Showing papers on "Fourier transform published in 2001"
TL;DR: A fully-vectorial, three-dimensional algorithm to compute the definite-frequency eigenstates of Maxwell's equations in arbitrary periodic dielectric structures, including systems with anisotropy or magnetic materials, using preconditioned block-iterative eigensolvers in a planewave basis is described.
Abstract: We describe a fully-vectorial, three-dimensional algorithm to compute the definite-frequency eigenstates of Maxwell's equations in arbitrary periodic dielectric structures, including systems with anisotropy (birefringence) or magnetic materials, using preconditioned block-iterative eigensolvers in a planewave basis. Favorable scaling with the system size and the number of computed bands is exhibited. We propose a new effective dielectric tensor for anisotropic structures, and demonstrate that O Delta x;2 convergence can be achieved even in systems with sharp material discontinuities. We show how it is possible to solve for interior eigenvalues, such as localized defect modes, without computing the many underlying eigenstates. Preconditioned conjugate-gradient Rayleigh-quotient minimization is compared with the Davidson method for eigensolution, and a number of iteration variants and preconditioners are characterized. Our implementation is freely available on the Web.
2,861 citations
Book•
31 Jan 2001
TL;DR: The fractional Fourier transform (FFT) as discussed by the authors has been used in a variety of applications, such as matching filtering, detection, and pattern recognition, as well as signal recovery.
Abstract: Preface. Acknowledgments. Introduction. Signals, Systems, and Transformations. Wigner Distributions and Linear Canonical Transforms. The Fractional Fourier Transform. Time-Order and Space-Order Representations. The Discrete Fractional Fourier Transform. Optical Signals and Systems. Phase-Space Optics. The Fractional Fourier Transform in Optics. Applications of the Fractional Fourier Transform to Filtering, Estimation, and Signal Recovery. Applications of the Fractional Fourier Transform to Matched Filtering, Detection, and Pattern Recognition. Bibliography on the Fractional Fourier Transform. Other Cited Works. Credits. Index.
1,287 citations
TL;DR: This work estimates both the number of sources and the mixing matrix by the maxima of a potential function along the circle of unit length, and obtains the minimal l1 norm representation of each data point by a linear combination of the pair of basis vectors that enclose it.
743 citations
TL;DR: In this article, it was shown that the spectral correlation can be interpreted as a Fourier transform of the average squared envelope of the signal, which is much easier to obtain directly.
616 citations
TL;DR: Fourier transform profilometry is one of the popular non-contact 3D measurement methods, where a Ronchi grating or sinusoidal grating is projected onto a diffuse three-dimensional surface, and the resulting deformed grating image is detected by a CCD camera and processed by a computer as discussed by the authors.
588 citations
01 Sep 2001
TL;DR: An overview of applications which have so far received interest are given and some potential application areas remaining to be explored are noted.
Abstract: A brief introduction to the fractional Fourier transform and its properties is given. Its relation to phase-space representations (time- or space-frequency representations) and the concept of fractional Fourier domains are discussed. An overview of applications which have so far received interest are given and some potential application areas remaining to be explored are noted.
481 citations
TL;DR: ANN artificial neural network A/T absorbance/transmission ATR attenuated total reflectance DTGS deuterated triglycine sulfate FT Fourier transform FT-IR Fourier Transform Infrared IR infrared LPS lPS as discussed by the authors.
Abstract: ANN artificial neural network A/T absorbance/transmission ATR attenuated total reflectance DTGS deuterated triglycine sulfate FT Fourier transform FT-IR Fourier transform-infrared IR infrared LPS l...
467 citations
TL;DR: In this paper, an accelerated Stokesian Dynamics (ASD) algorithm was proposed to solve all hydrodynamic interactions in a viscous fluid at low particle Reynolds number with a significantly lower computational cost of O(N ln N).
