Characterizing three‐dimensional wavefields with high‐resolution spectra

Geophysics ◽  
1992 ◽  
Vol 57 (4) ◽  
pp. 522-531
Author(s):  
R. A. Meek ◽  
A. A. Vassiliou
Keyword(s):  
Fourier Transform ◽  
Maximum Entropy ◽  
Fourier Transforms ◽  
Spectral Estimation ◽  
Three Dimensional ◽  
Estimation Method ◽  
Synthetic Data ◽  
Estimation Algorithm ◽  
Three Dimensions ◽  
Coherent Noise

Three‐dimensional spectra (frequency‐x‐wavenumber‐y‐wavenumber or [Formula: see text] spectra) can be used to determine the frequency content, velocity, and direction of waves entering an array of receivers. This information is important in detecting aliasing problems, understanding coherent noise, designing arrays, and determining parameters for coherent noise filters. Because of the limited spatial dimensions of most arrays the discrete Fourier transform produces an estimate of the three‐dimensional (3-D) spectrum with severe wavenumber distortion. We extend a 2-D hybrid spectral estimation method to three dimensions by combining a temporal Fourier transform with a spatial 2-D maximum entropy spectral estimation technique. The method produces [Formula: see text] spectra with higher wavenumber resolution and less spectral distortion than corresponding 3-D Fourier spectra. The 2-D maximum entropy spectral estimation algorithm uses a sequence of Fourier transforms to extrapolate the estimated autocorrelation function of the data. We assume the wavenumber spectrum of the data comprises a sum of a few poles. Field and synthetic data are used to demonstrate how 3-D wavefields can be characterized with this method of spectral analysis. From these results we conclude that the method gives excellent wavenumber resolution but performs poorly in detecting small signals in the presence of high amplitude signals. We feel this limitation is not serious for characterizing strong amplitude coherent energy recorded by an array of receivers.

Diffraction by crystals

2002 ◽  
Author(s):  
David Blow
Keyword(s):  
Fourier Transform ◽  
Three Dimensional ◽  
Incident Beam ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Dimensional Structure ◽  
Angle Of Incidence ◽  
X Ray ◽  
Max Von Laue ◽  
The Fourier Transform

In Chapter 4 many two-dimensional examples were shown, in which a diffraction pattern represents the Fourier transform of the scattering object. When a diffracting object is three-dimensional, a new effect arises. In diffraction by a repetitive object, rays are scattered in many directions. Each unit of the lattice scatters, but a diffracted beam arises only if the scattered rays from each unit are all in phase. Otherwise the scattering from one unit is cancelled out by another. In two dimensions, there is always a direction where the scattered rays are in phase for any order of diffraction (just as shown for a one-dimensional scatterer in Fig. 4.1). In three dimensions, it is only possible for all the points of a lattice to scatter in phase if the crystal is correctly oriented in the incident beam. The amplitudes and phases of all the scattered beams from a three-dimensional crystal still provide the Fourier transform of the three-dimensional structure. But when a crystal is at a particular angular orientation to the X-ray beam, the scattering of a monochromatic beam provides only a tiny sample of the total Fourier transform of its structure. In the next section, we are going to find what is needed to allow a diffracted beam to be generated. We shall follow a treatment invented by Lawrence Bragg in 1913. Max von Laue, who discovered X-ray diffraction in 1912, used a different scheme of analysis; and Paul Ewald introduced a new way of looking at it in 1921. These three methods are referred to as the Laue equations, Bragg’s law and the Ewald construction, and they give identical results. All three are described in many crystallographic text books. Bragg’s method is straightforward, understandable, and suffices for present needs. I had heard J.J. Thomson lecture about…X-rays as very short pulses of radiation. I worked out that such pulses…should be reflected at any angle of incidence by the sheets of atoms in the crystal as if these sheets were mirrors.…It remained to explain why certain of the atomic mirrors in the zinc blende [ZnS] crystal reflected more powerfully than others.

