A Second Order Multi-Stencil Fast Marching Method With a Non-Constant Local Cost Model

2019 ◽  
Vol 28 (4) ◽  
pp. 1967-1979
Author(s):  
Susana Merino-Caviedes ◽  
Lucilio Cordero-Grande ◽  
Maria Teresa Perez ◽  
Pablo Casaseca-de-la-Higuera ◽  
Marcos Martin-Fernandez ◽  
...  
Keyword(s):  
Cost Model ◽  
Second Order ◽  
Fast Marching Method ◽  
Fast Marching ◽  
Marching Method

3‐D eikonal solvers: First‐arrival traveltimes

Geophysics ◽  
2002 ◽  
Vol 67 (4) ◽  
pp. 1225-1231 ◽  
Author(s):  
Seongjai Kim
Keyword(s):  
Grid Point ◽  
Level Set Methods ◽  
Second Order ◽  
Normal Velocity ◽  
Fast Marching Method ◽  
Fast Marching ◽  
Maximum Angle ◽  
First Arrival ◽  
Grid Points ◽  
Marching Method

The article is concerned with the development and comparison of three different algorithms for the computation of first‐arrival traveltimes: the fast marching method (FMM), the group marching method (GMM), and a second‐order finite‐difference eikonal solver. GMM is introduced as a variant of FMM. It proceeds the solution by advancing a selected group of grid points at a time, rather than sorting the solution in the narrow band to march forward a single grid point. The second‐order eikonal solver studied in the article is an expanding‐box, essentially nonoscillatory scheme for which the stability is enforced by the introduction of a down ‘n’ out marching and a post‐sweeping iteration. Techniques such as the maximum angle condition, the average normal velocity, and cache‐based implementation are introduced for the algorithms to improve the numerical accuracy and efficiency. The algorithms are implemented for solving the eikonal equation in 3‐D isotropic media, and their performances are compared. GMM is numerically verified to be faster than FMM. However, the second‐order algorithm turns out to be superior to these first‐order level‐set methods in both accuracy and efficiency; the incorporation of average normal velocity improves accuracy dramatically for the second‐order scheme.

scholarly journals On correctness of first and second order fast marching method

2011 ◽  
Vol 1 (2) ◽  
Author(s):  
Christoph Lass
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Unique Solution ◽  
Nonlinear Partial Differential Equations ◽  
Second Order ◽  
Fast Marching Method ◽  
Fast Marching ◽  
Order Case ◽  
Upwind Discretization ◽  
Marching Method

AbstractIn this article we will discuss the Fast Marching Method which was introduced by James A. Sethian to solve some types of nonlinear partial differential equations efficiently. We will show that this method yields the unique solution to an upwind discretization. Furthermore we will present the correct algorithm for the second order case where existence and unicity of the solution will be proven as well.

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.  

Generalized fast marching method: applications to image segmentation

2008 ◽  
Vol 48 (1-3) ◽  
pp. 189-211 ◽  
Author(s):  
Nicolas Forcadel ◽  
Carole Le Guyader ◽  
Christian Gout
Keyword(s):  
Image Segmentation ◽  
Fast Marching Method ◽  
Fast Marching ◽  
Marching Method

scholarly journals A Novel Approach to Extract Exact Liver Image Boundary from Abdominal CT Scan using Neutrosophic Set and Fast Marching Method

2019 ◽  
Vol 28 (4) ◽  
pp. 517-532 ◽  
Author(s):  
Sangeeta K. Siri ◽  
Mrityunjaya V. Latte
Keyword(s):  
Ct Scan ◽  
Median Filter ◽  
Neutrosophic Set ◽  
Intensity Level ◽  
Fast Marching Method ◽  
Fast Marching ◽  
Abdominal Ct ◽  
Novel Approach ◽  
Abdominal Ct Scan ◽  
Marching Method

Abstract 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.

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