Abstract: A new implementation of the conventional Stokesian Dynamics (SD) algorithm, called accelerated Stokesian Dynamics (ASD), is presented. The equations governing the motion of N particles suspended in a viscous fluid at low particle Reynolds number are solved accurately and efficiently, including all hydrodynamic interactions, but with a significantly lower computational cost of O(N ln N). The main differences from the conventional SD method lie in the calculation of the many-body long-range interactions, where the Ewald-summed wave-space contribution is calculated as a Fourier transform sum and in the iterative inversion of the now sparse resistance matrix. The new method is applied to problems in the rheology of both structured and random suspensions, and accurate results are obtained with much larger numbers of particles. With access to larger N, the high-frequency dynamic viscosities and short-time self-diffusivities of random suspensions for volume fractions above the freezing point are now studied. The ASD method opens up an entire new class of suspension problems that can be investigated, including particles of non-spherical shape and a distribution of sizes, and the method can readily be extended to other low-Reynolds-number-flow problems.
456 citations
TL;DR: In this paper, Heisenberg exchange parameters for bcc Fe, fcc Co, and fcc Ni were calculated using the nonrelativistic spin-polarized Green-function technique within the tight-binding linear muffin-tin orbital method and by employing the magnetic force theorem to calculate total energy changes associated with a local rotation of magnetization directions.
Abstract: We have calculated Heisenberg exchange parameters for bcc Fe, fcc Co, and fcc Ni using the nonrelativistic spin-polarized Green-function technique within the tight-binding linear muffin-tin orbital method and by employing the magnetic force theorem to calculate total energy changes associated with a local rotation of magnetization directions. We have also determined spin-wave stiffness constants and found the dispersion curves for metals in question employing the Fourier transform of calculated Heisenberg exchange parameters. Detailed analysis of convergence properties of the underlying lattice sums was carried out and a regularization procedure for calculation of the spin-wave stiffness constant was suggested. Curie temperatures were calculated both in the mean-field approximation and within the Green-function random-phase approximation. The latter results were found to be in a better agreement with available experimental data.
418 citations
07 Oct 2001
TL;DR: Hypercomplex numbers, specifically quaternions, are used to define a Fourier transform applicable to color images, and the properties of the transform are developed, and it is shown that the transform may be computed using two standard complex fast Fourier transforms.
Abstract: Hypercomplex Fourier transforms based on quaternions have been proposed by several groups for use in image processing, particularly of color images. So far, however, there has not been a coherent explanation of what the spectral domain coefficients produced by a hypercomplex Fourier transform represent and this paper attempts to present such an explanation for the first time making use of the polar form of a quaternion and a separation of a quaternion spectral coefficient into components parallel and perpendicular to the hypercomplex exponentials in the transform (the basis functions).
379 citations
TL;DR: The successful phasing of an oversampled hard x-ray diffraction pattern measured from a single nanocrystal of gold is reported, and this has recently been demonstrated.
Abstract: Inverse problems arise frequently in physics: The magnitude of the Fourier transform of some function is measurable, but not its phase. The "phase problem" in crystallography arises because the number of discrete measurements (Bragg peak intensities) is only half the number of unknowns (electron density points in space). Sayre first proposed that oversampling of diffraction data should allow a solution, and this has recently been demonstrated. Here we report the successful phasing of an oversampled hard x-ray diffraction pattern measured from a single nanocrystal of gold.
TL;DR: In this article, the structural changes that occur in semicrystalline poly(vinylidene fluoride) during a mechanical deformation process were studied by Fourier transform infrared (FTIR) spectroscopy and differential scanning calorimetry (DSC).
Abstract: Films of semicrystalline poly(vinylidene fluoride) (PVDF) in the β-phase were studied by Fourier transform infrared (FTIR) spectroscopy and differential scanning calorimetry (DSC). The main goal of this study was to improve the understanding of the structural changes that occur in β-PVDF during a mechanical deformation process. FTIR spectroscopy was used to examine the structural variations as a function of strain. DSC data allowed measurement of the melting temperatures and enthalpies of the material before and after deformation, providing information about the changes in the crystalline fraction. After the molecular vibrations were assigned to the corresponding vibrational modes, we investigated the energy and intensity variations of these vibrations at different deformations. A reorientation of the chains from perpendicular to parallel to the stress direction was observed to occur in the plastic region. During the deformation, a decrease in the degree of crystallinity of the material was observed, but ...
