Fast Marching Research Articles

Accelerated 2-D Real-Time Refraction-Corrected Transcranial Ultrasound Imaging.

In a recent study, we proposed a technique to correct aberration caused by the skull and reconstruct a transcranial B-mode image with a refraction-corrected synthetic aperture imaging (SAI) scheme. Given a sound speed map, the arrival times were calculated using a fast marching technique (FMT), which solves the Eikonal equation and, therefore, is computationally expensive for real-time imaging. In this article, we introduce a two-point ray tracing method, based on Fermat's principle, for fast calculation of the travel times in the presence of a layered aberrator in front of the ultrasound probe. The ray tracing method along with the reconstruction technique is implemented on a graphical processing unite (GPU). The point spread function (PSF) in a wire phantom image reconstructed with the FMT and the GPU implementation was studied with numerical synthetic data and experiments with a bone-mimicking plate and a sagittally cut human skull. The numerical analysis showed that the error on travel times is less than 10% of the ultrasound temporal period at 2.5 MHz. As a result, the lateral resolution was not significantly degraded compared with images reconstructed with FMT-calculated travel times. The results using the synthetic, bone-mimicking plate, and skull dataset showed that the GPU implementation causes a lateral/axial localization error of 0.10/0.20, 0.15/0.13, and 0.26/0.32 mm compared with a reference measurement (no aberrator in front of the ultrasound probe), respectively. For an imaging depth of 70 mm, the proposed GPU implementation allows reconstructing 19 frames/s with full synthetic aperture (96 transmission events) and 32 frames/s with multiangle plane wave imaging schemes (with 11 steering angles) for a pixel size of [Formula: see text]. Finally, refraction-corrected power Doppler imaging is demonstrated with a string phantom and a bone-mimicking plate placed between the probe and the moving string. The proposed approach achieves a suitable frame rate for clinical scanning while maintaining the image quality.

Concurrent optimization of topological configuration and continuous fiber path for composite structures — A unified level set approach

This study proposes a novel topology optimization approach for design of continuous steering fiber path for composite structures using a level set method. The radial basis function (RBF) is employed to construct the level set function (LSF). Fiber orientations are parameterized by LSF and fiber paths can be determined instinctively for the inherent advantages of the level set approach. Besides, the fast-marching method is employed to extrapolate the primary fiber paths to the secondary fiber paths, which can avoid the manufacturing drawbacks such as gaps and overlaps to a large extent. A detection and filtering technique is proposed here to alleviate the orientation disorder at the intersection of the diffusion surfaces. Two design schemes are developed to optimize both structural topology and fiber path. In a sequential procedure, topology optimization is conducted first with isotropic materials; and then fiber paths are optimized on the basis of fixed topological boundary. In a simultaneous optimization procedure, structural boundaries and fiber paths are optimized alternately through two inner loops. In this study, three numerical examples are presented to demonstrate the effectiveness of the proposed methods, and the results show that optimization of fiber path is beneficial to improvement of structural performance. In general, the simultaneous optimization scheme exhibits better optimal outcome in comparison with the sequential optimization scheme.

Improvement of microseismic source location during cavern excavation in faulted rock mass using fast marching method

Understanding the temporospatial distribution of microseismic events is critical for the early warning of induced geohazards during deep rock excavation. However, the accuracy of microseismic source location can be influenced by many geological and engineering factors, such as rock discontinuities and excavated openings. This study addresses the application of fast marching method (FMM) to improve the location accuracy in faulted rock masses and takes a case of powerhouse excavation in the Shuangjiangkou hydropower project as an example. The FMM-based method includes five steps, such as inputs, gridding, velocity assignment, calculation, and output, and can be readily processed using a travel time database. Our results exhibit that the wave paths obtained from the FMM-based method are consistent with those from the analytical solution based on the Snell law and better than those from the commonly used uniform velocity model. The results also signify that the FMM-based method can improve the location accuracy for P-wave propagating across a low-velocity layer and an excavated opening. Moreover, this method can be further improved, such as reasonable determination of grid spacing and thorough detection of major discontinuities.

