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Rapidly obtaining the coverage characteristics of leaching solution in In-situ Leaching Area of Sandstone Uranium Mines is a necessary condition for optimizing well locations reasonably. In the presented study, the improved algorithm of the Fast Marching Method (FMM) was studied for rapidly solving coverage characteristics to replace the groundwater numerical simulator. First, the effectiveness of the FMM was verified by simulating diffusion characteristics of the leaching solution in In-situ Leaching Area. Second, based on the radial flow pressure equation and the interaction mechanism of the front diffusion of production and injection well flow field, an improved FMM which is suitable for In-situ Leaching Mining, was developed to achieve the co-simulation of production and injection well. Finally, the improved algorithm was applied to engineering practice to guide the design and production. The results show that the improved algorithm can efficiently solve the coverage characteristics of leaching solution, which is consistent with those obtained from traditional numerical simulators. In engineering practice, the improved FMM can be used to rapidly analyze the leaching process, delineate Leaching Blind Spots, and evaluate the rationality of well pattern layout. Furthermore, it can help to achieve iterative optimization and rapid decision-making of production and injection well locations under large-scale mining area models.

Recent advancements in empirical observations of human psychological responses have revealed that the governing rules of human behavioral aspects can not only be predicted with adequate deterministic precision but also forged into mathematical formulations. These modeling studies enable crisis managers with reliable simulation tools to gain insights into critical facets of crowd disasters and enhance their decision-making abilities to facilitate safe egress in emergency situations. The macroscopic scale of representation in this context is often invoked to comprehend large-scale collective pattern formation in vast built environments, owing to its computational viability. The associated governing equations are typically constructed in a system of hyperbolic conservation law form, and conducting simulations in real-life complex geometric configurations can pose computational challenges. This article puts forward a high-resolution, shock-capturing meshfree particle method in an Eulerian framework for the numerical approximation of several widely adopted macroscopic pedestrian flow models. It serves as a superior alternative to traditional mesh-based methods, eliminating the need for specific mesh structures and connectivity between them. A classical Generalized Finite Difference Method (GFDM) in conjunction with several consistency conditions on spatial derivative coefficients is adopted to obtain a non-oscillatory and fairly conservative Godunov-type discretization of the governing system. The intercell flux is evaluated using a suitable Riemann solver, and a slope-limited reconstruction procedure of the corresponding Riemann states, adapted to arbitrary point distribution, is employed for improved accuracy. Moreover, the preferred direction of human motion is determined from a local density-dependent eikonal-type equation, which is solved using a generalized version of the Fast Marching Method. A thorough numerical investigation of three well-known second-order macroscopic models, namely Payne-Whitham (PW), Aw-Rascle (AR), and Aw-Rascle-Zhang (ARZ) is carried out through two hypothetical scenarios of crowd evacuation, not only to demonstrate the accuracy and applicability of the proposed approach but also to deepen understanding of their distinctive characteristics. A comparison of the flow flux with the fundamental diagram suggests that the density profile obtained with the ARZ model is equivalent to Hughes' first-order model. In contrast, the PW and AR models have proven to effectively replicate complex, unstable pedestrian phenomena such as stop-and-go waves. Finally, Helbing's counter-intuitive idea that strategically positioned barriers upstream of a bottleneck can essentially expedite evacuation is numerically investigated across various parameter choices. • A high-resolution, shock-capturing mesh-free particle method for three widely adopted pedestrian flow models. • Classical Generalized Finite Difference Method in conjunction with geometric conservation. • Complete characterization of complex, unstable crowd phenomena such as stop-and-go waves. • Investigation of bottleneck evacuation in the presence of strategically placed obstacles. [ABSTRACT FROM AUTHOR]

The precise determination of earthquake location is the fundamental basis in seismological community, and is crucial for analyzing seismic activity and performing seismic tomography. First arrivals are generally used to practically determine earthquake locations. However, first-arrival traveltimes are not sensitive to focal depths. Moreover, they cannot accurately constrain focal depths. To improve the accuracy, researchers have analyzed the depth phases of earthquake locations. The traveltimes of depth phases are sensitive to focal depths, and the joint inversion of depth phases and direct phases can be implemented to potentially obtain accurate earthquake locations. Generally, researchers can determine earthquake locations in layered models. Because layered models can only represent the first-order feature of subsurface structures, the advantages of joint inversion are not fully explored if layered models are used. To resolve the issue of current joint inversions, we use the traveltimes of three seismic phases to determine earthquake locations in heterogeneous models. The three seismic phases used in this study are the first P-, sPg- and PmP-waves. We calculate the traveltimes of the three seismic phases by solving an eikonal equation with an upwind difference scheme and use the traveltimes to determine earthquake locations. To verify the accuracy of the earthquake location method by the inversion of three seismic phases, we take the 2021 MS6.4 Yangbi, Yunnan earthquake as an example and locate this earthquake using synthetic and real seismic data. Numerical tests demonstrate that the eikonal equation-based earthquake location method, which involves the inversion of multiple phase arrivals, can effectively improve earthquake location accuracy. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Engineering Geology / Gongcheng Dizhi Xuebao is the property of Journal of Engineering Geology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper presents a formulation for deterministically calculating optimized paths for a multi-agent system consisting of heterogeneous vehicles. The key idea is the calculation of the shortest time for each agent to reach every grid point from its known initial position. Such arrival time map is efficiently computed using the Fast Marching Method (FMM), a computational algorithm originally designed for solving boundary value problems of the Eikonal equation. By leveraging the FMM, we demonstrate that the minimal time rendezvous point and paths for all member vehicles can be uniquely determined with minimal computational overhead. The scalability and adaptability of the present method during online execution are investigated, followed by a comparison with a baseline method that highlights the effectiveness of the proposed approach. Then, the potential of the present method is showcased through a virtual rendezvous scenario involving the coordination of a ship, an underwater vehicle, an aerial vehicle, and a ground vehicle, all converging at the optimal location within the Tampa Bay area in minimal time. The results show that the developed framework can efficiently construct continuous paths of heterogeneous vehicles by accommodating operational constraints via an FMM algorithm.

