A Closed-Form, Consistent and Robust Solution to Uncalibrated Photometric Stereo Via Local Diffuse Reflectance Maxima

Images of an object under different illumination are known to provide strong cues about the object surface. A mathematical formalization of how to recover the normal map of such a surface leads to the so-called uncalibrated photometric stereo problem. In the simplest instance, this problem can be reduced to the task of identifying only three parameters: the so-called generalized bas-relief (GBR) ambiguity. The challenge is to find additional general assumptions about the object, that identify these parameters uniquely. Current approaches are not consistent, i.e., they provide different solutions when run multiple times on the same data. To address this limitation, we propose exploiting local diffuse reflectance (LDR) maxima, i.e., points in the scene where the normal vector is parallel to the illumination direction (see Fig. 1). We demonstrate several noteworthy properties of these maxima: a closed-form solution, computational efficiency and GBR consistency. An LDR maximum yields a simple closed-form solution corresponding to a semi-circle in the GBR parameters space (see Fig. 2); because as few as two diffuse maxima in different images identify a unique solution, the identification of the GBR parameters can be achieved very efficiently; finally, the algorithm is consistent as it always returns the same solution given the same data. Our algorithm is also remarkably robust: It can obtain an accurate estimate of the GBR parameters even with extremely high levels of outliers in the detected maxima (up to 80 % of the observations). The method is validated on real data and achieves state-of-the-art results.

Extreme temperature events analyzed with Fast Fourier Transform

Extreme weather and climate events have received increased attention in the last few years, due to the often large loss of agriculture business and exponentially increasing costs associated with them and insurance planning. This increased attention raises the question as to whether extreme weather and climate events are truly increasing, whether this is only a perceived increase exacerbated by enhanced media coverage, or both. There are a number of ways extreme climate events can be defined, such as extreme daily temperatures, extreme daily rainfall amounts, and large areas experiencing unusually warm monthly temperatures, among others. In this study, we will focus our attention in frost and heatstroke events measuring it as the number of days under 0 ºC and number of days with daily maximum over 30ºC monthly respectively. We have studied the trends in these extreme events applying a Fast Fourier Transform to the series to clarify the tendency. Lack of long-term climate data suitable for analysis of extremes is the single biggest obstacle to quantifying whether extreme events have changed over the twentieth century, including high temporal and spatial resolution observations of temperatures. However, several series have been grouped in different ways: chosen the longest series independently, by provinces, by main watersheds and altitude. On the other hand, synthetic series generated by Luna and Balairón (AEMet) were also analyzed. The results obtained by different pooling data are discussed concluding the difficulties to assess the extreme events tendencies and high regional variation in the trends.

Statistical properties of fast Fourier transform coefficients computed from real-valued, covariance-stationary, periodic random sequences /

"July 1976."

Matrix-free mass spectrometric imaging using laser desorption ionisation Fourier transform ion cyclotron resonance mass spectrometry

Mass spectrometry imaging (MSI) is a powerful tool in metabolomics and proteomics for the spatial localization and identification of pharmaceuticals, metabolites, lipids, peptides and proteins in biological tissues. However, sample preparation remains a crucial variable in obtaining the most accurate distributions. Common washing steps used to remove salts, and solvent-based matrix application, allow analyte spreading to occur. Solvent-free matrix applications can reduce this risk, but increase the possibility of ionisation bias due to matrix adhesion to tissue sections. We report here the use of matrix-free MSI using laser desorption ionisation performed on a 12 T Fourier transform ion cyclotron resonance (FTICR) mass spectrometer. We used unprocessed tissue with no post-processing following thaw-mounting on matrix-assisted laser desorption ionisation (MALDI) indium-tin oxide (ITO) target plates. The identification and distribution of a range of phospholipids in mouse brain and kidney sections are presented and compared with previously published MALDI time-of-flight (TOF) MSI distributions.

An Algorithm for Fresnel Diffraction Computing Based on Fractional Fourier Transform

The fractional Fourier transform (FrFT) is used for the solution of the diffraction integral in optics. A scanning approach is proposed for finding the optimal FrFT order. In this way, the process of diffraction computing is speeded up. The basic algorithm and the intermediate results at each stage are demonstrated.

On the Range of the Fourier Transform Associated with the Spherical Mean Operator

We characterize the range of some spaces of functions by the Fourier transform associated with the spherical mean operator R and we give a new description of the Schwartz spaces. Next, we prove a Paley-Wiener and a Paley-Wiener-Schawrtz theorems.

Channel model and lower capacity bound for the transmission based on nonlinear Fourier transform

The integrability of the nonlinear Schräodinger equation (NLSE) by the inverse scattering transform shown in a seminal work [1] gave an interesting opportunity to treat the corresponding nonlinear channel similar to a linear one by using the nonlinear Fourier transform. Integrability of the NLSE is in the background of the old idea of eigenvalue communications [2] that was resurrected in recent works [3{7]. In [6, 7] the new method for the coherent optical transmission employing the continuous nonlinear spectral data | nonlinear inverse synthesis was introduced. It assumes the modulation and detection of data using directly the continuous part of nonlinear spectrum associated with an integrable transmission channel (the NLSE in the case considered). Although such a transmission method is inherently free from nonlinear impairments, the noisy signal corruptions, arising due to the ampli¯er spontaneous emission, inevitably degrade the optical system performance. We study properties of the noise-corrupted channel model in the nonlinear spectral domain attributed to NLSE. We derive the general stochastic equations governing the signal evolution inside the nonlinear spectral domain and elucidate the properties of the emerging nonlinear spectral noise using well-established methods of perturbation theory based on inverse scattering transform [8]. It is shown that in the presence of small noise the communication channel in the nonlinear domain is the additive Gaussian channel with memory and signal-dependent correlation matrix. We demonstrate that the effective spectral noise acquires colouring", its autocorrelation function becomes slow decaying and non-diagonal as a function of \frequencies", and the noise loses its circular symmetry, becoming elliptically polarized. Then we derive a low bound for the spectral effiency for such a channel. Our main result is that by using the nonlinear spectral techniques one can significantly increase the achievable spectral effiency compared to the currently available methods [9]. REFERENCES 1. Zakharov, V. E. and A. B. Shabat, Sov. Phys. JETP, Vol. 34, 62{69, 1972. 2. Hasegawa, A. and T. Nyu, J. Lightwave Technol., Vol. 11, 395{399, 1993. 3. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4312{4328, 2014. 4. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4329{4345 2014. 5. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4346{4369, 2014. 6. Prilepsky, J. E., S. A. Derevyanko, K. J. Blow, I. Gabitov, and S. K. Turitsyn, Phys. Rev. Lett., Vol. 113, 013901, 2014. 7. Le, S. T., J. E. Prilepsky, and S. K. Turitsyn, Opt. Express, Vol. 22, 26720{26741, 2014. 8. Kaup, D. J. and A. C. Newell, Proc. R. Soc. Lond. A, Vol. 361, 413{446, 1978. 9. Essiambre, R.-J., G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, J. Lightwave Technol., Vol. 28, 662{701, 2010.

Nonlinear Fourier transform for optical communications

The nonlinear Fourier transform, also known as eigenvalue communications, is a transmission and signal processing technique that makes positive use of the nonlinear properties of fibre channels. I will discuss recent progress in this field.

Optical communication based on the periodic nonlinear Fourier transform signal processing

In this work we introduce the periodic nonlinear Fourier transform (PNFT) and propose a proof-of-concept communication system based on it by using a simple waveform with known nonlinear spectrum (NS). We study the performance (addressing the bit-error-rate (BER), as a function of the propagation distance) of the transmission system based on the use of the PNFT processing method and show the benefits of the latter approach. By analysing our simulation results for the system with lumped amplification, we demonstrate the decent potential of the new processing method.

Fault diagnosis scheme for open-circuit faults in switched reluctance motor drives using fast Fourier transform algorithm with bus current detection

Reliability of power converters is of crucial importance in switched reluctance motor drives used for safety-critical applications. Open-circuit faults in power converters will cause the motor to run in unbalanced states, and if left untreated, they will lead to damage to the motor and power modules, and even cause a catastrophic failure of the whole drive system. This study is focused on using a single current sensor to detect open-circuit faults accurately. An asymmetrical half-bridge converter is considered in this study and the faults of single-phase open and two-phase open are analysed. Three different bus positions are defined. On the basis of a fast Fourier transform algorithm with Blackman window interpolation, the bus current spectrums before and after open-circuit faults are analysed in details. Their fault characteristics are extracted accurately by the normalisations of the phase fundamental frequency component and double phase fundamental frequency component, and the fault characteristics of the three bus detection schemes are also compared. The open-circuit faults can be located by finding the relationship between the bus current and rotor position. The effectiveness of the proposed diagnosis method is validated by the simulation results and experimental tests.

