scholarly journals Geodesic Computations on Surfaces

2013 ◽  
Author(s):  
Karthik Krishnan
Keyword(s):  
Geodesic Distance ◽  
Front Propagation ◽  
Geodesic Curve ◽  
Fast Marching Method ◽  
Triangle Mesh ◽  
Fast Marching ◽  
Geometry Processing ◽  
Distance Field ◽  
Triangulated Surface ◽  
Termination Criteria

The computation of geodesic distances on a triangle mesh has many applications in geometry processing. The fast marching method provides an approximation of the true geodesic distance field. We provide VTK classes to compute geodesics on triangulated surface meshes. This includes classes for computing the geodesic distance field from a set of seeds and to compute the geodesic curve between source and destination point(s) by back-tracking along the gradient of the distance field. The fast marching toolkit (Peyre et. al.) is internally used. A variety of options are exposed to guide front propagation including the ability to specify propagation weights, constrain to a region, specify exclusion regions, and distance based termination criteria. Interpolators that plug into a contour widget, are provided to enable interactive tracing of paths on meshes.

scholarly journals Road Information Extraction from High-Resolution Remote Sensing Images Based on Road Reconstruction

2019 ◽  
Vol 11 (1) ◽  
pp. 79 ◽  
Author(s):  
Tingting Zhou ◽  
Chenglin Sun ◽  
Haoyang Fu
Keyword(s):  
Fast Marching Method ◽  
Road Extraction ◽  
Fast Marching ◽  
Distance Field ◽  
Distance Fields ◽  
Source Distance ◽  
Road Surfaces ◽  
Road Width ◽  
Marching Method ◽  
Boundary Distance

Traditional road extraction algorithms, which focus on improving the accuracy of road surfaces, cannot overcome the interference of shelter caused by vegetation, buildings, and shadows. In this paper, we extract the roads via road centerline extraction, road width extraction, broken centerline connection, and road reconstruction. We use a multiscale segmentation algorithm to segment the images, and feature extraction to get the initial road. The fast marching method (FMM) algorithm is employed to obtain the boundary distance field and the source distance field, and the branch backing-tracking method is used to acquire the initial centerline. Road width of each initial centerline is calculated by combining the boundary distance fields, before a tensor field is applied for connecting the broken centerline to gain the final centerline. The final centerline is matched with its road width when the final road is reconstructed. Three experimental results show that the proposed method improves the accuracy of the centerline and solves the problem of broken centerline, and that the method reconstructing the roads is excellent for maintain their integrity.

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

SPE Journal ◽  
2021 ◽  
pp. 1-21
Author(s):  
Hongquan Chen ◽  
Tsubasa Onishi ◽  
Jaeyoung Park ◽  
Akhil Datta-Gupta
Keyword(s):  
Finite Difference ◽  
Analytical Solutions ◽  
Eikonal Equation ◽  
Front Propagation ◽  
Fast Marching Method ◽  
Fast Marching ◽  
Reservoir Properties ◽  
Grid Systems ◽  
Marching Method ◽  
Diffusive Time

Summary Diffusive-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-porositydual-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.

scholarly journals Vessel tree extraction using radius-lifted keypoints searching scheme and anisotropic fast marching method

2016 ◽  
Vol 10 (4) ◽  
pp. 224-234 ◽  
Author(s):  
Da Chen ◽  
Jean-Marie Mirebeau ◽  
Laurent D Cohen
Keyword(s):  
Geodesic Distance ◽  
Riemannian Metric ◽  
Difficult Problem ◽  
Tubular Structure ◽  
Fast Marching Method ◽  
Fast Marching ◽  
Geodesic Paths ◽  
Isotropic Geodesic ◽  
Initial Source ◽  
Vessel Tree