Recently, X-ray computed tomography-imaging modality is considered as golden standard for diagnosis of coronavirus lungs infection. In worldwide, infectious patients increase rapidly that lead to weariness in health services staff, as well as instant treatment required to avoid patients' health deterioration due to infection development. Image processing would be reinforcing health services by considering computer-based segmentation. However, a ground glass computed tomography image fashion of coronavirus lungs infection characterized by disappearance of edge region of interest and lack of object structure. In this study, these challenges addressed by introducing a new algorithm that combined both morphological reconstruction and fast marching method. The proposed algorithm applied on archived computed tomography dataset for coronavirus infected patients, results showed consistent determination of ground glass infection region compared to manual delineation of senior physician. The proposed algorithm restricted to empirical adjustment of FMM's threshold that would be addressed in upcoming study. [ABSTRACT FROM AUTHOR]

Given a set of generators, the geodesic Voronoi diagram (GVD) defines how the base surface is decomposed into separate regions such that each generator dominates a region in terms of geodesic distance to the generators. Generally speaking, each ordinary bisector point of the GVD is determined by two adjacent generators while each branching point of the GVD is given by at least three generators. When there are sufficiently many generators, straight-line distance serves as an effective alternative of geodesic distance for computing GVDs. However, for a set of sparse generators, one has to use exact or approximate geodesic distance instead, which requires a high computational cost to trace the bisectors and the branching points. We observe that it is easier to infer the branching points by stretching the ordinary segments than competing between wavefronts from different directions. Based on the observation, we develop an unfolding technique to compute the ordinary points of the GVD, as well as a growth-based technique to stretch the traced bisector segments such that they finally grow into a complete GVD. Experimental results show that our algorithm runs 3 times as fast as the state-of-the-art method at the same accuracy level.

The Fast Marching Method (FMM) is an efficient tool for the solution of the Eikonal equation to characterize frontal propagation in heterogeneous and anisotropic media. Previous studies have applied the FMM in solving the Eikonal equation to obtain the "diffusive time of flight" (DTOF), which is used to characterize the pressure front propagation in subsurface porous media. In the DTOF (τ) based one-dimensional flow simulation, the accuracy of the pressure solution relies significantly upon the drainage volume characterization and the DTOF calculation, both of which are influenced by the reservoir heterogeneity. We study first order discretization schemes of the Eikonal equation in porous media with different levels of heterogeneity and determine the impact of the corresponding DTOF solutions upon the one-dimensional flow simulation. The local solution of the Eikonal equation is formulated based on a piecewise uniform approximation of the DTOF gradient that satisfies a causality requirement within each simplex that provides the available nodal DTOF values. A homogenization approach is developed for use within the local solution for corner point grid cells, in which effective properties are obtained across adjacent grid cells. Comparison of the computational cost and error from different discretizations of the Eikonal equation and the corresponding pressure solution with increasing heterogeneity, demonstrates the need for increased angular resolution compared to the most usual cell centered 5-point discretization. The study also demonstrates the need for more accurate solutions in the near well region, suggesting a multi-stencil approach with higher angular and linear resolution near the well, and a less accurate and less costly calculation in the bulk of the computational grid. [ABSTRACT FROM AUTHOR]

A highly restricted workspace of the robotic arm may hinder to perform safely any autonomous mobile manipulation task with planetary exploration rovers. To ensure mission safety as well as high efficiency, a coupled path and motion planner for mobile manipulation is presented in this work. First, a Fast Marching Method based path planner generates a safe trajectory to reach the goal vicinity, avoiding obstacles and non-traversable areas in the scenario. The path planner is able to control the final rover orientation to ensure that the goal is finally reachable by the arm. Second, a 3D Fast Marching Method based motion planner generates the arm joints motion profile, by creating a 3D tunnel-like cost volume surrounding the already computed rover base trajectory. This tunnel makes use of an offline-computed safe workspace of the manipulator, thus ensuring that no self-collision will occur during the planned motion. The presented algorithm has been tested with multiple simulation experiments, benchmarked with an off-the-shelf motion planning library, and validated in a field test campaign with the rover SherpaTT of DFKI Robotics Innovation Center. The tests consisted in SherpaTT approaching an interesting area on the scenario and performing a mobile manipulation sample scanning operation. These experiments have demonstrated that the proposed motion planner increases efficiency as well as ensures mission safety. This is thanks to, on the one hand, a coordinated base-arm movement that results in maximized efficiency in time terms, and, on the other hand, considering the manipulator workspace offline in the mobile manipulation motion planner to guarantee self-collision avoidance.

