scholarly journals Fourier-Transform-Based Surface Measurement and Reconstruction of Human Face Using the Projection of Monochromatic Structured Light

Sensors ◽  
2021 ◽  
Vol 21 (7) ◽  
pp. 2529
Author(s):  
Bingquan Chen ◽  
Hongsheng Li ◽  
Jun Yue ◽  
Peng Shi
Keyword(s):  
Fourier Transform ◽  
Structured Light ◽  
Surface Measurement ◽  
Human Face ◽  
Image Processing Algorithm ◽  
Optical Filtering ◽  
Linearly Polarized ◽  
Potential Applications ◽  
Filtering Technique ◽  
The Fourier Transform

This work presents a new approach of surface measurement of human face via the combination of the projection of monochromatic structured light, the optical filtering technique, the polarization technique and the Fourier-transform-based image-processing algorithm. The theoretical analyses and experimental results carried out in this study showed that the monochromatic feature of projected fringe pattern generated using our designed laser-beam-based optical system ensures the use of optical filtering technique for removing the effect of background illumination; the linearly-polarized characteristic makes it possible to employ a polarizer for eliminating the noised signal contributed by multiply-scattered photons; and the high-contrast sinusoidal fringes of the projected structured light provide the condition for accurate reconstruction using one-shot measurement based on Fourier transform profilometry. The proposed method with the portable and stable optical setup may have potential applications of indoor medical scan of human face and outdoor facial recognition without strict requirements of a dark environment and a stable object being observed.

scholarly journals Revisiting Feller Diffusion: Derivation and Simulation

2019 ◽  
pp. 1-15
Author(s):  
Ranjiva Munasinghe ◽  
Leslie Kanthan ◽  
Pathum Kossinna
Keyword(s):  
Fourier Transform ◽  
Probability Density Function ◽  
Probability Density ◽  
Method Of Characteristics ◽  
Sample Path ◽  
Planck Equation ◽  
Simulation Algorithm ◽  
Quantitative Finance ◽  
Potential Applications ◽  
The Fourier Transform

We propose a simpler derivation of the probability density function of Feller Diffusion by using the Fourier Transform on the associated Fokker-Planck equation and then solving the resulting equation via the Method of Characteristics. We use the derived probability density to formulate an exact simulation algorithm whereby a sample path increment is drawn directly from the density. We then proceed to use the simulation to verify key statistical properties of the process such as the moments and the martingale property. The simulation is also used to confirm properties related to hitting time probabilities. We also mention potential applications of the simulation in the setting of quantitative finance.

Shape-function-based non-uniform Fourier transforms for seismic modeling with irregular grids

Geophysics ◽  
2021 ◽  
pp. 1-71
Author(s):  
Fang Ouyang ◽  
Jianguo Zhao ◽  
Shikun Dai ◽  
Longwei Chen ◽  
Shangxu Wang
Keyword(s):  
Fourier Transform ◽  
Fourier Transforms ◽  
Shape Function ◽  
High Accuracy ◽  
Irregular Sampling ◽  
Shape Functions ◽  
Lower Accuracy ◽  
Potential Applications ◽  
The Fourier Transform ◽  
Seismic Models

Multi-dimensional Fourier transform on an irregular grid is a useful tool for various seismic forward problems caused by complex media and wavefield distributions. Using a shape-function-based strategy, we develop four different algorithms for 1D and 2D non-uniform Fourier transforms, including two high-accuracy Fourier transforms (LSF-FT and QSF-FT) and two non-uniform fast Fourier transforms (LSF-NUFFT and QSF-NUFFT), respectively based on linear and quadratic shape functions. The main advantage of incorporating shape functions into the Fourier transform is that triangular elements can be used to mesh any complex wavefield distribution in the 2D case. These algorithms, therefore, can be used in conjunction with any irregular sampling strategies. The accuracy and efficiency of the four non-uniform Fourier transforms are investigated and compared by applying them in the frequency-domain seismic wave modeling. All algorithms are compared with exact solutions. Numerical tests show that the quadratic shape-function-based algorithms are more accurate than those based on linear shape function. Moreover, LSF-FT/QSF-FT exhibits higher accuracy but much slower calculation speed, while LSF-NUFFT/QSF-NUFFT is highly efficient but has lower accuracy at near-source points. In contrast, a combination of these algorithms by using QSF-FT at near-source points and LSF-NUFFT/QSF-NUFFT at others, achieves satisfactory efficiency and high accuracy at all points. Although our tests are restricted to seismic models, these improved non-uniform fast Fourier transform algorithms may also have potential applications in other geophysical problems, such as forward modeling in complex gravity and magnetic models.

scholarly journals A New Pseudo-Spectral Method Using the Discrete Cosine Transform

2020 ◽  
Vol 6 (4) ◽  
pp. 15
Author(s):  
Izumi Ito
Keyword(s):  
Fluid Dynamics ◽  
Fourier Transform ◽  
Discrete Cosine Transform ◽  
Superior Performance ◽  
Cosine Transform ◽  
Extended Sequence ◽  
Potential Applications ◽  
The Fourier Transform ◽  
Pseudo Spectral Method ◽  
Pseudo Spectral