Feasibility study of clinical target volume definition for soft-tissue sarcoma using muscle fiber orientations derived from diffusion tensor imaging

Objective. Soft-tissue sarcoma spreads preferentially along muscle fibers. We explore the utility of deriving muscle fiber orientations from diffusion tensor MRI (DT-MRI) for defining the boundary of the clinical target volume (CTV) in muscle tissue. Approach. We recruited eight healthy volunteers to acquire MR images of the left and right thigh. The imaging session consisted of (a) two MRI spin-echo-based scans, T1- and T2-weighted; (b) a diffusion weighted (DW) spin-echo-based scan using an echo planar acquisition with fat suppression. The thigh muscles were auto-segmented using the convolutional neural network. DT-MRI data were used as a geometry encoding input to solve the anisotropic Eikonal equation with the Hamiltonian Fast-Marching method. The isosurfaces of the solution modeled the CTV boundary. Main results. The auto-segmented muscles of the thigh agreed with manually delineated with the Dice score ranging from 0.8 to 0.94 for different muscles. To validate our method of deriving muscle fiber orientations, we compared anisotropy of the isosurfaces across muscles with different anatomical orientations within a thigh, between muscles in the left and right thighs of each subject, and between different subjects. The fiber orientations were identified reproducibly across all comparisons. We identified two controlling parameters, the distance from the gross tumor volume to the isosurface and the eigenvalues ratio, to tailor the proposed CTV to the satisfaction of the clinician. Significance. Our feasibility study with healthy volunteers shows the promise of using muscle fiber orientations derived from DW MRI data for automated generation of anisotropic CTV boundary in soft tissue sarcoma. Our contribution is significant as it serves as a proof of principle for combining DT-MRI information with tumor spread modeling, in contrast to using moderately informative 2D CT planes for the CTV delineation. Such improvements will positively impact the cancer centers with a small volume of sarcoma patients.

Hypocenter Determination using a Non-Linear Method in Bali, Lombok, and Nusa Tenggara Regions: Preliminary Result

Bali, Lombok, and Nusa Tenggara are the region in the south of the Indonesia Archipelago. This region has relatively high seismicity due to subduction activity and faulting. The first step of the tomography study for inferring the geometry structure beneath Bali, Lombok, and Nusa Tenggara is to conduct precise hypocenter location. In this study, we used waveform data from the Indonesian Agency for Meteorology, Climatology, and Geophysics (BMKG), which the study area is between 1120 – 1280 E and 40 – 130 S. Our preliminary results, we have re-picked 7,967 P-wave and 3,254 S-wave arrival times for 933 events in the period from January to March 2019. The non-linear method was conducted using the oct-tree sampling algorithm from the NLLoc program to determine the hypocenter’s location. We also compared the results with BMKG catalog data. Our results show better clustering earthquakes with RMS error mostly close to zero and represent the geological structure in this region. The results show a shift in the location of the epicenters between 0.1 km to 1000 km, while for the focus depth between 0.006 - 500 km, with the azimuth shift being dominated to the northeast and southwest. The future and ongoing works, we will conduct a tomography study to imaging 3-D seismic velocity models beneath Bali, Lombok, and Nusa Tenggara regions using the fast-marching method.

Collision avoidance and path planning for industrial manipulator using slice-based heuristic fast marching tree

With the emergence of Industry 4.0 , high productivity is critically dependent on robot manipulators . However, building an efficient and safe work environment with robot manipulators remains a challenge of hardware capability. The optimal path planning of the robot manipulator usually encounters shortcomings in low computational speed and tedious training after changing assembly lines and increases the risk during human–robot collaboration (HRC). To solve such a problem, we propose a path planning, named slice-based heuristic fast marching tree, based on joint space to achieve real-time path planning speed without modeling or training the workspace in advance. Our experimental results indicate that the time consumed for path planning in static environments is only from 0.51 s to 1.63 s, tested by a 6-DOF general-purpose industrial manipulator and different cylindrical obstacle placements. The time for path replanning in dynamic environments is from 0.62 s to 0.88 s. • Path planning is in 1.63 s with static obstacles and 0.88 s with dynamic obstacles. • The proposed path planning is faster, smoother, and shorter than RRT, RRT*, and FMT*. • The joint angles of revolutions in total are less than RRT, RRT*, FMT*.

A novel path following approach for autonomous ships based on fast marching method and deep reinforcement learning

Path following is one of the indispensable tools for autonomous ships, which ensures that autonomous ships are sufficiently capable of navigating in specified collision-free waters. This study proposes a novel path following approach for autonomous ships based on the fast marching (FM) method and deep reinforcement learning (DRL). The proposed approach is capable of controlling a ship to follow different paths and ensuring that the path tracking errors are always within a set range. With the help of the FM method, a grid-based path deviation map is specially produced to indicate the minimum distance between grid points and the path. Besides, a path deviation perceptron is specifically designed to simulate a range sensor for sensing the set path deviation boundaries based on the path deviation map. Afterwards, an agent is trained to control a ship following a circular path based on the DRL. Particularly, the approach is validated and evaluated through simulations. The obtained results show that the proposed method is always capable of maintaining high overall efficiency with the same strategy to follow different paths. Moreover, the ability of this approach exhibits a significant contribution to the development of autonomous ships.

