Fast Marching Research Articles

An efficient three-dimensional face recognition system based random forest and geodesic curves

3D Face recognition is being extensively recognized as a biometric performance refers to its non-intrusive environment. In spite of large research on 2-D face recognition, it suffers from low recognition rate due to illumination variations, pose changes, poor image quality, occlusions and facial expression variations, while 3D face models are insensitive to all these conditions. In this paper, we present an efficient 3D face recognition approach based on Geodesic Distance (GD) of Riemannian geometry and Random Forest (RF), named GD-FM+RF. Therefore, to compute the geodesic distance between the specified pairs of the points of 3D faces, we applied Fast Marching (FM) algorithm, in order to solve the Eikonal equation. Then, these extracted features presented by the geodesic facial curves are used by Principal Component Analysis (PCA) algorithm to analyze class separability. Afterwards, these features were utilized as input of RF classifier. In order to test our approach and assess its effectiveness, simulated series of tests were implemented on 3D SHape REtrieval Contest 2008 database (SHREC'08). As a result, our proposed approach enhances the recognition rate and achieves promising results compared to state of the art methods, getting 99.11% in terms of recognition rate.

Real-time registration of 3D echo to x-ray fluoroscopy based on cascading classifiers and image registration

Three-dimensional (3D) transesophageal echocardiography (TEE) is one of the most significant advances in cardiac imaging. Although TEE provides real-time 3D visualization of heart tissues and blood vessels and has no ionizing radiation, x-ray fluoroscopy still dominates in guidance of cardiac interventions due to TEE having a limited field of view and poor visualization of surgical instruments. Therefore, fusing 3D echo with live x-ray images can provide a better guidance solution. This paper proposes a novel framework for image fusion by detecting the pose of the TEE probe in x-ray images in real-time. The framework does not require any manual initialization. Instead it uses a cascade classifier to compute the position and in-plane rotation angle of the TEE probe. The remaining degrees of freedom are determined by fast marching against a template library. The proposed framework is validated on phantoms and patient data. The target registration error for the phantom was 2.1 mm. In addition, 10 patient datasets, seven of which were acquired from cardiac electrophysiology procedures and three from trans-catheter aortic valve implantation procedures, were used to test the clinical feasibility as well as accuracy. A mean registration error of 2.6 mm was achieved, which is well within typical clinical requirements.

Scenario Reduction of Realizations Using Fast Marching Method in Robust Well Placement Optimization of Injectors

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.

Shared-memory block-based fast marching method for hierarchical meshes

The fast marching method is commonly used in expanding front simulations in various fields, such as, fluid dynamics, computer graphics, and in microelectronics, to restore the signed-distance field property of the level-set function, also known as re-distancing. To improve the performance of the re-distancing step, parallel algorithms for the fast marching method as well as support for hierarchical meshes have been developed; the latter to locally support higher resolutions of the simulation domain whilst limiting the impact on the overall computational demand. In this work, the previously developed multi-mesh fast marching method is extended by a so-called block-based decomposition step to improve serial and parallel performance on hierarchical meshes. OpenMP tasks are used for the underlying coarse-grained parallelization on a per mesh basis. The developed approach offers improved load balancing as the algorithm employs a high mesh partitioning degree, enabling to balance mesh partitions with varying mesh sizes. Various benchmarks and parameter studies are performed on representative geometries with varying complexities. The serial performance is increased by up to 21% whereas parallel speedups ranging from 7.4 to 19.1 for various test cases on a 24-core Intel Skylake computing platform have been achieved, effectively doubling the parallel efficiency of the previous approach.

A novel approach to optimising well trajectory in heterogeneous reservoirs based on the fast-marching method

To achieve efficient recovery of subsurface energy resources, a suitable trajectory needs to be identified for the production well. In this study, a new approach is presented for automated identification of optimum well trajectories in heterogeneous oil/gas reservoirs. The optimisation procedures are as follows. First, a productivity potential map is generated based on the site characterisation data of a reservoir (when available). Second, based on the fast-marching method, well paths are generated from a number of entrance positions to a number of exit points at opposite sides of the reservoir. The well trajectory is also locally constrained by a prescribed maximum curvature to ensure that the well trajectory is drillable. Finally, the optimum well trajectory is selected from all the candidate paths based on the calculation of a benefit-to-cost ratio. If required, a straight directional well path, may also be derived through a linear approximation to the optimised non-linear trajectory by least squares analysis. Model performance has been demonstrated in both 2D and 3D. In the 2D example, the benefit-to-cost ratio of the optimised well is much higher than that of a straight well; in the 3D example, laterals of various curvatures are generated. The applicability of the method is tested by exploring different reservoir heterogeneities and curvature constraints. This approach can be applied to determine the entrance/exit positions and the well path for subsurface energy system development, which is useful for field applications.