The pseudo-spectral (PS) method on the basis of the Fourier transform is a numerical method for estimating derivatives. Generally, the discrete Fourier transform (DFT) is used when implementing the PS method. However, when the values on both sides of the sequences differ significantly, oscillatory approximations around both sides appear due to the periodicity resulting from the DFT. To address this problem, we propose a new PS method based on symmetric extension. We mathematically derive the proposed method using the discrete cosine transform (DCT) in the forward transform from the relation between DFT and DCT. DCT allows a sequence to function as a symmetrically extended sequence and estimates derivatives in the transformed domain. The superior performance of the proposed method is demonstrated through image interpolation. Potential applications of the proposed method are numerical simulations using the Fourier based PS method in many fields such as fluid dynamics, meteorology, and geophysics.

scholarly journals Dynamically Modulating Plasmonic Field by Tuning the Spatial Frequency of Excitation Light

Nanomaterials ◽  
2020 ◽  
Vol 10 (8) ◽  
pp. 1449
Author(s):  
Sen Wang ◽  
Minghua Sun ◽  
Shanqin Wang ◽  
Maixia Fu ◽  
Jingwen He ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Spatial Frequency ◽  
Excitation Light ◽  
Potential Applications ◽  
Frequency Components ◽  
Simulation Results ◽  
The Fourier Transform ◽  
Theoretical Analyses ◽  
Plasmon Polaritons ◽  
Good Agreement

Based on the Fourier transform (FT) of surface plasmon polaritons (SPPs), the relation between the displacement of the plasmonic field and the spatial frequency of the excitation light is theoretically established. The SPPs’ field shifts transversally or longitudinally when the spatial frequency components f x or f y are correspondingly changed. The SPPs’ focus and vortex field can be precisely located at the desired position by choosing the appropriate spatial frequency. Simulation results are in good agreement with the theoretical analyses. Dynamically tailoring the plasmonic field based on the spatial frequency modulation can find potential applications in microparticle manipulation and angular multiplexed SPP focusing and propagation.

scholarly journals Determining Surface Shape of Translucent Objects with the Combination of Laser-Beam-Based Structured Light and Polarization Technique

Sensors ◽  
2021 ◽  
Vol 21 (19) ◽  
pp. 6587
Author(s):  
Bingquan Chen ◽  
Peng Shi ◽  
Yanhua Wang ◽  
Yongze Xu ◽  
Hongyang Ma ◽  
...  
Keyword(s):  
Laser Beam ◽  
Structured Light ◽  
Optical Filter ◽  
Surface Shape ◽  
Sinusoidal Signal ◽  
Surface Measurement ◽  
3D Surface ◽  
Polarization Technique ◽  
Linearly Polarized ◽  
Theoretical Analyses

In this study, we focus on the 3D surface measurement and reconstruction of translucent objects. The proposed approach of surface-shape determination of translucent objects is based on the combination of the projected laser-beam-based sinusoidal structured light and the polarization technique. The theoretical analyses are rigorously completed in this work, including the formation, propagation, and physical features of the generated sinusoidal signal by the designed optical system, the reflection and transmission of the projected monochromatic fringe pattern on the surface of the translucent object, and the formation and the separation of the direct-reflection and the global components of the surface radiance of the observed object. The results of experimental investigation designed in accordance with our theoretical analyses have confirmed that accurate reconstructions can be obtained using the one-shot measurement based on the proposed approach of this study and Fourier transform profilometry, while the monochromaticity and the linearly-polarized characteristic of the projected sinusoidal signal can be utilized by using a polarizer and an optical filter simultaneously for removing the global component, i.e., the noised signal contributed by multiply-scattered photons and the background illuminance in the frame of our approach. Moreover, this study has also revealed that the developed method is capable of getting accurate measurements and reconstructions of translucent objects when the background illumination exists, which has been considered as a challenging issue for 3D surface measurement and reconstruction of translucent objects.

scholarly journals Strain Sensitivity Enhancement of Broadband Ultrasonic Signals in Plates Using Spectral Phase Filtering

2021 ◽  
Vol 11 (6) ◽  
pp. 2582
Author(s):  
Lucas M. Martinho ◽  
Alan C. Kubrusly ◽  
Nicolás Pérez ◽  
Jean Pierre von der Weid
Keyword(s):  
Fourier Transform ◽  
Guided Waves ◽  
Strain Level ◽  
Energy Concentration ◽  
Short Time Fourier Transform ◽  
Time Frequency ◽  
Frequency Representation ◽  
The Fourier Transform ◽  
Short Time ◽  
Sensitivity Gain

The focused signal obtained by the time-reversal or the cross-correlation techniques of ultrasonic guided waves in plates changes when the medium is subject to strain, which can be used to monitor the medium strain level. In this paper, the sensitivity to strain of cross-correlated signals is enhanced by a post-processing filtering procedure aiming to preserve only strain-sensitive spectrum components. Two different strategies were adopted, based on the phase of either the Fourier transform or the short-time Fourier transform. Both use prior knowledge of the system impulse response at some strain level. The technique was evaluated in an aluminum plate, effectively providing up to twice higher sensitivity to strain. The sensitivity increase depends on a phase threshold parameter used in the filtering process. Its performance was assessed based on the sensitivity gain, the loss of energy concentration capability, and the value of the foreknown strain. Signals synthesized with the time–frequency representation, through the short-time Fourier transform, provided a better tradeoff between sensitivity gain and loss of energy concentration.

Determination of starch crystallinity with the Fourier-transform terahertz spectrometer

2021 ◽  
Vol 262 ◽  
pp. 117928
Author(s):  
Shusaku Nakajima ◽  
Shuhei Horiuchi ◽  
Akifumi Ikehata ◽  
Yuichi Ogawa
Keyword(s):  
Fourier Transform ◽  
The Fourier Transform ◽  
Starch Crystallinity
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