TL;DR: A new class of the "frequency domain"-based signal/image enhancement algorithms including magnitude reduction, log-magnitude reduction, iterative magnitude and a log-reduction zonal magnitude technique, based on the so-called sequency ordered orthogonal transforms, which include the well-known Fourier, Hartley, cosine, and Hadamard transforms.
Abstract: This paper presents a new class of the "frequency domain"-based signal/image enhancement algorithms including magnitude reduction, log-magnitude reduction, iterative magnitude and a log-reduction zonal magnitude technique. These algorithms are described and applied for detection and visualization of objects within an image. The new technique is based on the so-called sequency ordered orthogonal transforms, which include the well-known Fourier, Hartley, cosine, and Hadamard transforms, as well as new enhancement parametric operators. A wide range of image characteristics can be obtained from a single transform, by varying the parameters of the operators. We also introduce a quantifying method to measure signal/image enhancement called EME. This helps choose the best parameters and transform for each enhancement. A number of experimental results are presented to illustrate the performance of the proposed algorithms.
Book•
01 Oct 2001TL;DR: A thorough treatment of Fourier series on the circle and their applications to approximation theory, probability, and plane geometry (the isoperimetric theorem) can be found in this article.
Abstract: This book provides a concrete introduction to a number of topics in harmonic analysis, accessible at the early graduate level or, in some cases, at an upper undergraduate level. Necessary prerequisites to using the text are rudiments of the Lebesgue measure and integration on the real line. It begins with a thorough treatment of Fourier series on the circle and their applications to approximation theory, probability, and plane geometry (the isoperimetric theorem). Frequently, more than one proof is offered for a given theorem to illustrate the multiplicity of approaches. The second chapter treats the Fourier transform on Euclidean spaces, especially the author's results in the three-dimensional piecewise smooth case, which is distinct from the classical Gibbs - Wilbraham phenomenon of one-dimensional Fourier analysis. The Poisson summation formula treated in Chapter 3 provides an elegant connection between Fourier series on the circle and Fourier transforms on the real line, culminating in Landau's asymptotic formulas for lattice points on a large sphere. Much of modern harmonic analysis is concerned with the behavior of various linear operators on the Lebesgue spaces Lp (Rn). Chapter 4 gives a gentle introduction to these results, using the Riesz - Thorin theorem and the Marcinkiewicz interpolation formula. One of the long-time users of Fourier analysis is probability theory. In Chapter 5 the central limit theorem, iterated log theorem, and Berry - Esseen theorems are developed using the suitable Fourier-analytic tools. The final chapter furnishes a gentle introduction to wavelet theory, depending only on the L2 theory of the Fourier transform (the Plancherel theorem). The basic notions of scale and location parameters demonstrate the flexibility of the wavelet approach to harmonic analysis. The text contains numerous examples and more than 200 exercises, each located in close proximity to the related theoretical material.
TL;DR: In this article, two-dimensional Fourier transform electronic spectra of the cyanine dye IR144 in methanol are used to explore new aspects of optical 2D spectroscopy on a femtosecond timescale.