High Speed Micro Holographic PIV Measurements of Microorganisms

2008 ◽  
Author(s):  
M. Zarzecki ◽  
F. J. Diez
Keyword(s):  
Velocity Field ◽  
High Speed ◽  
Fourier Transforms ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Imaging Method ◽  
Time Resolved ◽  
Feeding Methods ◽  
Holographic Particle Image Velocimetry ◽  
Three Components

Holographic particle image velocimetry (PIV) is a novel application of holography that allows for tracking of small particle sized objects in a small volume. Whereas regular PIV allows for the two in-plane components of the velocity field to be measured, and stereoscopic PIV allows for the three-components of the velocity field to be measured in a thin plane, holographic PIV allows for the three-components of the velocity to be measured for each individual particle present in the measuring volume, thus allowing to fully resolve fluid flows that are inherently 3D in nature. There are many examples of three dimensional flows in nature including turbulence flows, but another very interesting application very well suited for this technique involves tracking living microorganisms in order to study their motion and their means of propulsion. As part of this research a micro organism was tracked in three dimensions using a high speed microscopic holographic imaging method. The ability to track organisms in 3D allows better understanding and characterizing of their behavior including their propulsion methods, their feeding methods and their interaction with each other. The time resolved holograms were reconstructed in Matlab using Fast Fourier Transforms. A laser pointer was used as a source of coherent light, and a high speed PIV camera (Photron APX Ultima) was used to capture the images. A beam expander was used to increase the diameter of the laser beam allowing for a larger tracking area. Results with this system will show the trajectories in 3D of microorganisms as well as the three components of the velocity field showing the interaction of the organisms with their environment.

scholarly journals Dynamic triaxial constitutive model for rock subjected to initial stress

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 149-163
Author(s):  
Junzhe Li ◽  
Guang Zhang ◽  
Mingze Liu ◽  
Shaohua Hu ◽  
Xinlong Zhou
Keyword(s):  
Constitutive Model ◽  
Impact Load ◽  
Three Dimensional ◽  
Estimation Method ◽  
Constant Strain Rate ◽  
Strain Curve ◽  
Initial Pressure ◽  
Expansion Method ◽  
Three Dimensions ◽  
Model Parameters

AbstractBuilding on the existing model, an improved constitutive model for rock is proposed and extended in three dimensions. The model can avoid the defect of non-zero dynamic stress at the beginning of impact loading, and the number of parameters is in a suitable range. The three-dimensional expansion method of the component combination model is similar to that of the Hooke spring, which is easy to operate and understand. For the determination of model parameters, the shared parameter estimation method based on the Levenberg–Marquardt and the Universal Global Optimization algorithm is used, which can be well applied to models with parameters that do not change with confinement and strain rates. According to the established dynamic constitutive equation, the stress–strain curve of rock under the coupling action of the initial hydrostatic pressure load and constant strain-rate impact load can be estimated theoretically. By comparing the theoretical curve with the test data, it is shown that the dynamic constitutive model is suitable for the rock under the initial pressure and impact load.

scholarly journals DeepSynth: Three-dimensional nuclear segmentation of biological images using neural networks trained with synthetic data

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Kenneth W. Dunn ◽  
Chichen Fu ◽  
David Joon Ho ◽  
Soonam Lee ◽  
Shuo Han ◽  
...  
Keyword(s):  
Neural Networks ◽  
Image Processing ◽  
Deep Learning ◽  
Three Dimensional ◽  
Synthetic Data ◽  
Training Data ◽  
Three Dimensions ◽  
Great Promise ◽  
Biological Images ◽  
Nuclear Segmentation

AbstractThe scale of biological microscopy has increased dramatically over the past ten years, with the development of new modalities supporting collection of high-resolution fluorescence image volumes spanning hundreds of microns if not millimeters. The size and complexity of these volumes is such that quantitative analysis requires automated methods of image processing to identify and characterize individual cells. For many workflows, this process starts with segmentation of nuclei that, due to their ubiquity, ease-of-labeling and relatively simple structure, make them appealing targets for automated detection of individual cells. However, in the context of large, three-dimensional image volumes, nuclei present many challenges to automated segmentation, such that conventional approaches are seldom effective and/or robust. Techniques based upon deep-learning have shown great promise, but enthusiasm for applying these techniques is tempered by the need to generate training data, an arduous task, particularly in three dimensions. Here we present results of a new technique of nuclear segmentation using neural networks trained on synthetic data. Comparisons with results obtained using commonly-used image processing packages demonstrate that DeepSynth provides the superior results associated with deep-learning techniques without the need for manual annotation.

scholarly journals SPICE-Based SAR Tomography Over Forest Areas Using a Small Number of P-band Airborne F-SAR Images Characterized by Non-Uniformly Distributed Baselines