A Path Planning Method for Ship Collision Avoidance Considering Spatial–Temporal Interaction Effects

Efficient and reliable path planning is crucial for smart ships when avoiding collisions with static and dynamic obstacles in complex marine environments. This research proposes a novel path planning method based on the fast marching method to specifically assist with safe navigation for autonomous ships. At the very beginning, a unified representation is specially produced to describe the path planning space based on the parametric fast marching speed function. In addition, the spatial–temporal interaction effects of dynamic obstacles are considered and integrated into the construction of planning space. Subsequently, a path optimization strategy is put forward based on the trajectory prediction of dynamic objects. Particularly, the effectiveness of the method has been validated and evaluated through a number of simulations, which proves that such a method is practical in narrow and crowded waterways.

Age-Related Tortuosity of Carotid and Vertebral Arteries: Quantitative Evaluation With MR Angiography.

Background and PurposeThe vascular tortuosity (VT) of the internal carotid artery (ICA), and vertebral artery (VA) can impact blood flow and neuronal function. However, few studies involved quantitative investigation of VT based on magnetic resonance imaging (MRI). The main purpose of our study was to evaluate the age and gender effects on ICA and VA regarding the tortuosity and flow changes by applying automatic vessel segmentation, centerline tracking, and phase mapping on MR angiography.MethodsA total of 247 subjects (86 males and 161 females) without neurological diseases participated in this study. All subjects obtained T1-weighted MRI, 3D time-of-flight MR angiography, and 2D phase-contrast (PC) MRI scans. To generate quantitative tortuosity metrics from TOF images, the vessel segmentation and centerline tracking were implemented based on Otsu thresholding and fast marching algorithms, respectively. Blood flow and velocity were measured using PC MRI. Among the 247 subjects, 144 subjects (≤ 60 years, 49 males/95 females) were categorized as the young group; 103 subjects (>60 years, 37 males/66 females) were categorized as the old group.ResultsIndependent t-test showed that older subjects had higher tortuosity metrics, whereas lower blood flow and velocity than young subjects (p < 0.0025, Bonferroni-corrected). Cerebral blood flow calculated using the sum flux of four target arteries normalized by the brain mass also showed significantly lower values in older subjects (p < 0.001). The age was observed to be positively correlated with the VT metrics. Compared to the males, the females demonstrated higher geometric indices within VAs as well as faster age-related vascular profile changes. After adjusting age and gender as covariates, maximum blood velocity is negatively correlated with geometric measurements. No association was observed between blood flux and geometric measures.ConclusionsVascular auto-segmentation, centerline tracking, and phase mapping provide promising quantitative assessments of tortuosity and its effects on blood flow. The neck arteries demonstrate quantifiable and significant age-related morphological and hemodynamic alterations. Moreover, females showed more distinct vascular changes with age. Our work is built upon a comprehensive quantitative investigation of a large cohort of populations covering adult lifespan using MRI, the results can serve as reference ranges of each decade in the general population.

Information-Driven Fast Marching Autonomous Exploration With Aerial Robots

Autonomous exploration in unknown environments is a fundamental task of Unmanned Aerial Vehicles (UAVs). To choose exploration goals wisely, we propose an information-driven exploration strategy by applying the fast marching method to exploration of UAVs. A frontier point detection algorithm is designed to obtain Candidate Goals (CGs) by utilizing the structural characteristics of the octree-based map. With the sum of the information gain during the exploration journey as an evaluation indicator, we present a novel utility function to evaluate CGs by considering the trade-off between information gain and travel consumption. Given the effect of the environment on UAVs, UAVs are required to march aggressively in the Euclidean Symbol Distance Field (ESDF) to calculate the flight time, which is defined as the travel consumption. The uncertainty of the environment is minimized gradually by maximizing the utility function during each exploration journey. To take full advantage of the mobility of UAVs, we perform B-spline trajectory optimization and yaw angle planning based on the fast marching paths. We conduct sufficient comparison and evaluation experiments in simulation environments. Experimental results show the superiority of the proposed exploration strategy. The code related to the experiments will be published at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/BoLeiChen/fastmarching-exploration</uri> .