Seismic wave traveltime calculation plays an important role in many areas of seismology, such as seismic tomography, migration and microseismic location. Solving the eikonal equation with the finite difference method is an essential method for calculating traveltime. The conventional method of solving the eikonal equation needs to calculate the traveltime field of each source. As the number of grids increases, it will consume a lot of time and memory. We introduce the EikoNet based on a deep neural network. Its samples are generated by sampling in the three-dimensional space, using the given velocity model as labels to optimize the network. Furthermore, it can transmit information about seismic wavefield and velocity structure during calculation and is highly suited for GPU. The EikoNet can quickly determine the traveltime between any two points in a three-dimensional domain without meshes, significantly improving calculation efficiency and reducing memory consumption. Numerical experiments of the EikoNet and the fast marching method (FMM) on several velocity models show that the EikoNet has higher efficiency while maintaining high accuracy.

Medical doctors identify benign or malignant colon polyps by their size and shape. Since this identification is related to whether or not resection surgery is necessary, a technology for estimating absolute size and shape from endoscopic images is required. In previous research, the method for recovering the size and shape of polyps using a blood vessel region as a reference object has been proposed. This paper proposes a method to recover the size and shape of polyps by using a cylindrical endoscopic hood as a reference object. The experimental results confirm that the proposed method can estimate reflectance factor without using blood vessel information. [ABSTRACT FROM AUTHOR]

Recent stochastic homogenization results for the Francfort–Marigo model of brittle fracture under anti-plane shear indicate the existence of a representative volume element. This homogenization result includes a cell formula which relies on Dirichlet boundary conditions. For other material classes, the boundary conditions do not effect the effective properties upon the infinite volume limit but may have a strong influence on the necessary size of the computational domain. We investigate the influence of the boundary conditions on the effective crack energy evaluated on microstructure cells of finite size. For periodic boundary conditions recent computational methods based on FFT-based solvers exploiting the minimum cut/maximum flow duality are available. In this work, we provide a different approach based on fast marching algorithms which enables a liberal choice of the boundary conditions in the 2D case. We conduct representative volume element studies for two-dimensional fiber reinforced composite structures with tough inclusions, comparing Dirichlet with periodic boundary conditions. [ABSTRACT FROM AUTHOR]

Copyright of Reviews of Geophysics & Planetary Physics is the property of Editorial Office of Reviews of Geophysics & Planetary Physics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The traditional Fast Marching Method (FMM) based on the finite-difference scheme can solve the traveltime of first arrivals; however, the accuracy and efficiency of FMM are usually affected by the finite-difference schemes and grid size. The Vidale finite-difference scheme and double-grid technology are adopted to replace the traditional first-order and second-order finite-difference schemes in this paper to improve the computation accuracy and efficiency. The traditional FMM does not provide the corresponding raypath calculation methods, and in view of the interoperability of FMM and the linear travel time interpolation (LTI) method, we introduce the linear interpolation method into FMM ray tracing to compute the raypath and take into consideration the secondary source located inside the grid cell to improve the accuracy and stability of the raypath calculation. With these measures and the application of the multistage approach, we successfully completed the improved Multistage FMM (MFMM) ray tracing, which can track first arrivals and any type of primary and multiple reflection waves. Through the theoretical and actual field model tests, the computation accuracy and efficiency of the improved MFMM are proven to be higher than that under traditional first-order and second-order finite-difference schemes, the correctness and effectiveness of the interpolation method for raypath calculation are verified, and the improved MFMM has demonstrated good adaptability and stability for complex models. The improvements for the MFMM in this paper are successfully applied in two-dimensional cases and need to be extended to three-dimensional situations. [ABSTRACT FROM AUTHOR]

The well placement problem in the petroleum industry is usually solved by integrating an optimizer with a reservoir simulation model. This is a time-consuming approach requiring thousands of simulation runs depending on the complexity of the reservoir system. This paper introduces two well placement optimization models: a Fast-Marching Model (FMM) based on fluid flow physics and a Hybrid Model integrating reservoir simulations and FMM results with a gradient boosting algorithm. These models prioritize speed and accuracy when integrated with genetic algorithm optimization, demonstrated using a synthetic unconventional field. From 290 randomly selected locations across the synthetic unconventional field, simulation runs were performed to determine cumulative gas production and used as ground truth. Using reservoir properties at these locations as inputs, Relative Opportunity Ranking (ROR) maps were generated using the FMM and Hybrid Model approaches. The ROR maps were then linked with a genetic algorithm to determine optimal well locations, iteratively updating ROR maps with penalty maps until all wells were appropriately placed. Results indicated that the standalone FMM generated ROR maps were highly correlated with the simulation results. Time complexity analysis revealed that both models were significantly faster than traditional methods, with the FMM independent of simulation and the Hybrid Model requiring only about 290 simulation runs. Ultimately, these models have shown tremendous potential for integration into current reservoir engineering workflows, reducing decision-making times in both greenfield and brownfield scenarios. • The proposed model combines reduced-physics and ML models to accelerate trajectory optimization for shale reservoirs. • Using proposed methods, Relative Opportunity Ranking maps were generated, which maps well location to potential recovery. • The standalone Fast-Marching Model generated results have 0.93 correlations score compared to actual simulation results. • The Hybrid Model displayed a higher resolution with 0.97 R2 score compared to actual simulation results. • 7 sequential well trajectories are optimized using both approaches which shows consistency across results. [ABSTRACT FROM AUTHOR]

The liver is considered as one of the complicated organs in human body. It has close proximity to the neighboring organs in abdomen with numerous anatomical variations. It is difficult to find out the severity of disease connected to the liver unless the scanned image is subjected to segmentation process. The difficulty level also varies with the diseases that affect the liver. Any of the disease alters its density, homogeneity, color and texture. Liver image segmentation is necessary to identify the complexity and severity of the disease and it remains as an open challenge to researchers. Among all liver segmentation algorithms, threshold segmentation is fastest, simplest and numerically less complex. The accuracy of threshold-based segmentation lies in the selection of threshold values which separates foreground and background. This paper proposes a novel multi-threshold liver segmentation model based on "Slope Difference Distribution" (SDD) of image histogram. It consists of three stages. In the first stage, the noise in Computed Tomography (CT) scan image is reduced using a median filter. In the second stage, automatic threshold values are obtained from SDD of image histogram. These threshold values separate the liver image accurately from abdominal CT scan image. In the third stage, seed points are selected automatically which grow outwardly using the Fast Marching Method (FMM) discovering liver border in CT scan image. The proposed model is tested on 55 CT scan images and it is providing satisfactory results. [ABSTRACT FROM AUTHOR]

Fluid‐driven fracture propagation is widely observed in various geological processes and crucial to many applications of geological engineering. Developing robust and accurate numerical strategies has significance in advancing the scientific understanding and engineering applications related with fluid‐driven fracture propagation. We present a finite element‐finite volume strategy using asymptotic fracture tip enrichment to model the fluid‐driven fracture propagation in three‐dimensional Cartesian meshes under the viscosity‐dominated regime, in which the fluid viscosity‐related process is the dominant energy dissipation mechanism. We use the finite element method to discretize the balance of linear momentum equation for the deformed solid and the finite volume method to discretize the Reynolds equation that governs the fluid flow. In order to track the evolving fracture front in heterogeneous media, we extend the implicit level set approach originally proposed for the displacement discontinuity method. Through this process, a signed distance‐based fracture propagation criterion naturally emerges and is suitable for the viscosity‐dominated regime when solid toughness becomes irrelevant. Critically, we enrich the fluid volume treatment near the fracture front using the tip asymptotic solution. This enrichment strategy is crucial to overcome the mesh nonconformity caused by the arbitrary intersections between propagating fracture front and underlying Cartesian meshes. We compare the numerical results with analytical solutions of the KGD problem and the penny‐shape problem, and illustrate the mesh size and time step‐insensitivity of the numerical results due to the tip enrichment technique. Also, we demonstrate the capabilities of the proposed method to model fluid‐driven fracture propagation in various heterogeneous media. [ABSTRACT FROM AUTHOR]

In the context of the eXtended Finite Element Method (X-FEM), the use of two level set functions allows the representation of the crack to be achieved regardless of the mesh. The initial crack geometry is represented by two distinct level set functions, and the crack propagation is simulated by an update of these two level set functions. In this paper, we propose a new approach, based on the Fast Marching Method (FMM), to update the level set functions. We also propose a new implementation of the FMM, designed for tetrahedral volume meshes. We then extend this method to all types of volume elements (tetrahedra, hexahedra, pentahedra, pyramids) available in a standard finite element library. The proposed approach allows one to use the same mesh to solve the mechanical problem and to update the level set functions. Non-planar quasi-static crack growth simulations are presented to demonstrate the robustness of the approach, compared to existing methods based on the integration of Hamilton-Jacobi equations or geometric approaches. [ABSTRACT FROM AUTHOR]

Microseismic (MS) event locations are vital aspect of MS monitoring technology used to delineate the damage zone inside the surrounding rock mass. However, complex geological conditions can impose significantly adverse effects on the final location results. To achieve a high-accuracy location in a complex cavern-containing structure, this study develops an MS location method using the fast marching method (FMM) with a second-order difference approach (FMM2). Based on the established velocity model with three-dimensional (3D) discrete grids, the realization of the MS location can be achieved by searching the minimum residual between the theoretical and actual first arrival times. Moreover, based on the calculation results of FMM2, the propagation paths from the MS sources to MS sensors can be obtained using the linear interpolation approach and the Runge–Kutta method. These methods were validated through a series of numerical experiments. In addition, our proposed method was applied to locate the recorded blasting and MS events that occurred during the excavation period of the underground caverns at the Houziyan hydropower station. The location results of the blasting activities show that our method can effectively reduce the location error compared with the results based on the uniform velocity model. Furthermore, the obtained MS location was verified through the occurrence of shotcrete fractures and spalling, and the monitoring results of the in-situ multipoint extensometer. Our proposed method can offer a more accurate rock fracture location and facilitate the delineation of damage zones inside the surrounding rock mass.

The fast marching method (FMM) is an efficient, stable and adaptable travel time calculation method. In the realization of this method, it is necessary to select the minimum travel time node from the narrow band many times. The selection method has an important influence on the calculation efficiency of FMM. Traditional FMM adopts the binary tree heap sorting method to achieve this step. Fibonacci heap sort method to FMM will be applied in this study. Compared with the binary tree heap sorting method, the Fibonacci heap sort method can realize the minimum travel time node selection in the narrow band in a more efficient way when the number of the narrow-band nodes is huge. The new method will be verified through error analysis and two numerical model calculations.

Fiber steering leads to gaps and overlaps in plies and laminates. The position of these gaps and overlaps as well as their total volume/area is very much influenced by the seeding strategy when transforming from a theoretical to a manufacturing design. The theoretical designs obtained from a steered fiber laminate optimization routine are the starting point of a tow path planning step. The seed points together with the theoretical fiber angle determine the path of a tow. Normally, seed points are determined by a manufacturing engineer. In this paper, two different strategies to automate the selection of initial seed points and subsequent points based on the calculation of previous tow paths are proposed and evaluated. For two-dimensional plate problems both proposed methods reduce the gaps and overlaps. The method based on the median tow path is spreading gaps and overlaps more uniformly and yields fewer gaps and overlaps. A cut and restart procedure is discussed and implemented, which can be used to manually or automatically prevent/limit overlaps and fill large gaps. [ABSTRACT FROM AUTHOR]

Submarine cables are indispensable in today’s international data transmission. In the process of submarine cable path planning, any factors that may potentially affect reliability and cost should be considered. Still, the degree of importance of these factors is difficult to assess accurately. Currently, cable path planning is done manually, meter by meter, over thousands of kilometers by experts that rely on their experience and expertise. This paper provides a submarine cable path planning algorithm based on simulated annealing (SA) and the fast marching method (FMM). Accordingly, we name the algorithm FMM/SA. FMM/SA can be used as a guide and benchmark for cable path planners and also enhances understanding of the multiple considerations and their corresponding weights aiming to further improve the end-results beyond what is obtained currently by experts. In FMM/SA, SA is used to optimize weights of design considerations to minimize the Fréchet distance between existing cable paths and paths with minimized total life-cycle cost obtained by FMM. FMM/SA is demonstrated to be superior to two other algorithms based on random-restart hill-climbing and Monte Carlo using real-life cable paths.

In this paper, a new method is proposed to find a feasible energy-efficient path between an initial point and goal point on uneven terrain and then to optimally traverse the path. The path is planned by integrating the geometric features of the uneven terrain and the biped robot dynamics. This integrated information of biped dynamics and associated cost (energy) for moving toward the goal point is used to define the value of a new speed function at each point on the discretized surface of the terrain. The value is stored as a matrix called the dynamic transport cost (DTC). The path is obtained by solving the Eikonal equation numerically by fast marching method (FMM) on an orthogonal grid, by using the information stored in the DTC matrix. One step of walk on uneven terrain is characterized by 10 footstep parameters (FSPs); these FSPs represent the position of swinging foot at the starting and ending time of the walk, orientation, and state (left or right) of support foot. A walking dataset was created for different walking conditions (FSPs), which the biped robot is likely to encounter when it has to walk on the uneven terrain. The corresponding energy optimal hip and foot trajectory parameters (HFTPs) are obtained by optimization using a genetic algorithm (GA). The created walk dataset is generalized by training a feedforward neural network (NN) using the scaled conjugate gradient (SCG) algorithm. The Foot placement planner gives a sequence of foot positions and orientations along the obtained path, which is followed by the biped robot by generating real-time optimal foot and hip trajectories using the learned NN. Simulation results on different types of uneven terrains validate the proposed method. [ABSTRACT FROM AUTHOR]

Large volume metrology is a key enabler of autonomous precision manufacturing. For component positioning, the optical-based metrology technique of photogrammetry could be used more widely if its accuracy was improved. These positional measurements are subject to uncertainties which can be greater than manufacturing tolerances. One source of uncertainty is due to thermal gradients, which cause the refraction of the light rays in large-scale industrial environments. This paper uses light-based sensor data to reconstruct a heterogeneous spatial map of the refractive index in air. We use this reconstructed refractive index map to discount the refractive effects and thereby reduce the uncertainty of this positioning problem. This new inverse problem employs Voronoi tessellations to spatially parameterize the refractive index map, the Fast Marching Method to solve the forward problem of calculating the light rays through this medium, and a Bayesian approach in the inversion. Using simulated data, this methodology leads to positioning improvements of up to 37 %. [ABSTRACT FROM AUTHOR]

Effective detection and removal of the artifacts from dermoscopic images require the analysis of structures within lesions for accurate cancer detection. But the dermoscopic images acquired may be affected by image acquisition noise, variation in texture, color, and irrelevant structure such as hairs, air bubbles, and contour blurring around the lesion. Hence preprocessing is very essential for accurate diagnosis. The proposed algorithm includes the preprocessing, to remove acquisition noise using curvelet transform, illumination correction using contrast limited adaptive histogram equalization (CLAHE) algorithm for image enhancement, Frangi vesselness algorithm is utilized for detection and removal of hairs and vessels like structures present in enhanced image, fast marching inpainting method is applied for repairing the information of lesion from removed hair pixels. The performance of the proposed algorithm is analyzed based on commonly used parameters such as diagnostic accuracy (DA), sensitivity (SE), specificity (SP), and precision (P). The performance is evaluated on PH2 and International Symposium on Biomedical Imaging (ISBI) datasets than compared with existing methods. The proposed algorithm segments the skin lesion with the highest diagnostic accuracy of 81.49% and sensitivity of 93.88% for the PH2 dataset and 75.39% and 79.34% respectively for the ISBI dataset. Results are better than existing methods. The proposed algorithm with improved preprocessing for artifact detection and removal is highly accurate and able to retrieve the hair occluded information. [ABSTRACT FROM AUTHOR]

In this paper, a new method is proposed that integrates the 3D terrain information, ditch geometry, and biped dynamics for motion planning of a 14-DOF biped robot on 3D terrain containing a 3D ditch. The path planning is modeled as a wavefront propagation in Non-uniform medium represented by the Eikonal equation. A speed function expresses the inhomogeneity of uneven terrain. The Eikonal equation is solved by the Fast marching method (FMM) to obtain the global path. Ten Footstep variables (FSVs) characterize one step of walk on a 3D uneven terrain surface. The hip and foot trajectory parameters (HFTPs) are used to construct cubic spline-based hip and foot trajectories of the biped robot. The optimal value of HFTPs is obtained by a Genetic algorithm by minimization of energy and satisfying the constraint of dynamic balance. A walk-dataset is created that contains the optimal trajectories for different FSVs. The generated walk-dataset was used to train the biped to walk on rough terrain using a feed-forward Neural network for making a real-time estimate of optimal HFTPs. Simulation results validate the effectiveness of the proposed method of ditch crossing on different uneven terrains. [ABSTRACT FROM AUTHOR]

In this paper, we present a study on coverage missions carried out by UAV formations in 3D environments. These missions are designed to be applied in tracking and search and rescue missions, especially in the case of accidents. In this manner, the presented method focuses on the path planning stage, the objective of which is to compute a convenient trajectory to completely cover a certain area in a determined environment. The methodology followed uses a Gaussian mixture to approximate a probability of containment distribution along with the Fast Marching Square (FM2) as path planner. The Gaussians permit to define a zigzag trajectory that optimizes the path. Next, a first 2D geometric path perpendicular to the Voronoi diagram of the Gaussian distribution is calculated, obtained by skeletonization. To this path, the height above the ground is added plus the desired flight height to make it 3D. Finally, the FM2 method for formations is applied to make the path smooth and safe enough to be followed by UAVs. The simulation experiments show that the proposed method achieves good results for the zigzag path in terms of smoothness, safety and distance to cover the desired area through the formation of UAVs.

The traditional Fast Marching Method (FMM) based on the finite-difference scheme can solve the traveltime of first arrivals; however, the accuracy and efficiency of FMM are usually affected by the finite-difference schemes and grid size. The Vidale finite-difference scheme and double-grid technology are adopted to replace the traditional first-order and second-order finite-difference schemes in this paper to improve the computation accuracy and efficiency. The traditional FMM does not provide the corresponding raypath calculation methods, and in view of the interoperability of FMM and the linear travel time interpolation (LTI) method, we introduce the linear interpolation method into FMM ray tracing to compute the raypath and take into consideration the secondary source located inside the grid cell to improve the accuracy and stability of the raypath calculation. With these measures and the application of the multistage approach, we successfully completed the improved Multistage FMM (MFMM) ray tracing, which can track first arrivals and any type of primary and multiple reflection waves. Through the theoretical and actual field model tests, the computation accuracy and efficiency of the improved MFMM are proven to be higher than that under traditional first-order and second-order finite-difference schemes, the correctness and effectiveness of the interpolation method for raypath calculation are verified, and the improved MFMM has demonstrated good adaptability and stability for complex models. The improvements for the MFMM in this paper are successfully applied in two-dimensional cases and need to be extended to three-dimensional situations.

The Fast Marching Method (FMM) has been applied to characterize the transient drainage volume and to simulate flow as a function of time in porous media using the concept of the "diffusive time of flight" (DTOF). The DTOF (τ) provides a spatial coordinate which reduces the three dimensional pressure diffusivity equation to an equivalent one dimensional formulation. It is obtained from the solution to the Eikonal equation via the FMM. Previous applications of this approach have solved the flow equations numerically or by using an analytic asymptotic approximation. Both solution approaches rely upon three characteristics. (1) Accurate solution for the DTOF irrespective of the degree of heterogeneity within a reservoir model. (2) The approximation of the three dimensional pressure solution in terms of the τ coordinate. (3) Accurate representation and discretization of the drainage volume, on which the asymptotic and numerical flow simulations are based. The second and third of these characteristics are specific to reservoir engineering applications, and provide the focus of this study. Analysis of the drainage volume shows that the near well region requires special treatment, leading to a composite discretization for the drainage volume. This discretization has a direct impact upon the calculation of the well test pressure derivative when the asymptotic approximation is used for pressure transient interpretation. For flow simulation, the discretization directly impacts the calculation of the well index and the intercell transmissibility computed in the τ coordinate, and places additional constraints on the discretization of the drainage volume. These new results are validated by comparison with a commercial finite difference flow simulator, and are shown to be more accurate than earlier computational approaches. [ABSTRACT FROM AUTHOR]

We have developed and tested a new Eikonal first-arrival forward model scheme by combining a fast marching method (FMM) algorithm, an upwind Eikonal solver scheme first described by Sethian and Popovici in 1996, with a more accurate but less robust Eikonal scheme described by Vidale in 1990 as a finite difference method (VFD) in order to produce a robust forward model based in FMM, with application of VFD schemes for refinement of computed model times (FMM-VFD). The developed model was tested through a uniform velocity base case, and the Southern California Earthquake Center (SCEC) Harvard Velocity Model (CVM-H) of upper crust including the sedimentary basin under Los Angeles, CA. Its performance was evaluated by measuring error at different grid sizes against a set of reference times generated by an independent model. In comparison against first-order FMM (FMM-O1), second-order FMM (FMM-O2), and an improved FMM scheme known as factored FMM (FMM-F) against a set of generated reference times, FMM-VFD error was found to be significantly lower than first- and second-order FMM, and competitive with FMM-F, outperforming it in the presented scenarios. [ABSTRACT FROM AUTHOR]

A global path planning algorithm for unmanned surface vehicles (USVs) with short time requirements in large-scale and complex multi-island marine environments is proposed. The fast marching method-based path planning for USVs is performed on grid maps, resulting in a decrease in computer efficiency for larger maps. This can be mitigated by improving the algorithm process. In the proposed algorithm, path planning is performed twice in maps with different spatial resolution (SR) grids. The first path planning is performed in a low SR grid map to determine effective regions, and the second is executed in a high SR grid map to rapidly acquire the final high precision global path. In each path planning process, a modified inshore-distance-constraint fast marching square (IDC-FM2) method is applied. Based on this method, the path portions around an obstacle can be constrained within a region determined by two inshore-distance parameters. The path planning results show that the proposed algorithm can generate smooth and safe global paths wherein the portions that bypass obstacles can be flexibly modified. Compared with the path planning based on the IDC-FM2 method applied to a single grid map, this algorithm can significantly improve the calculation efficiency while maintaining the precision of the planned path.

A 3D shear wave velocity model of the subsurface of Popocatépetl volcano was obtained using ambient noise tomography, employing the principal cross-terms of the empirical Green's function. Daily cross-correlation waveforms were computed from the data recorded by four seismic broadband stations in 2012. Dispersion curves were estimated from the stack of anti-causal and causal parts for the three ground motion components. In the period ranging between 0.5 and 7 s, the radial component provided the most well-defined group velocity dispersion curves for Rayleigh waves. Dispersion curves for long paths (> 9.5 km) suggested the presence of a layered structure with group velocity values ranging from 0.5 to 3.0 km/s. Dispersion curves for short paths (< 7 km) and close to the volcano showed values similar to those for long paths but with a velocity inversion occurring between 3- and 5-s periods. Despite the scarce ray-path coverage, a tomography inversion provided the means to image an S-wave velocity anomaly (2.5–3.0 km/s) in the northern part of the crater at depths not larger than 6 km. The volcano-tectonic seismicity during 2012–2013 was found to be concentrated in the southern segment of this anomaly, which seems to mark a boundary between a solidified body (possibly a product of ancient volcanic craters) and the softer material. [ABSTRACT FROM AUTHOR]

The Voronoi diagram-based dual-front scheme is known as a powerful and efficient technique for addressing the image segmentation and domain partitioning problems. In the basic formulation of existing dual-front approaches, the evolving contour can be considered as the interfaces of adjacent Voronoi regions. Among these dual-front models, a crucial ingredient is regarded as the geodesic metrics by which the geodesic distances and the corresponding Voronoi diagram can be estimated. In this paper, we introduce a new dual-front model based on asymmetric quadratic metrics. These metrics considered are built by the integration of the image features and a vector field derived from the evolving contour. The use of the asymmetry enhancement can reduce the risk for the segmentation contours being stuck at false positions, especially when the initial curves are far away from the target boundaries or the images have complicated intensity distributions. Moreover, the proposed dual-front model can be applied for image segmentation in conjunction with various region-based homogeneity terms. The numerical experiments on both synthetic and real images show that the proposed dual-front model indeed achieves encouraging results. [ABSTRACT FROM AUTHOR]

The Ensemble Kalman filter (EnKF) is a widely used intelligent algorithm in the field of automatic history fitting. The method has a number of drawbacks, such as inaccurate gradient calculation, filter divergence, and pseudo-correlation of parameters, leading to parameter correction errors and model inversion distortion in the process of historical fitting. A history fitting method based on the fast marching method and covariance-localized Ensemble Kalman filter (FMM-CLEnKF) is established to reduce pseudo-correlation in the calculation process of the traditional distance truncation method. According to the static parameter field information of the reservoir geological model combined with the state equation, the fast marching method (FMM) is used to quickly track the propagation time of the pressure wave in every well, determine the sensitive area of a single well, and construct the localization matrix. Combined with the covariance localization Ensemble Kalman filter method, the gradient correction of the data assimilation method is realized, and the pseudo-correlation of parameters is reduced. Finally, the optimal model is improved by gradually fitting and updating the reservoir parameter model. The calculation results of a field example show that the FMM-CLEnKF method has a higher reservoir parameter inversion accuracy, data fitting speed, and production data fitting accuracy than the ensemble Kalman filter method. [ABSTRACT FROM AUTHOR]

Choosing a representative subset of realizations can reduce significantly the number of simulations and the computational cost associated with optimization under geological uncertainty. Methods that use dynamic criteria, such as full flow simulators, can choose effectively representative realizations and reduce the number of simulations during optimization. However, these methods are expensive computationally. This study aims at investigating the effect of using diffusive time of flight (DTOF) as a feature to select a representative subset of realizations for well placement optimization under uncertainty. The proposed approach is based on the calculation of DTOF for pressure propagation in a reservoir; it was calculated using the fast marching method (FMM). To determine reservoir connectivity, a threshold was used for a number of grid blocks at specific time intervals; it can be used as a measure to evaluate and select the realizations. The proposed methodology was utilized to optimize the location of vertical injection wells on three numerical models, which are three dimensional with equally probable realizations. The optimization results of the proposed method were compared with the results of optimization using the full set and the subset realizations obtained using the K-means clustering method. In this study, 10 realizations were selected from the full set as the representative subset. The selection was based on K-means clustering and FMM. Results show that the FMM-based approach outperforms the clustering method and it can capture the uncertainty range with only a small subset of realizations with a much lower computational burden compared to the full set. [ABSTRACT FROM AUTHOR]