2019 ◽  
Vol 11 (8) ◽  
pp. 975 ◽  
Author(s):  
Peng ◽  
Li ◽  
Wang ◽  
Zhu ◽  
Liang ◽  
...  
Keyword(s):  
Forest Canopy ◽  
Vertical Structure ◽  
Spectral Estimation ◽  
Three Dimensional ◽  
Estimation Method ◽  
Digital Terrain Model ◽  
Sar Images ◽  
Terrain Model ◽  
Airborne Sar ◽  
Mean Square Errors

Synthetic aperture radar tomography (TomoSAR) has been proven to be a useful way to reconstruct vertical structure over forest areas with P-band images, on account of its three-dimensional imaging ability. In the case of a small number of non-uniformly distributed acquisitions, compressive sensing (CS) is generally adopted in TomoSAR. However, the performance of CS depends on the selected hyperparameter, which is closely related to the noise of a pixel. In this paper, to overcome this limitation, we propose a sparse iterative covariance-based estimation (SPICE) approach based on the wavelet and orthogonal sparse basis (W&O-SPICE) for application over forest areas. SPICE is a sparse spectral estimation method that achieves a high vertical resolution, and takes account of the noise adaptively for each resolution cell. Thus, it does not require the user to select a hyperparameter. Furthermore, the used sparse basis not only ensures the sparsity of the forest canopy scattering contribution, but it can also keep the original sparse information of the ground contribution. The proposed method was tested in simulated experiments and the results demonstrated that W&O-SPICE can successfully reconstruct the vertical structure of a forest. Moreover, three P-band fully polarimetric airborne SAR images with non-uniformly distributed baselines were applied to reconstruct the vertical structure of a tropical forest in Mabounie, Gabon. The underlying topography and forest height were estimated, and the root-mean-square errors (RMSEs) were 6.40 m and 4.50 m with respect to the LiDAR digital terrain model (DTM) and canopy height model (CHM), respectively. In addition, W&O-SPICE showed a better performance than W&O-CS, beamforming, Capon, and the iterative adaptive approach (IAA).

Improving the Accuracy of Depth Estimation in Binocular Vision for Robotic Applications

2013 ◽  
Vol 284-287 ◽  
pp. 1862-1866 ◽  
Author(s):  
Kuan Yu Chen ◽  
Cheng Chin Chien ◽  
Chien Te Tseng
Keyword(s):  
Binocular Vision ◽  
Stereo Vision ◽  
Computational Models ◽  
Stereo Matching ◽  
Focal Length ◽  
Three Dimensional ◽  
Estimation Method ◽  
Depth Estimation ◽  
Estimation Algorithm ◽  
Dimensional Structure

Binocular vision or stereo vision for extraction of three-dimensional information from stereo images has been widely used in many applications like robot navigation, recovering the three-dimensional structure of a scene, and optical inspection systems. More recently, the majority of research in binocular vision has focused on the establishment of stereo matching. However, to date, there has been relatively little research conducted on the effect of computational models of binocular vision with variable focal length of lens. In this paper, a modified computational model of binocular vision is presented to develop a new depth estimation algorithm with no effect of changes in focal length. This method provides an obvious advantage in accuracy of depth estimation by reducing the effect of changing the lens focal length. The experimental results show that the proposed depth estimation method in binocular vision provides better accuracy than conventional method. Finally, we apply the new depth estimation method to a stereo-vision-based automatic docking system for a mobile robot to verify its accuracy.

scholarly journals Inferring cellular forces from image stacks

2017 ◽  
Vol 372 (1720) ◽  
pp. 20160261 ◽  
Author(s):  
Jim H. Veldhuis ◽  
Ahmad Ehsandar ◽  
Jean-Léon Maître ◽  
Takashi Hiiragi ◽  
Simon Cox ◽  
...  
Keyword(s):  
Cancer Metastasis ◽  
Three Dimensional ◽  
Synthetic Data ◽  
Cellular Systems ◽  
Force Balance ◽  
Three Dimensions ◽  
Surface Evolver ◽  
Force Microscopy ◽  
Wide Range ◽  
Cellular Forces

Although the importance of cellular forces to a wide range of embryogenesis and disease processes is widely recognized, measuring these forces is challenging, especially in three dimensions. Here, we introduce CellFIT-3D, a force inference technique that allows tension maps for three-dimensional cellular systems to be estimated from image stacks. Like its predecessors, video force microscopy and CellFIT, this cell mechanics technique assumes boundary-specific interfacial tensions to be the primary drivers, and it constructs force-balance equations based on triple junction (TJ) dihedral angles. The technique involves image processing, segmenting of cells, grouping of cell outlines, calculation of dihedral planes, averaging along three-dimensional TJs, and matrix equation assembly and solution. The equations tend to be strongly overdetermined, allowing indistinct TJs to be ignored and solution error estimates to be determined. Application to clean and noisy synthetic data generated using Surface Evolver gave tension errors of 1.6–7%, and analyses of eight-cell murine embryos gave estimated errors smaller than the 10% uncertainty of companion aspiration experiments. Other possible areas of application include morphogenesis, cancer metastasis and tissue engineering. This article is part of the themed issue ‘Systems morphodynamics: understanding the development of tissue hardware’.