Optimal Tree Topology for a Submarine Cable Network With Constrained Internodal Latency

This paper provides an optimized cable path planning solution for a tree-topology network in an irregular 2D manifold in a 3D Euclidean space, with an application to the planning of submarine cable networks. Our solution method is based on total cost minimization, where the individual cable costs are assumed to be linear to the length of the corresponding submarine cables subject to latency constraints between pairs of nodes. These latency constraints limit the cable length and number of hops between any pair of nodes. Our method combines the Fast Marching Method (FMM) and a new Integer Linear Programming (ILP) formulation for Minimum Spanning Tree (MST) where there are constraints between pairs of nodes. We note that this problem of MST with constraints is NP-complete. Nevertheless, we demonstrate that ILP running time is adequate for the great majority of existing cable systems. For cable systems for which ILP is not able to find the optimal solution within an acceptable time, we propose an alternative heuristic algorithm based on Prim's algorithm. In addition, we apply our FMM/ILP-based algorithm to a real-world cable path planning example and demonstrate that it can effectively find an MST with latency constraints between pairs of nodes.

Automatic Segmentation of outer edges of retinal layers in OCT scan images using Eikonal Equation

Optical coherence tomography (OCT) is a non-invasive diagnostic method specially used in retinal as it the most sensitive organs among human parts. It uses low coherence light waves to render the cross-section view of the retina in micrometer resolution. In the analysis of a retinal anomaly, the sectional visualization proves to be an immensely powerful mechanism. For prior detection of retinal diseases, slicing of the required portion from the dataset images into definite layers is a necessary step. It helps to map and measure their thickness. These measurements help with the diagnosis and provide proper guidance for the treatment of diseases of the retina.In this work, we are taking an account of calculating the precise geodesic distance approach for the OCT segmentation of images in two-dimensional spaces. The technique we are using takes into account horizontal and vertical intensity variation and get onto a weighted geodesic distance. By applying the fast marching approach on the Eikonal equation, this work is calculating the shortest path. Although the proposed Geodesic distance method using the Eikonal equation is a bit complex method it outperforms graph as well as other techniques in portraying precisely the retinal layers.

Accurate Liver Border Identification Model in CT Scan Images

The liver is an important organ in human body with certain variations in its edges, color, shape and pixel intensity distribution. These uncertainties may be because of various liver pathologies, hereditary or both. Along with it, liver has close proximity to its nearby organs. Hence, identifying liver in scanned images is a challenging step in image processing. This task becomes more imprecise when liver diseases are present at the edges. The liver segmentation is prerequisite for liver volumetry, computer-based surgery planning, liver surgery modelling, surgery training, 3D view generation, etc. The proposed hybrid segmentation method overcomes the problems and identifies liver boundary in Computed-Tomography (CT) scan images accurately. In this paper, the first step is to study statistics of pixel intensity distribution within liver image, and novel methodology is designed to obtain thresholds. Then, threshold-based segmentation is applied which separates the liver from abdominal CT scan images. In the second step, liver edge is corrected using improved chain code and Bresenham pixel interconnection methods. This provides a precise liver image. The initial points are located inside the liver region without user interventions. These initial points evolve outwardly using Fast Marching Method (FMM), identifying the liver boundary accurately in CT abdominal scan images.

Microseismic Location Error Due to Eikonal Traveltime Calculation

The accuracy of computed traveltimes in a velocity model plays a crucial role in localization of microseismic events. The conventional approach usually utilizes robust fast sweeping or fast marching methods to solve the eikonal equation numerically with a finite-difference scheme. These methods introduce traveltime errors that strongly depend on the direction of wave propagation. Such error results in moveout changes of the computed traveltimes and introduces significant location bias. The issue can be addressed by using a finite-difference scheme to solve the factored eikonal equation. This equation yields significantly more accurate traveltimes and therefore reduces location error, though the traveltimes computed with the factored eikonal equation still contain small errors with systematic bias. Alternatively, the traveltimes can be computed using a physics-informed neural network solver, which yields more randomized traveltimes and resulting location errors.

Fast Marching Method for Microseismic Source Location in Cavern-Containing Rockmass: Performance Analysis and Engineering Application

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.