Abstract: Two-dimensional Fourier transform electronic spectra of the cyanine dye IR144 in methanol are used to explore new aspects of optical 2D spectroscopy on a femtosecond timescale The experiments reported here are pulse sequence and coherence pathway analogs of the two-dimensional magnetic resonance techniques known as COSY (correlated spectroscopy) and NOESY (nuclear Overhauser effect spectroscopy) Noncollinear three pulse scattering allows selection of electronic coherence pathways by choice of phase matching geometry, temporal pulse order, and Fourier transform variables Signal fields and delays between excitation pulses are measured by spectral interferometry Separate real (absorptive) and imaginary (dispersive) 2D spectra are generated by measuring the signal field at the sample exit, performing a 2D scan that equally weights rephasing and nonrephasing coherence pathways, and phasing the 2D spectra against spectrally resolved pump–probe signals A 3D signal propagation function is used to correct the 2D spectra for excitation pulse propagation and signal pulse generation inside the sample At relaxation times greater than all solvent and vibrational relaxation timescales, the experimental 2D electronic spectra can be predicted from linear spectroscopic measurements without any adjustable parameters The 2D correlation spectra verify recent computational predictions of a negative region above the diagonal, a displacement of the 2D peak off the diagonal, and a narrowing of the 2D cross-width below the vibrational linewidth The negative region arises from 4-level four-wave mixing processes with negative transition dipole products, the displacement off the diagonal arises from a dynamic Stokes shift during signal radiation, and the narrow 2D cross-width indicates femtosecond freezing of vibrational motion
Book•
01 Jan 2001
TL;DR: The Fourier Transform Spectrometer and its Applications: Theory of the Ideal Instrument Fourier Analysis Nonideal (Real-World) Interferograms and Applications.
Abstract: Introduction Why Choose a Fourier Transform Spectrometer? Theory of the Ideal Instrument Fourier Analysis Nonideal (Real-World) Interferograms Working with Digital Spectra and Fourier Transforms Phase Corrections and Their Significance Effects of Noise in Its Various Forms Line Positions, Line Profiles, and Fitting Processing of Spectral Data Discussions, Interventions, Digressions, and Obscurations Chapter-by-Chapter Bibliography Chronological Bibliography Applications Bibliography Author Bibliography Index
TL;DR: For phase-amplitude problems, the original Fourier transform is found to be more important than the amplitude for the FRFT/LCT, and the WDF is used to explain why fractional/canonical convolution can be used for space-variant pattern recognition.
Abstract: The fractional Fourier transform (FRFT) is a useful tool for signal processing. It is the generalization of the Fourier transform. Many fractional operations, such as fractional convolution, fractional correlation, and the fractional Hilbert transform, are defined from it. In fact, the FRFT can be further generalized into the linear canonical transform (LCT), and we can also use the LCT to define several canonical operations. In this paper, we discuss the relations between the operations described above and some important time-frequency distributions (TFDs), such as the Wigner distribution function (WDF), the ambiguity function (AF), the signal correlation function, and the spectrum correlation function. First, we systematically review the previous works in brief. Then, some new relations are derived and listed in tables. Then, we use these relations to analyze the applications of the FRPT/LCT to fractional/canonical filter design, fractional/canonical Hilbert transform, beam shaping, and then we analyze the phase-amplitude problems of the FRFT/LCT. For phase-amplitude problems, we find, as with the original Fourier transform, that in most cases, the phase is more important than the amplitude for the FRFT/LCT. We also use the WDF to explain why fractional/canonical convolution can be used for space-variant pattern recognition.
TL;DR: In this paper, a dual-hyperbolic two-step radiation heating model is presented to investigate ultrashort laser pulse interactions with metal films, and the effect of heat conduction in the lattice is examined.
Abstract: A dual-hyperbolic two-step radiation heating model is presented to investigate ultrashort laser pulse interactions with metal films. This model extends Qiu and Tien's theory by including the effect of heat conduction in the lattice. In addition, the depth distribution of laser intensity is modified by adding the ballistic range to the optical penetration depth. The effects of temperature dependence of the thermophysical properties also are examined. For comparison, the proposed model and the existing theories, the parabolic two-temperature model, Qiu and Tien's theory, and Fourier's law, are solved using a mesh-free particle method. Numerical analysis is performed with gold films; the results are compared with experimental data of Qiu, Jubhasz, Suarez, Bron, and Tien, and Wellershoff, Hohlfeld, Gudde, and Matthais. It is shown that this current model predicts more accurate thermal response than the existing theories considered in this study. It is also found that the inclusion of the ballistic effect to t...
TL;DR: In this paper, the authors developed efficient algorithms for quaternion Fourier transform (QFT), QCV, and Qaternion correlation for color image processing, where the conventional two-dimensional (2D) Fourier Transform (FT) is used to implement these quaternions very efficiently.
Abstract: The concepts of quaternion Fourier transform (QFT), quaternion convolution (QCV), and quaternion correlation, which are based on quaternion algebra, have been found to be useful for color image processing. However, the necessary computational algorithms and their complexity still need some attention. We develop efficient algorithms for QFT, QCV, and quaternion correlation. The conventional complex two-dimensional (2-D) Fourier transform (FT) is used to implement these quaternion operations very efficiently. With these algorithms, we only need two complex 2-D FTs to implement a QFT, six complex 2-D FTs to implement a one-side QCV or a quaternion correlation and 12 complex 2-D FTs to implement a two-side QCV, and the efficiency of these quaternion operations is much improved. Meanwhile, we also discuss two additional topics. The first one is about how to use QFT and QCV for quaternion linear time-invariant (QLTI) system analysis. This topic is important for quaternion filter design and color image processing. Besides, we also develop the spectrum-product QCV. It is an improvement of the conventional form of QCV. For any arbitrary input functions, it always corresponds to the product operation in the frequency domain. It is very useful for quaternion filter design.
TL;DR: In this article, a method for detecting a watermark signal in digital image data is presented, which includes the steps of computing a logpolar Fourier transform of the image data to obtain a log-polar-fourier spectrum; projecting the logp polar Fourier spectrum down to a lower dimensional space to obtain an extracted signal; comparing the extracted signal to a target watermark signals; and declaring the presence or absence of the target watermarks signal in image data based on the comparison.
Abstract: A method for detecting a watermark signal in digital image data. The detecting method includes the steps of: computing a log-polar Fourier transform of the image data to obtain a log-polar Fourier spectrum; projecting the log-polar Fourier spectrum down to a lower dimensional space to obtain an extracted signal; comparing the extracted signal to a target watermark signal; and declaring the presence or absence of the target watermark signal in the image data based on the comparison. Also provided is a method for inserting a watermark signal in digital image data to obtain a watermarked image. The inserting method includes the steps of: computing a log-polar Fourier transform of the image data to obtain a log-polar Fourier spectrum; projecting the log-polar Fourier spectrum down to a lower dimensional space to obtain an extracted signal; modifying the extracted signal such that it is similar to a target watermark; performing a one-to-many mapping of the modified signal back to log-polar Fourier transform space to obtain a set of watermarked coefficients; and performing an inverse log-polar Fourier transform on the set of watermarked coefficients to obtain a watermarked image.
TL;DR: Two novel image processing techniques have been developed to refocus a moving target image from its smeared response in the synthetic aperture radar (SAR) image which is focused on the stationary ground.
Abstract: Two novel image processing techniques have been developed to refocus a moving target image from its smeared response in the synthetic aperture radar (SAR) image which is focused on the stationary ground. Both approaches may be implemented with efficient fast Fourier transform (FFT) routines to process the Fourier spatial spectrum of the image data. The first approach utilizes a matched target filter that is derived from the signal history along the range-Doppler migration path mapped onto the SAR image from the moving target trajectory in real space. The coherent spatial filter is specified by the apparent target range in the image and the magnitude of the relative target-to-radar velocity. The second approach eliminates the range-dependence by reconstructing the moving target image from a spectral function that is obtained from the SAR image data spectrum via a spatial frequency coordinate transformation.
24 Jun 2001
TL;DR: The technique is based on analytically computing the expectation of an exponential quadratic function of an i.r. unitary matrix and makes use of a Fourier integral representation of the constituent Dirac delta functions in the underlying density.
