Fourier Features Research Articles

Molecular Dynamics Study of Heat Conduction in Solid Materials.

Using the molecular dynamics method, the process of heat conduction in solid materials has been numerically studied for the configuration of lattice particles having the Lennard-Jones (12-6) potential. Under the condition of constant heat flux, the temperature distributions through the conduction layer are calculated with changing the amount of heat flux, layer temperature and layer thickness of the lattice particles, and the lattice configuration including defects. If averaged over sufficiently long time intervals, the molecular process of heat conduction exhibits the same features of Fourier's law as the macroscopic heat conduction. For less than four particle layers, the boundary conditions take part in the process of heat conduction, changing the relationships of the heat flux to the temperature gradient

Coherent Optical Pattern Recognition Using Computer-Generated Holograms

Coherent optical pattern recognition using computer-generated holograms A relatively inexpensive optical processing system is described which uses a TV camera to demonstrate visually many of the features of Fourier transform theory with particular application to character recognition. The method uses a computer-generated hologram of the character in the transform plane to detect the presence of the character.

Development of a personal-computer-based intelligent tutoring system

Gaussian kernel Support Vector Machines (SVMs) deliver state-of-the-art generalization performance for non-linear classification, but the time complexity of their training process is at least quadratic w.r.t. the size of training set, preventing them from scaling up on large datasets. To address this issue, we propose a novel approach to large-scale kernel SVMs in sublinear time w.r.t. the size of training set, which combines three well-known and efficient techniques with theoretical guarantees. First, we subsample massive samples to reduce the sample size. Then, we use the random Fourier feature mapping on the subsamples to construct explicit random feature space where we can train a linear SVM to approximate the corresponding Gaussian kernel SVM. Finally, we use parallel algorithms to make our approach more scalable. Deriving the upper bounds of kernel matrix approximation error, hypothesis error and excess risk w.r.t. the size of training set and the dimension of random feature space, we establish the theoretical foundation of our proposed approach. In this way, we can reduce the time complexity of training kernel SVMs without sacrificing much accuracy. Our proposed approach achieves high accuracy and has sublinear training time complexity, which exhibits good scalability theoretically and empirically.

Fourier classification images in cardiac nuclear medicine

At present, the diagnosis of cardiac left ventricular regional wall motion abnormalities (RWMA) in nuclear medicine is aided mainly by phase images and amplitude images, which picture the spatial distribution of the phase and of the amplitude of the first harmonics of pixel time activity curves, respectively. However, they do not utilize other information contained in the original radionuclide images, and they do not offer a direct diagnostic interpretation of the data. The proposed Fourier classification images (FCI) overcome these deficiencies. Their pixel intensities express directly the diagnostic class of RWMA. The FCI pixel intensities are functions of pixel coordinates, Fourier features of pixel time activity curves, and their distribution parameters, and they are not limited by the first harmonics model. The derivation of the pixel classifier includes normalization transformation of coordinates and activities. Fourier analysis of raw image data, and teaching the computer by examples of already diagnosed cases with the help of discriminant analysis. FCI offer direct and robust diagnosis of RWMA, superior to that derived from phase and amplitude images, especially in the detection of mild RWMA.

Optical surface inspection using real-time Fourier transform holography in photorefractives

We present real-time optical preprocessor intended to enhance small defects in a smooth surface. The heart of the system is a photorefractive Bi(12)SiO(20) phase-conjugate mirror which reflects only the low intensity features of the object's optical Fourier transform. By adjusting the beam ratios so that only the low intensity, high spatial frequency image components are phase conjugated and inverse transformed, an image consisting of just the defects is produced. To our knowledge, this is the first use of this technique on opaque and nonperiodic objects. We present experimental data showing enhancement of defects as small as 0.14 microm.

Elliptic Fourier features of a closed contour

A direct procedure for obtaining the Fourier coefficients of a chain-encoded contour is presented. Advantages of the procedure are that it does not require integration or the use of fast Fourier transform techniques, and that bounds on the accuracy of the image contour reconstruction are easy to specify. Elliptic properties of the Fourier coefficients are shown and used for a convenient and intuitively pleasing procedure of normalizing a Fourier contour representation. Extension of the contour representation to arbitrary objects at arbitrary aspect angle is discussed. The procedures have direct application to a variety of pattern recognition problems that involve analysis of well-defined image contours.

Investigation of the Nitrogen Hyperfine Structure of Vinylisocyanide by Microwave Fourier Transform Spectroscopy in the X-and Ku-Band

Abstract In memory of W. H. We discuss the features of a microwave Fourier transform spectrometer in the X-and Ku-band as applied to the investigation of the hyperfine structure of rotational transitions. The Nitrogen-hyperfine structure of vinylisocyanide was measured and analysed.

Walsh Spectral Estimates with Applications to the Classification of EEG Signals

A basis for the processing of EEG signals using the discrete, orthogonal set of Walsh functions is presented. The Walsh power spectrum is examined from the point of view of its statistical properties, especially as it relates to spectral resolution. Features, selected from the spectrum of sleep EEG data are compared to corresponding Fourier features. Each feature set is used to classify the data using a minimum-distance clustering algorithm. The results show that the Walsh spectral features classify the data in much the same way as the Fourier spectral features. This provides sufficient justification for usage ofWalsh spectral features in place of Fourier spectral features, enabling one to take advantage of the vast computational superiority of the fast Walsh transform over the fast Fourier transform.

On the use of fourier phase features for texture discrimination

Fourier features based on the phase rather than the amplitude do not seem to be useful for texture classification.

Masking independent of both separation and spatial frequency

A briefly presented single dark bar lowered the apparent contrast of a subsequently flashed patch of grating regardless of the spatial separation of the two patterns, up to 4° of visual angle. This forward masking effect occurred when the bars of the two patterns were identically oriented—but not when their orientation differed by 90% Such an orientation-selective interaction effect between widely separated patterns could result from Fourier-like distribution of visual information, but the magnitude of the masking effect is not affected by the patterns' similarity in the Fourier domain. Pattern coding by local features might explain only the orientation specificity and the lack of frequency tuning, while pattern coding by Fourier features might explain only the orientation specificity and the distribution effect. Therefore, neither class of features completely describes the initial coding of visual patterns.

Fast Fourier transform in the analysis of biomedical data.

The fast Fourier transform (f.f.t.) is a powerful technique which facilitates analysis of signals in the frequency domain. This paper reviews some of the important features of the fast Fourier transform which are relevant to its increasing application to biomedical data. A distinction is made between the power spectrum of ergodic signals, computed from the autocorrelation function, and the frequency spectrum of nonstationary biomedical signals. The major practical pitfalls that are encountered in applying the f.f.t. technique to biomedical data are discussed, and practical hints for avoiding such pitfalls are suggested.

A Comparative Study of Texture Measures for Terrain Classification

Three standard approaches to automatic texture classification make use of features based on the Fourier power spectrum, on second-order gray level statistics, and on first-order statistics of gray level differences, respectively. Feature sets of these types, all designed analogously, were used to classify two sets of terrain samples. It was found that the Fourier features generally performed more poorly, while the other feature sets all performned comparably.