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

Merino-Caviedes, Susana; Cordero‐Grande, Lucilio; Pérez, M. Teresa; Casaseca‐de‐la‐Higuera, Pablo; Martı́n-Fernández, Marcos; Deriche, Rachid; Alberola-López, Carlos

doi:10.1109/tip.2018.2880507

Cited by 3 publications

(2 citation statements)

References 17 publications

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“…First of all, we aim to test our algorithm against the Eikonal equation, which is the problem that is traditionally solved by methods like FMM, MSFM or FSM. In order to provide a fair experimental setup, we will conduct the same experiments performed in [30], as their results prove to be the current state-of-the-art. Ten different equations are tested, five in 2D (T 1 to T 5 , see Table 2 and Fig.…”

Section: Isotropic Equationsmentioning

confidence: 99%

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Wavefront Marching Methods: A Unified Algorithm to Solve Eikonal and Static Hamilton-Jacobi Equations

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Alonso‐Betanzos

2021

IEEE Trans. Pattern Anal. Mach. Intell.

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This paper presents a unified propagation method for dealing with both the classic Eikonal equation, where the motion direction does not affect the propagation, and the more general static Hamilton-Jacobi equations, where it does. While classic Fast Marching Method (FMM) techniques achieve the solution to the Eikonal equation with a O(M log M) (or O(M) assuming some modifications), solving the more general static Hamilton-Jacobi equation requires a higher complexity. The proposed framework maintains the O(M log M) complexity for both problems, while achieving higher accuracy than available state-of-the-art. The key idea behind the proposed method is the creation of 'mini wave-fronts', where the solution is interpolated to minimize the discretization error. Experimental results show how our algorithm can outperform the state-of-the-art both in precision and computational cost.

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Section: Isotropic Equationsmentioning

confidence: 99%

“…For the sake of simplicity, as the M S c approach in [30] provides multiple configurations, we will only show its best performance in each test. The gradient values are discretized over the grid nodes.…”

Section: Experiments With 2d and 3d Functionsmentioning

confidence: 99%

Wavefront Marching Methods: A Unified Algorithm to Solve Eikonal and Static Hamilton-Jacobi Equations

Cancela

Alonso‐Betanzos

2021

IEEE Trans. Pattern Anal. Mach. Intell.

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Computing thickness of irregularly-shaped thin walls using a locally semi-implicit scheme with extrapolation to solve the Laplace equation: Application to the right ventricle

Merino-Caviedes,

Martín-Fernández,

Pérez Rodríguez

et al. 2024

Computers in Biology and Medicine

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Study on the Improved Method for Calculating Traveltime and Raypath of Multistage Fast Marching Method

et al. 2022

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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.

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

Cited by 3 publications

References 17 publications

Wavefront Marching Methods: A Unified Algorithm to Solve Eikonal and Static Hamilton-Jacobi Equations

Wavefront Marching Methods: A Unified Algorithm to Solve Eikonal and Static Hamilton-Jacobi Equations

Computing thickness of irregularly-shaped thin walls using a locally semi-implicit scheme with extrapolation to solve the Laplace equation: Application to the right ventricle

Study on the Improved Method for Calculating Traveltime and Raypath of Multistage Fast Marching Method

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