China 
Africa 
Explore chapters and articles related to this topic
Light and Waves
Published in Toyohiko Yatagai, Fourier Theory in Optics and Optical Information Processing, 2022
In order to describe a plane wave in 2-D or 3-D space, consider a sinusoidal plane wave propagating to the direction with an angle of θ to the x axis in the 2-D (x,y) coordinate system, as shown in Fig. 1.3. Since its wavefront is perpendicular to the propagation direction, this wave is written as u(x,y,t)=Acos(kX−ωt),
Texture Feature Extraction
Published in R. Suganya, S. Rajaram, A. Sheik Abdullah, Big Data in Medical Image Processing, 2018
R. Suganya, S. Rajaram, A. Sheik Abdullah
where r and s denotes the orientations and scale and Is,r denotes the Gabor filtered images, obtained by convolving image I with Gabor functions of R orientations. On the other hand frequency and orientation representations of Gabor filters resemble the human visual system, and they have been found to be very effective for representing texture. In the spatial domain, a 2D Gabor filter is a Gaussian kernel function modulated by a sinusoidal plane wave. The rotation invariant texture feature can be extracted by modulating the conventional Gabor filter method with respect to a constant scale, i.e., by summing all the orientations of 30°, 45°, 60° and 90° at each scale level, which extracts features from a specific scale band covering all the orientations of the specified liver image.
Multimodal Ambulatory Fall Risk Assessment in the Era of Big Data
Published in Ervin Sejdić, Tiago H. Falk, Signal Processing and Machine Learning for Biomedical Big Data, 2018
The most important property of Gabor features is their robustness against rotation, scale, and translation. Furthermore, they are robust against photometric disturbances, such as illumination changes and noise. These properties are mainly due to the fact that the parameters of Gabor filters enable us to establish invariance in this regard [89]. In the spatial domain, a two-dimensional Gabor filter is a Gaussian function, modulated by an exponential or complex sinusoidal plane wave, defined as G(x,y)=f2πγηexp(−x′2+γy′22σ2)exp(j2πfx′+ϕ),
Viscoelastic wave propagation and resonance in a metal–plastic bonded laminate
Published in Mechanics of Advanced Materials and Structures, 2023
Naoki Mori, Yusuke Iwata, Takahiro Hayashi, Naoki Matsuda
When a sinusoidal plane wave of angular frequency ω is normally incident from the side of layer 4, the stress reflection coefficient for the trilayer laminate Rt is theoretically obtained as by Brekhovskikh’s formulation [4], where is the input acoustic impedances at the front surface of layer 4, and ϕ4 = k4d4 = ωd4/v4. By substituting Eq. (13), we reformulate Eq. (12) as where the coefficient is given by which has the similar form to Eq. (7). Equation (15) corresponds to the reflection coefficient for a bilayer laminate, which consists of layers 2 and 3 sandwiched by semi-infinite media 1 and 4. Namely, the reflection coefficient for a trilayer laminate is associated with the reflection coefficients for single layer plates and bilayer laminate.
Numerical study on how heterogeneity affects ultrasound high harmonics generation
Published in Nondestructive Testing and Evaluation, 2020
Negar Kamali, Ashkan Mahdavi, Sheng-Wei Chi
A single frequency sinusoidal plane wave, with a frequency of 2 MHz, is applied at one edge of the model and the response waves are measured at the nodes on the opposite edge and then averaged. According to Equations (15) and (16), the calculated maximum element and time-step sizes are 0.3 mm and 0.05 , respectively. Therefore, three levels of mesh refinement with mesh sizes, , and , and corresponding time-step sizes, 0.004 , 0.002 and 0.001 are adopted in the convergence study. It is demonstrated in Figures 4 and 5 that the numerical solutions converge and agree well with the analytical solution, with a maximum error of when mesh size is used.
A high precision crack classification system using multi-layered image processing and deep belief learning
Published in Structure and Infrastructure Engineering, 2020
This filter is used to distinguish cracks from the background in a crack image. A Gabor filter-bank proposed in Jain and Farrokhnia (1991) was implemented in this study. Gabor filtering can be used to estimate the mean and standard deviation of the energy of the filtered image. A Gabor impulse response has a sinusoidal plane wave of orientation and frequency. This can be modulated by a two-dimensional Gaussian envelope as defined by El-Tarhouni, Boubchir, Al-Maadeed, Elbendak, and Bouridane (2016) and Jain and Farrokhnia (1991): and show the frequency and phase of the sinusoidal plane wave, while and represent the space constants of the Gaussian envelop. The Gabor filter-bank used in this research has Gabor filters with a Gaussian kernel function, which is based on sinusoidal plane waves of various orientations from the same Gabor-root filter: where x, y and θ are defined as follows: