Fourier active appearance models

Gaining invariance to camera and illumination variations has been a well investigated topic in Active Appearance Model (AAM) fitting literature. The major problem lies in the inability of the appearance parameters of the AAM to generalize to unseen conditions. An attractive approach for gaining invariance is to fit an AAM to a multiple filter response (e.g. Gabor) representation of the input image. Naively applying this concept with a traditional AAM is computationally prohibitive, especially as the number of filter responses increase. In this paper, we present a computationally efficient AAM fitting algorithm based on the Lucas-Kanade (LK) algorithm posed in the Fourier domain that affords invariance to both expression and illumination. We refer to this as a Fourier AAM (FAAM), and show that this method gives substantial improvement in person specific AAM fitting performance over traditional AAM fitting methods.

Structural characterization of hydrogen peroxide‐oxidized anthracites by X-ray diffraction, Fourier transform infrared spectroscopy, and Raman spectra

The structural characteristics of raw coal and hydrogen peroxide (H2O2)-oxidized coals were investigated using scanning electron microscopy, X-ray diffraction (XRD), Raman spectra, and Fourier transform infrared (FT-IR) spectroscopy. The results indicate that the derivative coals oxidized by H2O2 are improved noticeably in aromaticity and show an increase first and then a decrease up to the highest aromaticity at 24 h. The stacking layer number of crystalline carbon decreases and the aspect ratio (width versus stacking height) increases with an increase in oxidation time. The content of crystalline carbon shows the same change tendency as the aromaticity measured by XRD. The hydroxyl bands of oxidized coals become much stronger due to an increase in soluble fatty acids and alcohols as a result of the oxidation of the aromatic and aliphatic C‐H bonds. In addition, the derivative coals display a decrease first and then an increase in the intensity of aliphatic C‐H bond and present a diametrically opposite tendency in the aromatic C‐H bonds with an increase in oxidation time. There is good agreement with the changes of aromaticity and crystalline carbon content as measured by XRD and Raman spectra. The particle size of oxidized coals (<200 nm in width) shows a significant decrease compared with that of raw coal (1 μm). This study reveals that the optimal oxidation time is ∼24 h for improving the aromaticity and crystalline carbon content of H2O2-oxidized coals. This process can help us obtain superfine crystalline carbon materials similar to graphite in structure.

Fourier spectral methods for fractional-in-space reaction-diffusion equations

Fractional differential equations are becoming increasingly used as a powerful modelling approach for understanding the many aspects of nonlocality and spatial heterogeneity. However, the numerical approximation of these models is demanding and imposes a number of computational constraints. In this paper, we introduce Fourier spectral methods as an attractive and easy-to-code alternative for the integration of fractional-in-space reaction-diffusion equations described by the fractional Laplacian in bounded rectangular domains ofRn. The main advantages of the proposed schemes is that they yield a fully diagonal representation of the fractional operator, with increased accuracy and efficiency when compared to low-order counterparts, and a completely straightforward extension to two and three spatial dimensions. Our approach is illustrated by solving several problems of practical interest, including the fractional Allen–Cahn, FitzHugh–Nagumo and Gray–Scott models, together with an analysis of the properties of these systems in terms of the fractional power of the underlying Laplacian operator.

On the efficacy of Fourier series approximations for pricing European options

This paper investigates several competing procedures for computing the prices of vanilla European options, such as puts, calls and binaries, in which the underlying model has a characteristic function that is known in semi-closed form. The algorithms investigated here are the half-range Fourier cosine series, the half-range Fourier sine series and the full-range Fourier series. Their performance is assessed in simulation experiments in which an analytical solution is available and also for a simple affine model of stochastic volatility in which there is no closed-form solution. The results suggest that the half-range sine series approximation is the least effective of the three proposed algorithms. It is rather more difficult to distinguish between the performance of the halfrange cosine series and the full-range Fourier series. However there are two clear differences. First, when the interval over which the density is approximated is relatively large, the full-range Fourier series is at least as good as the half-range Fourier cosine series, and outperforms the latter in pricing out-of-the-money call options, in particular with maturities of three months or less. Second, the computational time required by the half-range Fourier cosine series is uniformly longer than that required by the full-range Fourier series for an interval of fixed length. Taken together,these two conclusions make a case for pricing options using a full-range range Fourier series as opposed to a half-range Fourier cosine series if a large number of options are to be priced in as short a time as possible.