Geodesic methods have been widely applied to image analysis. They are particularly efficient to extract a tubular structure, such as a blood vessel, given its two endpoints in a 2D or 3D medical image. We address here a more difficult problem: the extraction of a full vessel tree structure given a single initial root point, by growing a collection of keypoints or new initial source points, connected by minimal geodesic paths. In this article, those keypoints are iteratively added, using a new detection criteria, which utilize the weighted geodesic distances with respect to a radius-lifted Riemannian metric, the standard Euclidean curve length and a path score. Two main weaknesses of classical keypoints searching approach are that the weighted geodesic distance and the Euclidean path length do not take into account the orientation of the tubular structure or object boundaries, due to the use of an isotropic geodesic Riemannian metric, and suffer from a leakage problem. In contrast, we use an anisotropic geodesic Riemannian metric, and develop new criteria for selecting keypoints based on the path score and automatically stopping the tree growth. Experimental results demonstrate that our method can obtain the expected results, which can extract vessel structures at a finer scale, with increased accuracy.

scholarly journals A Comparison of Local Path Planning Techniques of Autonomous Surface Vehicles for Monitoring Applications: The Ypacarai Lake Case-study

Sensors ◽  
2020 ◽  
Vol 20 (5) ◽  
pp. 1488
Author(s):  
Federico Peralta ◽  
Mario Arzamendia ◽  
Derlis Gregor ◽  
Daniel G. Reina ◽  
Sergio Toral
Keyword(s):  
Path Planning ◽  
Random Trees ◽  
Fast Marching Method ◽  
Fast Marching ◽  
Planning Techniques ◽  
Advantages And Disadvantages ◽  
Autonomous Surface Vehicle ◽  
Local Path Planning ◽  
Custom Made ◽  
Local Path

Local path planning is important in the development of autonomous vehicles since it allows a vehicle to adapt their movements to dynamic environments, for instance, when obstacles are detected. This work presents an evaluation of the performance of different local path planning techniques for an Autonomous Surface Vehicle, using a custom-made simulator based on the open-source Robotarium framework. The conducted simulations allow to verify, compare and visualize the solutions of the different techniques. The selected techniques for evaluation include A*, Potential Fields (PF), Rapidly-Exploring Random Trees* (RRT*) and variations of the Fast Marching Method (FMM), along with a proposed new method called Updating the Fast Marching Square method (uFMS). The evaluation proposed in this work includes ways to summarize time and safety measures for local path planning techniques. The results in a Lake environment present the advantages and disadvantages of using each technique. The proposed uFMS and A* have been shown to achieve interesting performance in terms of processing time, distance travelled and security levels. Furthermore, the proposed uFMS algorithm is capable of generating smoother routes.

A Generalized Fast Marching Method on Unstructured Triangular Meshes

2013 ◽  
Vol 51 (6) ◽  
pp. 2999-3035 ◽  
Author(s):  
E. Carlini ◽  
M. Falcone ◽  
Ph. Hoch
Keyword(s):  
Fast Marching Method ◽  
Triangular Meshes ◽  
Fast Marching ◽  
Marching Method

scholarly journals Tsunami wave propagation by voronoi diagram

2018 ◽  
Vol 7 (3) ◽  
pp. 1233
Author(s):  
V Yuvaraj ◽  
S Rajasekaran ◽  
D Nagarajan
Keyword(s):  
Wave Propagation ◽  
Voronoi Diagram ◽  
Tsunami Wave ◽  
Fast Marching Method ◽  
Coastal Regions ◽  
Fast Marching ◽  
Tsunami Waves ◽  
The Finite Difference Method ◽  
Run Up ◽  
Marching Method

Cellular automata is the model applied in very complicated situations and complex problems. It involves the Introduction of voronoi diagram in tsunami wave propagation with the help of a fast-marching method to find the spread of the tsunami waves in the coastal regions. In this study we have modelled and predicted the tsunami wave propagation using the finite difference method. This analytical method gives the horizontal and vertical layers of the wave run up and enables the calculation of reaching time.  

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