Influence of parameters of drying on laser induced diffuse reflectance of banana discs

Banana discs of 1 cm thickness were immersed into different antioxidant solutions to slow down potentially disturbing discoloration during drying. Samples were randomly split into 8 groups according to the 2^p experimental design. Two antioxidant solutions with 1.66% and 4.59% ascorbic acid, two levels of drying temperature with 50°C and 80°C, two levels of drying time with 6h and 8h were used or adjusted. Laser diodes of seven wavelengths (532, 635, 650, 780, 808, 850 and 1064 nm) were selected to illuminate the surface and light penetration pattern was evaluated on the basis of radial profiles. Profiles acquired at three wavelengths (532, 635 and 650 nm) were found to respond sensitively to adjusted parameters. As a result of drying, intensity decay was observed to move closer to incident point. Significant effect (p<0.01) of temperature, drying time and their interaction was found on extracted descriptive attributes of intensity profiles: full width at half maximum (FWHM), distance of inflection point (DIP) and slope of logarithmic decay (SLD). Beyond their presence, antioxidant concentration was neutral factor without significant contribution to the model. Results were in agreement with reference spectroscopic measurements, especially with NDVI index. Promising results suggest that evaluated method might be suitable for monitoring purposes during drying of fruits.

In vivo characterization of myocardial tissue post myocardial infarction using combined fluorescence and diffuse reflectance spectroscopy

Accurately assessing the extent of myocardial tissue injury induced by Myocardial infarction (MI) is critical to the planning and optimization of MI patient management. With this in mind, this study investigated the feasibility of using combined fluorescence and diffuse reflectance spectroscopy to characterize a myocardial infarct at the different stages of its development. An animal study was conducted using twenty male Sprague-Dawley rats with MI. In vivo fluorescence spectra at 337 nm excitation and diffuse reflectance between 400 nm and 900 nm were measured from the heart using a portable fiber-optic spectroscopic system. Spectral acquisition was performed on (1) the normal heart region; (2) the region immediately surrounding the infarct; and (3) the infarcted region—one, two, three and four weeks into MI development. The spectral data were divided into six subgroups according to the histopathological features associated with various degrees/severities of myocardial tissue injury as well as various stages of myocardial tissue remodeling, post infarction. Various data processing and analysis techniques were employed to recognize the representative spectral features corresponding to various histopathological features associated with myocardial infarction. The identified spectral features were utilized in discriminant analysis to further evaluate their effectiveness in classifying tissue injuries induced by MI. In this study, it was observed that MI induced significant alterations (p < 0.05) in the diffuse reflectance spectra, especially between 450 nm and 600 nm, from myocardial tissue within the infarcted and surrounding regions. In addition, MI induced a significant elevation in fluorescence intensities at 400 and 460 nm from the myocardial tissue from the same regions. The extent of these spectral alterations was related to the duration of the infarction. Using the spectral features identified, an effective tissue injury classification algorithm was developed which produced a satisfactory overall classification result (87.8%). The findings of this research support the concept that optical spectroscopy represents a useful tool to non-invasively determine the in vivo pathophysiological features of a myocardial infarct and its surrounding tissue, thereby providing valuable real-time feedback to surgeons during various surgical interventions for MI.

In Vivo Characterization of Myocardial Tissue Post Myocardial Infarction Using Combined Fluorescence and Diffuse Reflectance Spectroscopy

Accurately assessing the extent of myocardial tissue injury induced by Myocardial infarction (MI) is critical to the planning and optimization of MI patient management. With this in mind, this study investigated the feasibility of using combined fluorescence and diffuse reflectance spectroscopy to characterize a myocardial infarct at the different stages of its development. An animal study was conducted using twenty male Sprague-Dawley rats with MI. In vivo fluorescence spectra at 337 nm excitation and diffuse reflectance between 400 nm and 900 nm were measured from the heart using a portable fiber-optic spectroscopic system. Spectral acquisition was performed on - (1) the normal heart region; (2) the region immediately surrounding the infarct; and (3) the infarcted region - one, two, three and four weeks into MI development. The spectral data were divided into six subgroups according to the histopathological features associated with various degrees / severities of myocardial tissue injury as well as various stages of myocardial tissue remodeling, post infarction. Various data processing and analysis techniques were employed to recognize the representative spectral features corresponding to various histopathological features associated with myocardial infarction. The identified spectral features were utilized in discriminant analysis to further evaluate their effectiveness in classifying tissue injuries induced by MI. In this study, it was observed that MI induced significant alterations (p < 0.05) in the diffuse reflectance spectra, especially between 450 nm and 600 nm, from myocardial tissue within the infarcted and surrounding regions. In addition, MI induced a significant elevation in fluorescence intensities at 400 and 460 nm from the myocardial tissue from the same regions. The extent of these spectral alterations was related to the duration of the infarction. Using the spectral features identified, an effective tissue injury classification algorithm was developed which produced a satisfactory overall classification result (87.8%). The findings of this research support the concept that optical spectroscopy represents a useful tool to non-invasively determine the in vivo pathophysiological features of a myocardial infarct and its surrounding tissue, thereby providing valuable real-time feedback to surgeons during various surgical interventions for MI.