Green’s functions in non-local three-dimensional linear elasticity

2009 ◽  
Vol 465 (2111) ◽  
pp. 3463-3487 ◽  
Author(s):  
Olaf Weckner ◽  
Gerd Brunk ◽  
Michael A. Epton ◽  
Stewart A. Silling ◽  
Ebrahim Askari
Keyword(s):  
Green's Functions ◽  
Fourier Transforms ◽  
Green’S Functions ◽  
Three Dimensional ◽  
Point Load ◽  
Three Dimensions ◽  
Weak Formulation ◽  
Element Discretization ◽  
Linear Elastic Body ◽  
Non Local

In this paper, we compare small deformations in an infinite linear elastic body due to the presence of point loads within the classical, local formulation to the corresponding deformations in the peridynamic, non-local formulation. Owing to the linearity of the problem, the response to a point load can be used to obtain the response to general body force loading functions by superposition. Using Laplace and Fourier transforms, we thus obtain an integral representation for the three-dimensional peridynamic solution with the help of Green’s functions. We illustrate this new theoretical result by dynamic and static examples in one and three dimensions. In addition to this main result, we also derive the non-local three-dimensional jump conditions, as well as the weak formulation of peridynamics together with the associated finite element discretization.

scholarly journals Intensity-based axial localization approaches for multifocal plane microscopy

2016 ◽  
Author(s):  
Ramraj Velmurugan ◽  
Jerry Chao ◽  
Sripad Ram ◽  
E. Sally Ward ◽  
Raimund J. Ober
Keyword(s):  
Point Source ◽  
Three Dimensional ◽  
Estimation Method ◽  
Location Estimation ◽  
Three Dimensions ◽  
Single Particles ◽  
Localization Accuracy ◽  
Superresolution Microscopy ◽  
Axial Location ◽  
Pixel Location

AbstractMultifocal plane microscopy (MUM) can be used to visualize biological samples in three dimensions over large axial depths and provides for the high axial localization accuracy that is needed in applications such as the three-dimensional tracking of single particles and superresolution microscopy. This report analyzes the performance of intensity-based axial localization approaches as applied to MUM data using Fisher information calculations. In addition, a new non-parametric intensity-based axial location estimation method, Multi-Intensity Lookup Algorithm (MILA), is introduced that, unlike typical intensity-based methods that make use of a single intensity value per data image, utilizes multiple intensity values per data image in determining the axial location of a point source. MILA is shown to be robust against potential bias induced by differences in the sub-pixel location of the imaged point source. The method's effectiveness on experimental data is also evaluated.

Misalignment Effect on a Three-Dimensional Cruciform Welded Joint

2013 ◽  
Author(s):  
Shuichi Yamatoki ◽  
Seitaro Arimatsu ◽  
Koji Gotoh
Keyword(s):  
Welded Joint ◽  
Three Dimensional ◽  
Estimation Method ◽  
Three Dimensions ◽  
Design Phase ◽  
Misalignment Effect ◽  
Hull Design ◽  
New Equation ◽  
3D Effect ◽  
Modified Equation

In the ship-hull design phase, the distance of a misalignment of a cruciform welded joint is enlarged, by up to 100 mm for example, until its effect is thought to be minimized. To control tolerance, we used a technique to estimate the coefficient of the misalignment effect: the ratio of the stress with misalignment to stress without misalignment. Current methods, created using the two-dimensional (2D) misalignment model and focusing on small misalignments, cannot be applied in the design phase. Misalignment models are needed, as there have been no studies of these joints and it is impractical to do finite element (FE) analysis in each case. We propose an estimation method of the coefficient of misalignment effect in three dimensions (3D). First, we created a new equation to estimate the coefficient in 2D. The equation accommodates larger misalignments. Second, we found the membrane component of a misaligned member stress is reduced as a 3D effect and the coefficient converges given a certain misalignment value. Third, a modified equation taking the effect into account indicates the coefficient in 3D.

Sign in / Sign up

Export Citation Format

Share Document