Particle field imaging using digital in-line holography

Digital holography is the direct recording of holograms using a CCD camera and is an alternative to the use of a film or a plate. In this communication in-line digital holographic microscopy has been explored for its application in particle imaging in 3D. Holograms of particles of about 10 mu m size have been digitally reconstructed. Digital focusing was done to image the particles in different planes along the depth of focus. Digital holographic particle imaging results were compared with conventional optical microscope imaging. A methodology for dynamic analysis of microparticles in 3D using in-line digital holography has been proposed.

Small-amplitude cyclic voltammetry: Part I. A simple fourier synthesis approach

Current-potential relationships are derived for small-amplitude periodic inputs for linear electrochemical systems using a Fourier synthesis procedure. Specific results have been obtained for a triangular potential waveform for two simple model systems.

Small amplitude cyclic voltammetry - a simple fourier synthesis approach

Abstaract is not available.

On the Fourier refinement of protein structures

The situation normally encountered in the high-resolution refinement of protein structures is one in which the inaccurate positions of P out of a total of N atoms are known whereas those of the remaining atoms are unknown. Fourier maps with coefficients (FN -- F'P) × exp (i[alpha]'P) and (mFN -- nF'P) exp (i[alpha]'P), where FN is the observed structure factor and F'P and [alpha]'P are the magnitude and the phase angle of the calculated structure factor corresponding to the inaccurate atomic positions, are often used to correct the positions of the P atoms and to determine those of the Q unknown atoms. A general theoretical approach is presented to elucidate the effect of errors in the positions of the known atoms on the corrected positions of the known atoms and the positions of the unknown atoms derived from such maps. The theory also leads to the optimal choice of parameters used in the different syntheses. When the errors in the positions of the input atoms are systematic, their effects are not taken care of automatically by the syntheses.

Evaluation of two-dimensional quantizers for Fourier transform binary holograms

Quantization formats of four digital holographic codes (Lohmann,Lee, Burckhardt and Hsueh-Sawchuk) are evaluated. A quantitative assessment is made from errors in both the Fourier transform and image domains. In general, small errors in the Fourier amplitude or phase alone do not guarantee high image fidelity. From quantization considerations, the Lee hologram is shown to be the best choice for randomly phase coded objects. When phase coding is not feasible, the Lohmann hologram is preferable as it is easier to plot.

A novel method for the age estimation of Saddletail snapper (Lutjanus malabaricus) using Fourier Transform-near infrared (FT-NIR) spectroscopy

Near infrared (NIR) spectroscopy was investigated as a potential rapid method of estimating fish age from whole otoliths of Saddletail snapper (Lutjanus malabaricus). Whole otoliths from 209 Saddletail snapper were extracted and the NIR spectral characteristics were acquired over a spectral range of 800–2780 nm. Partial least-squares models (PLS) were developed from the diffuse reflectance spectra and reference-validated age estimates (based on traditional sectioned otolith increments) to predict age for independent otolith samples. Predictive models developed for a specific season and geographical location performed poorly against a different season and geographical location. However, overall PLS regression statistics for predicting a combined population incorporating both geographic location and season variables were: coefficient of determination (R2) = 0.94, root mean square error of prediction (RMSEP) = 1.54 for age estimation, indicating that Saddletail age could be predicted within 1.5 increment counts. This level of accuracy suggests the method warrants further development for Saddletail snapper and may have potential for other fish species. A rapid method of fish age estimation could have the potential to reduce greatly both costs of time and materials in the assessment and management of commercial fisheries.

Effect of fourier domain quantization on matched filtering

It is shown that the use of a coarsely quantized binary digital hologram as a matched filter on an optical computer does not degrade signal-to-noise ratio (SNR) appreciably.

Fourier transform of the collagen triple-helical structure and its significance

The Fourier transforms of the collagen molecular structure have been calculated taking into consideration various side chain atoms, as well as the presence of bound water molecules. There is no significant change in the calculated intensity distribution on including the side chain atoms of non-imino-acid residues. Taking into account the presence of about two bound water molecules per tripeptide unit, the agreement with the observed x-ray pattern is slightly improved. Fourier transforms have also been calculated for the detailed molecular geometries proposed from other laboratories. It is found that there are no major differences between them, as compared to our structure, either in the positions of peak intensity or in the intensity distribution. Hence it is not possible to judge the relative merits of the various molecular geometries for the collagen triple helix from a comparison of the calculated transforms with the meagre data available from its x-ray fibre pattern. It is also concluded that the collagen molecular structure should be regarded as a somewhat flexible chain structure, capable of adapting itself to the requirements of the different side groups which occur in each local region.