Abstract: An important open problem in multiple-antenna communications theory is to compute the capacity of a wireless link subject to flat Rayleigh block-fading, with no channel-state information (CSI) available either to the transmitter or to the receiver. The isotropically random (i.r.) unitary matrix-having orthonormal columns, and a probability density that is invariant to premultiplication by an independent unitary matrix-plays a central role in the calculation of capacity and in some special cases happens to be capacity-achieving. We take an important step toward computing this capacity by obtaining, in closed form, the probability density of the received signal when transmitting i.r. unitary matrices. The technique is based on analytically computing the expectation of an exponential quadratic function of an i.r. unitary matrix and makes use of a Fourier integral representation of the constituent Dirac delta functions in the underlying density. Our formula for the received signal density enables us to evaluate the mutual information for any case of interest, something that could previously only be done for single transmit and receive antennas. Numerical results show that at high signal-to-noise ratio (SNR), the mutual information is maximized for M=min(N, T/2) transmit antennas, where N is the number of receive antennas and T is the length of the coherence interval, whereas at low SNR, the mutual information is maximized by allocating all transmit power to a single antenna.
01 Jan 2001
TL;DR: Efficient algorithms for QFT, QCV, and quaternion correlation are developed and the spectrum-product QCV is developed, which is an improvement of the conventional form of QCV and very useful for quaternions filter design.
Abstract: The recently developed concepts of quaternion Fourier transform (QFT), quaternion convolution (QCV), and quaternion correlation, which are based on quaternion algebra, have been found to be useful for color image processing. However, the necessary computational algorithms and their complexity still need some attention. In this paper, we will develop efficient algorithms for QFT, QCV, and quaternion correlation. The conventional complex two-dimensional (2-D) Fourier transform (FT) is used to implement these quaternion operations very efficiently. By these algorithms, we only need two complex 2-D FTs to implement a QFT, six complex 2-D FTs to implement a one-side QCV or a quaternion correlation and 12 complex 2-D FTs to implement a two-side QCV, and the efficiency of these quaternion operations is much improved. Meanwhile, we also discuss two additional topics. The first one is about how to use QFT and QCV for quaternion linear time-invariant (QLTI) system analysis. This topic is important for quaternion filter design and color image processing. Besides, we also develop the spectrum-product QCV. It is the improvement of the conventional form of QCV. For any arbitrary input functions, it always corresponds to the product operation in the frequency domain. It will be very useful for quaternion filter design.
01 Jan 2001
TL;DR: This paper builds a Java retrieval framework to compare shape retrieval using FDs derived from different signatures, and examines common issues and techniques for shape representation and normalization.
Abstract: Shape is one of the most important features in Content Based Image Retrieval (CBIR). Many shape representations and retrieval methods exists. However, most of those methods either do not well represent shape or are difficult to do normalization (making matching hard). Among them, methods based Fourier descriptors (FD) achieve both well representation and well normalization. Different shape signatures have been exploited to derive FDs, however, FDs derived from different signatures can have significant different effect on the result of retrieval. In this paper, we build a Java retrieval framework to compare shape retrieval using FDs derived from different signatures. Common issues and techniques for shape representation and normalization are also analyzed in the paper. Data is given to show the retrieval result.
TL;DR: The double-exponential transformation was first proposed by Takahasi and Mori in 1974 for the efficient evaluation of integrals of an analytic function with end-point singularity as mentioned in this paper.
TL;DR: In this paper, an atomic-orbital formulation of second-order Moller-Plesset (MP2) theory for periodic systems is presented, where the inherent spatial decay properties of the density matrix and the atomic orbital basis are exploited to reduce computational cost and scaling.
Abstract: We present an atomic-orbital formulation of second-order Moller–Plesset (MP2) theory for periodic systems. Our formulation is shown to have several advantages over the conventional crystalline orbital formulation. Notably, the inherent spatial decay properties of the density matrix and the atomic orbital basis are exploited to reduce computational cost and scaling. The multidimensional k-space integration is replaced by independent Fourier transforms of weighted density matrices. The computational cost of the correlation correction becomes independent of the number of k-points used. Focusing on the MP2 quasiparticle energy band gap, we also show using an isolated fragment model that the long range gap contributions decay rapidly as 1/R5, proof that band gap corrections converge rapidly with respect to lattice summation. The correlated amplitudes in the atomic orbital (AO) basis are obtained in a closed-form fashion, compatible with a semidirect algorithm, thanks to the Laplace transform of the energy deno...
