MSFM-Based Seismic Traveltime Calculation Using Coarse-Grid Interpolation

A fast marching algorithm for the factored eikonal equation

Accurate estimation of local neuron size of complex 3D neuron structures imaged by microscopy is very important for quantification of neuronal morphology, such as neuron tracing applications. Previously, the Rayburst sampling algorithm was developed to estimate the neuron size in volumetric microscopy images. However, it requires an accurate detection of the neuron centerline, which is not easy and time-consuming. In this paper, we propose to estimate the neuron local radius of any region of interest in a given neuron, by first detecting its corresponding neuron centerline point using Multistencils Fast Marching (MSFM) method and then estimating the local neuron radius by the Rayburst sampling algorithm. The experimental results on different datasets show that the proposed method could obtain very accurate local neuron radius efficiently.

Using the continuous seismic ambient noise data recorded by 28 land seismic stations in the area surrounding the South China Sea and 2 island stations on Dongsha Island and Taiping Island during January 2011 and December 2016, we calculated the cross-correlation functions between station-pairs utilizing the cross-correlation method, and extracted the Rayleigh surface wave group velocity and phase velocity dispersion curves based on it. The group velocity and phase velocity images of South China Sea over period range of 12 similar to 40 s were inverted by using Fast Marching and Subspace method. Then, the 3D S-wave velocity structure up to 60 km in depth was inverted by joint inversion. During the inversion process, we added a water layer into the inversion model, considering that several kilometers seawater layer could strongly change the surface wave dispersion behavior. In fact, it is proved that an additional water layer can significantly improve the reliability of the inversion results. From the inverted result, there exists strong lateral variations in the crust and upper mantle structures within the study areas. These variations spatially correlate with the main structural units in this area. At depth of 5 similar to 10 km, the Yinggehai-Song Hong Basin is of low velocity, which may be related with the thick sediments layer under the sea. At depth of 5 similar to 15 km, the high velocity anomaly in our model correlates well with location of the South China Sea Basin, which may infer that the crust thickness of the sea basin area is much thinner than that of the continental margin area. At depth of 20 similar to 30 km, the high-velocity feature of the sea basin extended further to the continental margin area. This reflects the gradual thickening of the crust thickness from the sea basin to the continental margin, which is consistent with the deep seismic profile result obtained using OBS data. In the depth range over 35 similar to 60 km, the high-velocity feature of the South China Sea Basin is still obvious and the velocity increases with the depth in general, by which we surmise that the lithosphere thickness of the sea basin should be greater than 60 km.

We present an algorithm for computing the closest point, transform to an explicitly described manifold on a rectilinear grid in low dimensional spaces. The closest point transform finds the closest point on a manifold and the Euclidean distance to a manifold for the points in a grid. We consider manifolds composed of simple geometric shapes, such as, a set of points, piecewise linear curves or triangle meshes. The algorithm solves the eikonal equation |∇u| = 1 with the method of characteristics. For many problems, the computational complexity of the algorithm is linear in both the number of grid points and the complexity of the manifold. Many query problems can be aided by using orthogonal range queries (ORQ). There are several standard data structures for performing ORQ's in 3-D, including kd-trees, octrees, and cell arrays. We develop additional data structures based on cell arrays. We study the characteristics of each data structure and compare their performance. We present a new algorithm for solving the single-source, non-negative weight, shortest-paths problem. Dijkstra's algorithm solves this problem with computational complexity O ((E + V)log V) where E is the number of edges and V is the number of vertices. The new algorithm, called Marching with a Correctness Criterion (MCC), has computational complexity O (E + RV), where R is the ratio of the largest to smallest edge weight. Sethian's Fast Marching Method (FMM) may be used to solve static Hamilton-Jacobi equations. It has computational complexity O (N log N), where N is the number of grid points. The FMM has been regarded as an optimal algorithm because it is closely related to Dijkstra's algorithm. The new shortest-paths algorithm discussed above can be used to develop an ordered, upwind, finite difference algorithm for solving static Hamilton-Jacobi equations. This algorithm requires difference schemes that difference not only in coordinate directions, but in diagonal directions as well. It has computational complexity O(RN), where R is the ratio of the largest to smallest propagation speed and N is the number of grid points.

Feature extraction from mammographic images using fast marching methods

The initial model is the crucial to full waveform inversion. First arrival traveltime tomography can provide a more accurate near-surface model, improve the accuracy of the FWI and accelerate convergence. In this paper, the initial model is based on fast marching method (FMM) traveltime tomography to obtain the near-surface velocity model. The second-order FMM is used to solve the Eikonal equation; although our implementation belongs to the family of adjoint-state tomographies, we do not need to compute the adjoint-state variable as an intermediate product for the gradient. The first arrival traveltime tomography based on FMM can provide a more accurate near-surface initial model for FWI, and improve the convergence rate of FWI. On synthetic data examples, we show the advantages of the proposed approach. Moreover, the use of parallel computing improves computational efficiency.

Fast and accurate traveltime computation for quasi-P waves in anisotropic media is an essential ingredient of many seismic processing and interpretation applications such as Kirchhoff modeling and migration, microseismic source localization, and traveltime tomography. Fast-sweeping methods are widely used for solving the anisotropic eikonal equation due to their flexibility in solving general equations compared to the fast-marching method. However, it has been observed that fast sweeping can be much less efficient than fast marching for models with curved characteristics and practical grid sizes. By representing a tilted transversely isotropic (TTI) equation as a sequence of elliptically isotropic (EI) eikonal equations, we determine that the fast-marching algorithm can be used to compute fast and accurate traveltimes for TTI media. The tilt angle is absorbed into the description of the effective EI model; therefore, the adopted approach does not compromise on the solution accuracy. Through tests on benchmark synthetic models, we test our fast-marching algorithm and discover considerable improvement in accuracy by using factorization and a second-order finite-difference stencil. The adopted methodology opens the door to the possibility of using the fast-marching algorithm for a wider class of anisotropic eikonal equations.