Liver segmentation from abdominal computed tomography (CT) scan images is a complicated and challenging task. Due to the haziness in the liver pixel range, the neighboring organs of the liver have the same intensity level and existence of noise. Segmentation is necessary in the detection, identification, analysis, and measurement of objects in CT scan images. A novel approach is proposed to meet the challenges in extracting liver images from abdominal CT scan images. The proposed approach consists of three phases: (1) preprocessing, (2) CT scan image transformation to neutrosophic set, and (3) postprocessing. In preprocessing, noise in the CT scan is reduced by median filter. A “new structure” is introduced to transform a CT scan image into a neutrosophic domain, which is expressed using three membership subsets: true subset (T), false subset (F), and indeterminacy subset (I). This transform approximately extracts the liver structure. In the postprocessing phase, morphological operation is performed on the indeterminacy subset (I). A novel algorithm is designed to identify the start points within the liver section automatically. The fast marching method is applied at start points that grow outwardly to detect the accurate liver boundary. The evaluation of the proposed segmentation algorithm is concluded using area- and distance-based metrics.

The conventional masked image restoration algorithms all utilise the correlation between the masked region and its neighbouring pixels, which does not work well for the larger masked image. The latest research utilises Generative Adversarial Networks (GANs) model to generate a better result for the larger masked image but does not work well for the complex masked region. To get a better result for the complex masked region, the authors propose a novel fast GANs model for masked image restoration. The method used in authors’ research is based on GANs model and fast marching method (FMM). The authors trained an FMMGAN model which consists of a neighbouring network, a generator network, a discriminator network, and two parsing networks. A large number of experimental results on two open datasets show that the proposed model performs well for masked image restoration.

Fast methods are very popular algorithms to compute time-of-arrival maps (distance maps measured in time units) solving the Eikonal equation. Since fast marching was proposed in 1995, it has been applied to many different applications, such as robotics, medical computer vision, fluid simulation, and so on. From then on, many alternatives to the original method have been proposed with two main objectives: reducing its computational time and improving its accuracy. In this paper, we collect the main single-threaded approaches, which improve the computational time of the standard fast marching method and study them within a common mathematical framework. Then, they are evaluated using isotropic environments, which are representative of their possible applications. The studied methods are the fast marching method with the binary heap, the fast marching method with Fibonacci heap, the simplified fast marching method, the untidy fast marching method, the fast iterative method, the group marching method, the fast sweeping method, the locking sweeping method, and the double dynamic queue method.

Generating a collision-free and dynamically feasible trajectory with a better clearance in a cluttered environment is still a challenge. We propose two dynamically feasible B-spline based rapidly exploring random tree (RRT) approaches, which are named DB-RRT and FMDB-RRT, to achieve path planning and trajectory planning simultaneously for omnidirectional mobile robots. DB-RRT combines the convex hull property of the B-spline and RRT's rapid expansion capability to generate a safe and dynamically feasible trajectory. Firstly, we analyze the tree's sustainable growth ability and put forward the dynamically feasible region. A geometric method is proposed to judge whether finding a dynamically feasible trajectory quickly. Secondly, we design two steer functions to guide the tree's growth, improve efficiency, and decrease the number of iterations. To further increase the clearance and reduce the randomness of the trajectory, we propose FMDB-RRT, which uses the path of fast marching to guide the rapid growth of DB-RRT. Then, assuming that the number of sampled points is sufficient to represent the dynamically feasible region, the DB-RRT is proved to be probabilistically complete. Finally, by conducting experimental comparisons with other algorithms in different environments and deploying the proposed algorithm to an omnidirectional mobile robot, the effectiveness and good performance of the algorithm have been verified. [ABSTRACT FROM AUTHOR]

An improved understanding of pillar strength and pillar failure mechanisms is required to optimize tabular mine layout designs. The paper describes the application of a limit equilibrium model for pillar failure analysis. It is shown that the model is capable of reproducing a hardening or softening response for uniformly compressed strip or square pillars. The stress–strain behavior depends on three non-dimensional parameters Q, M and β. Q represents the ratio of the limit failed uniaxial strength to the intact material strength, M is the ratio of the failed limit strength envelope slope to the intact strength envelope slope and β is proportional to the pillar width to height ratio. The model is implemented in a displacement discontinuity solution scheme using unstructured triangular elements to allow irregular plan-view pillar shapes and mining step increments to be represented. The seam-parallel confining stress distribution in the fracture zone is determined using a fast marching solution algorithm. A case study of an experimental pillar extraction site in a platinum mine is presented to illustrate the capability of the model to simulate the evolution of pillar failure as pillar extraction proceeds. Good qualitative agreement to observed failure trends are obtained but the detailed calibration of the model parameters remains a challenge. Further work is required to enhance the representation of pillar edge spalling processes. [ABSTRACT FROM AUTHOR]