TL;DR: The idea disclosed in this work is that a nonstationary approach can be approximated using signal bases that are especially suited for the analysis/synthesis of non stationary signals using orthogonal signal bases of the chirp type that in practice correspond to the fractional Fourier transform signal basis.
Abstract: Traditional multicarrier techniques perform a frequency-domain decomposition of a channel characterized by frequency-selective distortion in a plurality of subchannels that are affected by frequency flat distortion. The distortion in each independent subchannel can then be easily compensated by simple gain and phase adjustments. Typically, digital Fourier transform schemes make the implementation of the multicarrier system feasible and attractive with respect to single-carrier systems. However, when the channel is time-frequency-selective, as it usually happens in the rapidly fading wireless channel, this traditional methodology fails. Since the channel frequency response is rapidly time-varying, the optimal transmission/reception methodology should be able to process nonstationary signals. In other words, the subchannel carrier frequencies should be time-varying and ideally decompose the frequency distortion of the channel perfectly at any instant in time. However, this ideally optimal approach presents significant challenges both in terms of conceptual and computational complexity. The idea disclosed in this work is that a nonstationary approach can be approximated using signal bases that are especially suited for the analysis/synthesis of nonstationary signals. We propose in fact the use of a multicarrier system that employs orthogonal signal bases of the chirp type that in practice correspond to the fractional Fourier transform signal basis. The significance of the methodology relies on the important practical consideration that analysis/synthesis methods of the fractional Fourier type can be implemented with a complexity that is equivalent to the traditional fast Fourier transform.
TL;DR: The proposed approach is quite general and can be used for any given crystallite shape and different distribution functions; moreover, the Fourier transform formalism allows the introduction in the line-profile expression of other contributions to line broadening in a relatively easy and straightforward way.
Abstract: Diffraction patterns for polydisperse systems of crystalline grains of cubic materials were calculated considering some common grain shapes: sphere, cube, tetrahedron and octahedron Analytical expressions for the Fourier transforms and corresponding column-length distributions were calculated for the various crystal shapes considering two representative examples of size-distribution functions: lognormal and Poisson Results are illustrated by means of pattern simulations for a fcc material Line-broadening anisotropy owing to the different crystal shapes is discussed The proposed approach is quite general and can be used for any given crystallite shape and different distribution functions; moreover, the Fourier transform formalism allows the introduction in the line-profile expression of other contributions to line broadening in a relatively easy and straightforward way
01 Jan 2001
TL;DR: A new method for describing 3D-shape in order to perform similarity search for polygonal mesh models is proposed, which presents a descriptor which is invariant with respect to translation, rotation, scaling, and reflection and robust withrespect to level-ofdetail.
Abstract: In this paper, we propose a new method for describing 3D-shape in order to perform similarity search for polygonal mesh models. The approach is based on characterization of spatial properties of 3D-objects by suitable feature vectors, i.e., the goal is to define 3D-shape descriptors in such a way that similar objects are represented by “close” points in the feature vector space. We present a descriptor which is invariant with respect to translation, rotation, scaling, and reflection and robust with respect to level-ofdetail. A coarse voxelization of a 3D-model is used as the input for the 3D Discrete Fourier Transform (3D DFT), while the absolute values of obtained (complex) coefficients are considered as components of the feature vector. Multiple levels of abstraction of the feature are embedded by the applied transform. The performance of the proposed method is compared to some previous approaches by means of precision/recall tests. Generally, results show that the new approach introduces improvements in the 3D-model retrieval process.
TL;DR: Experimental results on real gray-level images show that it is possible to recover an image to within a specified degree of accuracy and to classify objects reliably even when a large set of descriptors is used.