An Accelerated Dual Fast Marching Tree Applied to Emergency Geometric Trajectory Generation

This paper addresses the generation of aircraft emergency trajectories with obstacle avoidance. After presenting in detail the fast marching tree algorithm, in this paper we propose an improvement of its performance. First, the free space checking function is sped up. Then, the algorithm is used twice, firstly with the sampling of a few points to generate an approximate trajectory, and secondly with a sampling of points close to the first computed trajectory to refine it. The proposed method significantly reduces the computing time of the emergency geometric trajectory generation.

An efficient path planning algorithm for the biped robot in a static environment using fast sweeping method

Obtaining the collision-free path for the biped walking machine/robot in an obstacle clustered environment is a challenging task. To overcome this difficulty, researchers around the world are implementing several collision-free path planning algorithms. It is significant to note that an effective path-planning methodology helps the biped robot to achieve a collision-free path with a minimum travel path. In the current investigation, the authors have proposed a new path planning procedure, that is, Fast Sweeping Method (FSM), to obtain the optimal path for the biped robot in a static environment. To check the effectiveness of the developed procedure, in the present investigation, the authors have tested it in both simulations as well as on an actual biped robot in a static domain. Further, the results of the current algorithm are compared with two established path planning algorithms, namely the Fast Marching Method (FMM) and A-star algorithms. In the end, it has been detected that the proposed algorithm obtains the best collision-free optimal path when compared with the Fast Marching Method (FMM) and A-star algorithms.

A high order compact time/space finite difference scheme for the 2D and 3D wave equation with a damping layer

We consider fourth order accurate compact schemes, in both space and time, for the second order wave equation with a variable speed of sound. For unbounded domains we add a fourth order accurate sponge layer to damp the outgoing waves. We demonstrate that usually this is more efficient than lower order schemes despite being implicit and conditionally stable. Fast time marching of the implicit scheme is accomplished by iterative methods such as multi-grid. Computations confirm the design convergence rate for the in-homogeneous, variable wave speed equation.

The stochastic simulation of karst conduit network structure using anisotropic fast marching, and its application to a geologically complex alpine karst system

Anisotropic fast-marching algorithms are computationally efficient tools for generating realistic maps of karst conduit networks, constrained by both the spatial extent and the orientation of karstifiable geologic units. Existing models to generate conduit network maps are limited either by high computational requirements (for chemistry-based models) or by their inability to incorporate the effects of elevation and orientation gradients (for isotropic fast-marching models). The new anisotropic fast-marching approach described here provides a significant improvement, though it imitates rather than reproduces actual speleogenetic processes. It can rapidly generate a stochastic ensemble of plausible networks from basic geologic information, which can also be used as input to karst-appropriate flow models. This paper introduces an open-source, easy-to-use implementation through the Python package pyKasso, then describes its application to a well-mapped geologically complex long-term study site: the Gottesacker alpine karst system (Germany/Austria). Groundwater flow in this system is exceptionally well understood from speleological investigations and tracer tests. Conduit formation primarily occurs at the base of the karst aquifer, following plunging synclines. Although previous attempts to reproduce the conduit network at this site yielded implausible network maps, pyKasso quickly generated networks faithful to the known conduit system. However, the model was only able to generate these realistic networks when the inlet-outlet connections of the system were correctly assigned, highlighting the importance of pairing modeling efforts with field tracer tests. Therefore, a model ensemble method is also presented, to optimize field efforts by identifying the most informative tracer tests to perform.

Black‐Yellow Bandgap Trade‐Off During Thermal Stability Tests in Low‐Temperature Eu‐Doped CsPbI3

The black γ‐phase of CsPbI3 with its bandgap at ≈1.75 eV can enable the take‐off of tandem solar cells as soon as intrinsic instability to the yellow δ‐phase is solved. Here, a black γ‐phase is formed at low temperature (80–90 °C) by incorporating Eu through EuCl3 or EuI2. It is forced to become yellow by thermal heating under nitrogen. It is demonstrated how spectroscopic ellipsometry and the related critical points analysis provide a new diagnostic tool to monitor the transformation through the bandgap footprint. As two sides of the same coin, the consumption of the black γ‐phase and the growth of the yellow δ‐phase are addressed and modeled in the range of 60–100 °C using the Avrami's theory. This approach allows extracting the activation energies of the phase transformation that are 0.95 eV versus 1.15 eV using EuI2 and EuCl3, respectively. In situ transmission electron microscopy analyses combined with fast marching simulations highlight that the phase transformation occurs through constant nucleation and growth. Europium has indeed the capability to tackle those processes and to extend the durability of the black γ‐phase at 30 °C in N2 to ≈250 days, hugely above the one observed without Eu (≈hours).

Cooperative P-Wave Velocity Measurement with Full Waveform Moment Tensor Inversion in Transversely Anisotropic Media.