Computing Pressure Front Propagation Using the Diffusive-Time-of-Flight in Structured and Unstructured Grid Systems via the Fast-Marching Method

SummaryDiffusive-time-of-flight (DTOF), representing the travel time of pressure front propagation, has found many applications in unconventional reservoir performance analysis. The computation of DTOF typically involves upwind finite difference of the Eikonal equation and solution using the fast-marching method (FMM). However, the application of the finite difference-based FMM to irregular grid systems remains a challenge. In this paper, we present a novel and robust method for solving the Eikonal equation using finite volume discretization and the FMM.The implementation is first validated with analytical solutions using isotropic and anisotropic models with homogeneous reservoir properties. Consistent DTOF distributions are obtained between the proposed approach and the analytical solutions. Next, the implementation is applied to unconventional reservoirs with hydraulic and natural fractures. Our approach relies on cell volumes and connections (transmissibilities) rather than the grid geometry, and thus can be easily applied to complex grid systems. For illustrative purposes, we present applications of the proposed method to embedded discrete fracture models (EDFMs), dual-porosity dual-permeability models (DPDK), and unstructured perpendicular-bisectional (PEBI) grids with heterogeneous reservoir properties. Visualization of the DTOF provides flow diagnostics, such as evolution of the drainage volume of the wells and well interactions.The novelty of the proposed approach is its broad applicability to arbitrary grid systems and ease of implementation in commercial reservoir simulators. This makes the approach well-suited for field applications with complex grid geometry and complex well architecture.

Submarine Cable Path Planning Based on Weight Selection of Design Considerations

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). It is called FMM/SA and 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.

Interactive Image Inpainting of Large-Scale Missing Region

Image inpainting is a challenging reconstruction of the damaged image in photography, especially for more valued artwork than before. The damages are mostly caused by scratches and worn out, so they cannot be easily fixed physically. Thus, many scientists proposed sophisticated methods for restoring the damaged image into a new one similar to an original image. However, these methods have not solved the problem effectively if the missing region is large. In this paper, we focus on how to restore a large missing region in image inpainting. This algorithm is composed of two steps: structure propagation and color propagation. In structure propagation, we segment a large region (non-homogeneous) into several small regions (homogeneous) based on the salient structure of missing region. Then, we applied a simple pixel-based inpainting method called the Fast Marching Method (FMM) to fill in the missing homogeneous regions by color propagation. In the experimental section, we applied several kinds of missing regions, such as irregular and regular missing regions, in large sizes. The results show that our proposed method performs well in various conditions.

Application of Snell's law in reflection raytracing using the multistage fast marching method

Accurate calculations of travel times and raypaths of reflection waves are important for reflection travel time tomography. The multistage shortest path method (MSPM) and multistage fast marching method (MFMM) have been widely used in reflection wave raytracing, and both of them are characterized by high efficiency and accuracy. However, the MSPM does not strictly follow Snell's law at the interface because it treats the interface point as a sub-source, resulting in a decrease in accuracy. The MFMM achieves high accuracy by solving the Eikonal equation in local triangular mesh. However, the implementation process is complex. Here we propose a new method which uses linear interpolation to compute the incident travel time of interface points and then using Snell's law to compute the reflection travel time of grid points just above the interface. Our new method is much simpler than the MFMM; furthermore, numerical simulations show that the accuracy of the MFMM and our new method are basically the same, thus the reflection tomography algorithms which use our new method are easier to implement without decreasing accuracy. Besides, our new method can be extended easily to other grid-based raytracing methods.

Dual Fast Marching Tree Algorithm for Human-Like Motion Planning of Anthropomorphic Arms With Task Constraints

This article presents a dual fast marching tree algorithm that consists of constrained fast marching tree planning in a Cartesian space (C_FMT <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∗</sup> ) and human-like fast marching tree planning in self-motion manifolds (H_FMT <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∗</sup> ) for human-like motion planning for anthropomorphic arms with task constraints. The key idea of the proposal is to exploit dual sampling in a Cartesian space and self-motion manifolds to explore the entire configuration space. The C_FMT <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∗</sup> reduces the constrained planning problem to the unconstrained instance by sampling in the obstacle-free Cartesian space and satisfying the task constraints; it can solve most of these constrained path planning tasks quickly and obtain lower cost solutions compared to the existing techniques. In addition, a validity checking method of Cartesian sampling points based on self-motion manifolds is introduced to ensure the probabilistic completeness of the new planner. By analyzing musculoskeletal models of the human arm and the muscle strength property, a torque effort criterion was deduced to generate biomimetic motion for anthropomorphic arms. Then, an H_FMT <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∗</sup> that incorporates the FMT <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∗</sup> algorithm with the torque effort criterion is also proposed and used to bias the tree growth toward human-like movements in the self-motion manifolds of the obtained path. Finally, the proposed approach has been illustrated with several real examples executed with a humanoid robot. The obtained results show that the paths obtained with the proposed approach are quicker and more human-like.