We introduce the Fast Marching farthest point sampling (FastFPS) approach for the progressive sampling of planar domains and curved manifolds in triangulated, point cloud or implicit form. By using Fast Marching methods 2 , 3, 6 for the incremental computation of distance maps across the sampling domain, we obtain a farthest point sampling technique superior to earlier point sampling principles in two important respects. Firstly, our method performs equally well in both the uniform and the adaptive case. Secondly, the algorithm is applicable to both images and higher dimensional surfaces in triangulated, point cloud or implicit form. This paper presents the methods underlying the algorithm and gives examples for the processing of images and triangulated surfaces. A companion report 4 provides details regarding the application of the FastFPS algorithm to point clouds and implicit surfaces.

An accurate and effective FMM-based approach for freehand 3D ultrasound reconstruction

One of the most popular level set algorithms is the so-called fast marching method. In this paper, a medical image segmentation method is proposed based on the combination of fast marching method and watershed transformation. First, the original image is smoothed using nonlinear diffusion filter, then the smoothed image is over-segmented by the watershed algorithm. Last, the image is segmented automatically using the modified fast marching method. Due to introducing over-segmentation, the arrival time the seeded point to the boundary of region should be calculated. For other pixels inside the region of the seeded point, the arrival time is not calculated because of the region homogeneity. So the algorithm's speed improves greatly. Moreover, the speed function is defmed again based on the statistical similarity degree of the nearby regions. Experiments show that the algorithm can fast and accurately obtain segmentation results ofmedical images.

Shape‐from‐shading (SfS) is a fundamental problem in computer vision. Its goal is reconstruction of surface depth (i.e., distance from camera plane) based on a single image of the surface. The problem was introduced in the early 1970s by Horn. A very common assumption in this field is that image projection is orthographic. We will present the orthographic shape‐from‐shading problem and an algorithm for its solution: the fast marching method of Kimmel and Sethian. We shall than reexamine the basis of SfS, which is the image irradiance equation, under a perspective projection assumption. The resultant equation does not depend on the depth function directly, but on its natural logarithm, and as such it is invariant to scale changes of the depth function. A reconstruction method based on the perspective formula is then described; it is a modification of the aforementioned orthographic fast marching method. Then, a comparison of the orthographic fast marching, perspective fast marching, and the perspective algorithm of Prados and Faugeras on synthetic images is are presented. The two perspective methods equate with each other and show better reconstruction results than the orthographic. We then compare the orthographic and perspective versions of the fast marching method on endoscopic images. The perspective algorithm outperformed the orthographic one. These findings suggest that the more realistic set of assumptions of perspective SfS improves reconstruction significantly with respect to orthographic SfS. The findings also provide evidence that perspective SfS can be used for real‐life applications in fields such as endoscopy.

Summary Seismic travel time tomography has been proven as an effective tool in reconstruction of Earth's p-wave velocity model in offshore projects. Data of different resolutions and scales are to be integrated to reconstruct the underlying velocity field which may be further correlated to other geotechnical and geomechanical parameters. In this study, we apply a probabilistic method to invert criosshole seismic tomography travel time data which utilizes geostatistical priors, i.e. models that features the spatial pattern and continuity of the underlying velocity field inferred from limited amount of data in the boreholes. The method starts with a Bayesian analysis over the Kriging mean and correlation model parameters, and posterior samples from this step is input to a geostatistical simulator that generates realistic prior models as an input to the probabilistic inversion process. Extended Metropolis sampler then is hired to generate samples of posterior realizations of p-wave velocity model. The proposed method is applied on a synthetic ground model of p-wave velocity and results indicate the efficiency of the algorithm in reconstructing the underlying p-wave velocity model with the possibility of uncertainty quantification through multiple realizations generated.

Liver segmentation is the fundamental step in computer-aided liver disease diagnosis and surgery planning. In this study, we developed a fully automatic liver extraction scheme based on an adaptive fast marching method (FMM). Firstly, a thresholding operation was applied to remove the ribs, spines and kidneys. Followed by a smooth filter for noise reduction. Secondly, a nonlinear gray scale converter was used to enhance the contrast of the liver parenchyma. The enhanced image is then eroded with 3-voxel radius so that small regions are deleted. The seed points located in the liver were selected automatically. Finally, using the processed image as a speed function, FMM was employed to generate the liver contour. Clinical validation has performed on 30 abdominal computed tomography (CT) datasets. The proposed algorithm achieved an overall true positive rate (TPR) of 0.98. It takes about 0.30 s for a 512×512-pixel slice. The method has been applied successfully for fast and accurate liver segmentation.

Fast marching method assisted permeability upscaling using a hybrid deep learning method coupled with particle swarm optimization

The interface of fluids can develop corners and discontinuities while it advances. The Level-set method is one of the most popular methods used for the problem of tracking a propagating interface. The Fast marching method (FMM) is an effective method for monotonically propagating fronts. In this paper we present an o ( n ) improved level-set algorithm. This new method is based on the narrow band approach as in the FMM. However, it uses a multi-point correction strategy to advance a group of grid points at a time, rather than sorting the solution in the narrow band, to march forward to a single grid point, and then update the rid points one by one. The numerical results by two and three dimensions, shows the validity of the new method. This method has been applied to the tracking of an interface in a dynamic virtual environment.