results ◽  
Response Curves ◽  
Amplitude Response ◽  
Transient Technique ◽  
Absolute Amplitude ◽  
The Fourier Transform

abstract A transient technique for seismograph calibration was developed and tested by a variety of methods. In the application of this technique a known transient in the form of an electrical signal is injected, through (a) a Willmore-type calibration bridge or (b) an independent coil, into the seismometer and the corresponding output transient of the system is recorded. The ratio of the Fourier transform of this transient to that of the input pulse yields phase and relative amplitude response of the seismograph as a function of period. Absolute amplitude response may be calculated if two easily determined constants of the seismometer are known. This technique makes practical the daily calibration of continuously-recording seismographs without disturbing the instruments more than a very few minutes. The transient technique was tested and proven satisfactory with results of more conventional steady-state methods, using both digital and analog analyses of the output transients. A variety of output transients corresponding to various theoretical response curves has been calculated for two standard input transients. By comparison of the calculated output transients with experimental results it is possible to obtain the response of the instrument with considerable precision quickly and without computation.

THEORETICAL TRANSFORMS OF THE GRAVITY ANOMALIES OF TWO IDEALIZED BODIES

Geophysics ◽  
1978 ◽  
Vol 43 (3) ◽  
pp. 631-633 ◽  
Author(s):  
Robert D. Regan ◽  
William J. Hinze
Keyword(s):  
Fourier Transform ◽  
Frequency Domain ◽  
Three Dimensional ◽  
Gravity Anomalies ◽  
Vertical Line ◽  
The Fourier Transform ◽  
Line Elements ◽  
Distribution Of Magnetization

Odegard and Berg (1965) have shown that the interpretational process can be simplified for several idealized bodies by utilizing the Fourier transform of the resultant theoretical gravity anomalies. Additional studies relating similar conclusions for other idealized bodies have been reported by Gladkii (1963), Roy (1967), Sharma et al (1970), Davis (1971), Eby (1972), and Saha (1975), and a summary of the spatial and frequency domain equations is given in Regan and Hinze (1976, Table 1); however, the transforms of the three‐dimensional prism and vertical line elements, often utilized in interpretation, have not been previously examined in this manner. Although Bhattacharyya and Chen (1977) have developed and utilized the transform of the 3-D prism in their method for determining the distribution of magnetization in a localized region, it is still of value to present the interpretive advantages of the transform equation itself.

The Remaining Cases Where m = 2 and B = 3 or B = 4

2016 ◽  
Author(s):  
Isroil A. Ikromov ◽  
Detlef Müller
Keyword(s):  
Fourier Transform ◽  
Domain Decomposition ◽  
Frequency Domain ◽  
Fourier Integral ◽  
Basic Approach ◽  
Small Letter ◽  
The Fourier Transform ◽  
Frequency Domain Decomposition

This chapter discusses the remaining cases for l = 1. With the same basic approach as in Chapter 5, the chapter again performs an additional dyadic frequency domain decomposition related to the distance to a certain Airy cone. This is needed in order to control the integration with respect to the variable x₁ in the Fourier integral defining the Fourier transform of the complex measures ν‎subscript Greek small letter delta superscript Greek small letter lamda. It first applies a suitable translation in the x₁-coordinate before performing a more refined analysis of the phase Φ‎superscript Music sharp sign. The chapter then treats the case where λ‎ρ‎(̃‎δ‎) ≲ 1 and hereafter deals with the case where λ‎ρ‎(̃‎δ‎) ≲ 1 and B = 4. Finally, the chapter turns to the case where B = 3.

INVARIANT PATTERN RECOGNITION USING RIDGELET PACKETS AND THE FOURIER TRANSFORM

2009 ◽  
Vol 07 (02) ◽  
pp. 215-228 ◽  
Author(s):  
G. Y. CHEN ◽  
P. BHATTACHARYA
Keyword(s):  
Pattern Recognition ◽  
Fourier Transform ◽  
State Of The Art ◽  
Experimental Results ◽  
Noisy Environments ◽  
Rotation Invariant ◽  
Pattern Recognition Techniques ◽  
Orthonormal Bases ◽  
The Fourier Transform ◽  
Very High

In this paper, we propose two novel invariant algorithms for pattern recognition by using ridgelet packets and the Fourier transform. Ridgelet packets provide many orthonormal bases that can effectively capture directional features present in pattern images. The Fourier transform is good at eliminating the orientation differences. By combining these two tools, very efficient rotation invariant pattern recognition techniques are created. Experimental results show that the proposed methods achieve very high classification rates and they outperform other state-of-the-art methods for rotation invariant pattern recognition under both noise-free and noisy environments.