Imaging the structure of the Sun Pyramid (Teotihuacán, Mexico) from passive seismic methods

The Sun Pyramid in Teotihuacán, Mexico, belongs to the cultural heritage of Mexico and the world. Built nearly a millennium ago, the Pyramid is poorly known in terms of its mechanical properties. In order to assess these properties, we measured and studied the ambient seismic noise which has become a popular tool to explore non-invasively geological and human-made structures. This research is aimed to contribute to the structural diagnosis and seismic vulnerability assessment of this emblematic Mexican pre-Hispanic monument. We analyzed the horizontal-to-vertical spectral ratio and the cross-correlations of seismic ambient noise recorded during four hours by 15 broadband stations, distributed on different levels of the structure, and propose a three-dimensional velocity model for the Sun Pyramid in Teotihuacán. The processed data includes the stacking of cross-correlations. We identified arrivals corresponding to a rich mixture of body and surface waves. Group velocity dispersion curves were extracted from the symmetrized cross-correlation of vertical displacements between station pairs. The retrieved travel times between station pairs allowed a tomographic analysis based on the Fast Marching Method (FMM). Besides, simultaneous inversions of the local dispersion curves (obtained from the group velocity tomography) and the HVSR mitigate non-uniqueness of the retrieved P- and S-wave velocities. Our model reveals two main features of the Sun Pyramid: i) The low-velocity anomalies in the cover layer correlate well with the presence of support walls or counterforts that, apparently, were part of the construction technique seeking to provide support to weak parts of the Sun Pyramid. ii) The core of the structure, with soft material subjected to the action of infiltrated water, is susceptible to causing wall failures. These results could be useful to design conservation strategies for this emblematic Mexican pre-Hispanic monument.

Semi-automatic segmentation of whole-body images in longitudinal studies

We propose a semi-automatic segmentation pipeline designed for longitudinal studies considering structures with large anatomical variability, where expert interactions are required for relevant segmentations. Our pipeline builds on the regularized Fast Marching (rFM) segmentation approach by Risser et al (2018). It consists in transporting baseline multi-label FM seeds on follow-up images, selecting the relevant ones and finally performing the rFM approach. It showed increased, robust and faster results compared to clinical manual segmentation. Our method was evaluated on 3D synthetic images and patients’ whole-body MRI. It allowed a robust and flexible handling of organs longitudinal deformations while considerably reducing manual interventions.

Abstract 14957: Comparison of Coronary Tree Detection and Diameter Quantification From a Deep Learning Convolutional Neural Network With Quantitative Coronary Angiography

Introduction: QCA (Quantitative Coronary Angiography) is an accepted standard for assessing coronary artery stenosis severity. QCA computes the percentage diameter reduction of the lesion, improving upon visual inspection since it provides a numerical quantification of stenosis severity. However, it can be costly, and it requires human input to correct the boundaries of the vessel. AngioNet is a fully-automatic deep learning convolutional neural network trained to identify coronary trees and their vessel diameters in angiograms, and could be a cost-effective alternative to QCA. To explore the accuracy of AngioNet, we compared its ability to identify vessels and their diameter when compared with QCA. Methods: Angiograms with 3-vessel QCA reports from 89 patients acquired at Madras Medical Mission were used. The entire vessel tree was segmented for each angiogram using AngioNet. A fast-marching method was used to calculate the radius along the vessel’s centerline. Vessel diameter was compared in two regions corresponding to the regions marked in the QCA report: the most proximal region, containing the maximum vessel diameter, and the region of stenosis. If no stenosis was present, the distal region containing minimum diameter was selected. The difference in maximum and minimum vessel diameter between QCA and AngioNet was computed, and a Bland-Altman plot (see figure) was used to determine the interchangeability of both methods. Results: The mean absolute difference between both measurements was 0.27mm. The standardized difference was 0.215, corresponding to a 91.5% overlap of their distributions. Lastly, 97% of data points were within the limits of agreement, suggesting minimal clinical differences and that both methods may be interchangeable. Conclusions: Deep learning convolutional networks may be used to assess vessel diameters at a level that agrees well with those of QCA. AngioNet has the potential to automate the detection of stenosis severity.

Structural analysis of an L-infinity variational problem and relations to distance functions

In this work we analyse the functional ${\cal J}(u)=\|\nabla u\|_\infty$ defined on Lipschitz functions with homogeneous Dirichlet boundary conditions. Our analysis is performed directly on the functional without the need to approximate with smooth $p$-norms. We prove that its ground states coincide with multiples of the distance function to the boundary of the domain. Furthermore, we compute the $L^2$-subdifferential of ${\cal J}$ and characterize the distance function as unique non-negative eigenfunction of the subdifferential operator. We also study properties of general eigenfunctions, in particular their nodal sets. Furthermore, we prove that the distance function can be computed as asymptotic profile of the gradient flow of ${\cal J}$ and construct analytic solutions of fast marching type. In addition, we give a geometric characterization of the extreme points of the unit ball of ${\cal J}$. Finally, we transfer many of these results to a discrete version of the functional defined on a finite weighted graph. Here, we analyze properties of distance functions on graphs and their gradients. The main difference between the continuum and discrete setting is that the distance function is not the unique non-negative eigenfunction on a graph.

Development of efficient and robust Eikonal solver variants for first-arrival seismic modeling

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.