Precise stochastic approaches to quantitatively calculate the source uncertainties offers the opportunity to eliminate the influence of anisotropy on moment tensor inversion. The effects of ignoring anisotropy were tested by using homogeneous Green’s functions. Results indicate the influence of anisotropy and noise on fault plane rotation is very small for a pure shear source whether it is restricted to double couple solution or full moment tensor solution. Green’s functions with different prior rough anisotropy information were tested, indicating that the complex source is more sensitive to velocity models than the pure shear source and the fault plane rotation caused by full moment tensor solution is larger than the pure double couple solution. Collaborative P-wave velocity inversion with active measurements and passive acoustic emission data using the fast-marching method were conducted, and new Green’s functions established based on the tomography results. The resolved fault plane solution rotated only 3.5° when using the new Green’s functions, but the presence of spurious isotropic and compensated linear vector dipole components was not completely eliminated. It is concluded that the cooperative inversion is capable of greatly improving the accuracy of the fault plane solutions and reducing the spurious components in the full moment tensor solution.

Solving the eikonal equation for compressional and shear waves in anisotropic media using peridynamic differential operator

SUMMARY Traveltimes of compressional (P) and shear (S) waves have proven essential in many earthquake and exploration seismology applications. An accurate and efficient traveltime computation for P and S waves is crucial for the success of these applications. However, solving the eikonal equation with a complex phase velocity field in anisotropic media is challenging. The eikonal equation is a first-order nonlinear hyperbolic partial differential equation. It represents the high-frequency asymptotic approximation of the wave equation. The fast marching and sweeping methods are commonly used due to their efficiency in numerically solving the eikonal equation. However, these methods suffer from numerical inaccuracy in anisotropic media with sharp heterogeneity, irregular surface topography and complex phase velocity fields. This study presents a new method for the solution of the eikonal equation by employing the peridynamic differential operator (PDDO). The PDDO provides the non-local form of the eikonal equation by introducing an internal length parameter (horizon) and a weight function with directional non-locality. The operator is immune to discontinuities in the form of sharp changes in field or model variables and invokes the direction of traveltime in a consistent manner. The weight function controls the strength of association among points within the horizon. Solutions are constructed in a consistent manner without upwind assumptions through simple discretization. The robustness of this approach is established by considering different types of eikonal equations on complex velocity models in anisotropic media. The examples demonstrate its unconditional numerical stability and results compare well with the reference solutions.

3D Reconstruction of Non-Lambertian Surfaces by Perspective Shape-From-Shading With Fast Viscosity Solution

Shape-from-shading (SFS) is an important method to reconstruct three-dimensional (3D) shape of a surface in photometry and computer vision. Lambertian surface reflectance and orthographic camera projection are two fundamental assumptions which generally result in undesirable reconstructed results since inaccurate imaging model is adopted. In this paper, we propose a new fast 3D shape reconstruction approach via the SFS method relaxing the two assumptions. To this end, the Oren-Nayar reflectance and perspective projection models are used to establish an image irradiance equation which depicts the relationship between the 3D shape of non-Lambertian surfaces and its corresponding two-dimensional (2D) shading image. Considering the light attenuation of the near point source, the image irradiance equation is transformed into a static Hamilton-Jacobi partial differential equation (PDE) by solving a quadratic equation. The viscosity solution of the resultant Hamilton-Jacobi PDE is approximated by using optimal control theory and iterative fast marching method starting from a viscosity supersolution. The performance of the proposed approach is evaluated on both synthetic and real-world images and the experimental results demonstrate that the proposed approach is accurate and fast.

An Improved Parameter Dimensionality Reduction Approach Based on a Fast Marching Method for Automatic History Matching

History matching is a critical step in reservoir numerical simulation algorithms. It is typically hindered by difficulties associated with the high-dimensionality of the problem and the gradient calculation approach. Here, a multi-step solving method is proposed by which, first, a Fast marching method (FMM) is used to calculate the pressure propagation time and determine the single-well sensitive area. Second, a mathematical model for history matching is implemented using a Bayesian framework. Third, an effective decomposition strategy is adopted for parameter dimensionality reduction. Finally, a localization matrix is constructed based on the single-well sensitive area data to modify the gradient of the objective function. This method has been verified through a water drive conceptual example and a real field case. The results have shown that the proposed method can generate more accurate gradient information and predictions compared to the traditional analytical gradient methods and other gradient-free algorithms.

Learning-Based Motion Planning of a 14-DOF Biped Robot on 3D Uneven Terrain Containing a Ditch

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.