scholarly journals Multiscale Asymptotic Analysis and Parallel Algorithm of Parabolic Equation in Composite Materials

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Xin Wang ◽  
Xi-liang Duan ◽  
Yang Gao
Keyword(s):  
Fourier Transform ◽  
Parabolic Equation ◽  
Asymptotic Analysis ◽  
Frequency Domain ◽  
Expansion Method ◽  
Convergence Result ◽  
Oscillating Coefficients ◽  
Multiscale Fem ◽  
Periodic Configuration ◽  
The Fourier Transform

An efficient parallel multiscale numerical algorithm is proposed for a parabolic equation with rapidly oscillating coefficients representing heat conduction in composite material with periodic configuration. Instead of following the classical multiscale asymptotic expansion method, the Fourier transform in time is first applied to obtain a set of complex-valued elliptic problems in frequency domain. The multiscale asymptotic analysis is presented and multiscale asymptotic solutions are obtained in frequency domain which can be solved in parallel essentially without data communications. The inverse Fourier transform will then recover the approximate solution in time domain. Convergence result is established. Finally, a novel parallel multiscale FEM algorithm is proposed and some numerical examples are reported.

Linear Dynamic System Identification in the Frequency Domain Using Fractional Derivatives

2010 ◽  
Vol 17 (2) ◽  
pp. 279-288 ◽  
Author(s):  
Tomasz Janiczek ◽  
Janusz Janiczek
Keyword(s):  
Fourier Transform ◽  
Dynamic System ◽  
Frequency Domain ◽  
Fractional Differential Equations ◽  
Fractional Derivatives ◽  
Linear Dynamic System ◽  
Transform Method ◽  
Linear Dynamic ◽  
Fractional Differential ◽  
The Fourier Transform

Linear Dynamic System Identification in the Frequency Domain Using Fractional DerivativesThis paper presents a study of the Fourier transform method for parameter identification of a linear dynamic system in the frequency domain using fractional differential equations. Fundamental definitions of fractional differential equations are briefly outlined. The Fourier transform method of identification and their algorithms are generalized so that they include fractional derivatives and integrals.

A New Non-Aliasing Nonsubsampled Contourlet Transform

2011 ◽  
Vol 480-481 ◽  
pp. 893-898
Author(s):  
He Yan ◽  
Ying Jun Pan
Keyword(s):  
Frequency Domain ◽  
Spatial Domain ◽  
Experimental Results ◽  
Contourlet Transform ◽  
Primary Reason ◽  
Nonsubsampled Contourlet Transform ◽  
Visual Effect ◽  
Pyramidal Decomposition ◽  
Image Details

The factors of aliasing in the nonsubsampled Contourlet transform(NSCT) has been analyzed.The primary reason has been pointed that the à trous algorithm binary zero-interpolation brought about the width of the filter rapid increase and border distortion (that is aliasing). On that basis,a new approximate shift-invariant non-aliasing pyramidal decomposition was proposed instead of the à trous algorithm nonsubsampled pyramidal decomposition in the NSCT,So a new approximate shift-invariant non-aliasing nonsubsampled Contourlet transform(NANSCT) was constructed. Compared to the NSCT,the basis image of the NANSCT has better spatial domain regularity, frequency domain localization and decreased redundancy.The experimental results show that whether PSNR index or in visual effect, the proposed scheme outperforms the traditional Contourlet transform hard threshold denoising , Contourlet domain HMT denoising and the NSCT hard threshold denoising, and can achieve an excellent balance between suppressing noise effectively and preserving as many image details and edges as possiblet.

Locating Damage In Waveguides From Point FRF Measurements

2007 ◽  
Vol 347 ◽  
pp. 583-588
Author(s):  
Simon P. Shone ◽  
Brian R. Mace ◽  
Tim P. Waters
Keyword(s):  
Fourier Transform ◽  
Dispersion Relation ◽  
Frequency Response ◽  
Inverse Fourier Transform ◽  
Spatial Domain ◽  
Experimental Results ◽  
Response Functions ◽  
Frequency Response Functions ◽  
Wavenumber Domain ◽  
Unknown Damage

A method is presented for locating discontinuities in a uniform waveguide from two or more point frequency response functions (FRFs). The phase of the FRF exhibits modulation when plotted against wavenumber because of interference of waves reflected from the discontinuity, and this is related to the distance of the excitation point from the discontinuity. Such discontinuities might be known boundaries or unknown damage sites. An inverse Fourier transform is used to transform from the wavenumber domain to the spatial domain in order to extract the locations of the discontinuities. The use of the transform relies upon knowledge of the dispersion relation for the waveguide. Experimental results are presented for several uniform isotropic beams which were damaged to differing extents by sawing transverse slots in them. The results show the method to be successful in locating the slots.

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