Multi-stencils fast marching method for factored eikonal equations with quadratic anisotropy

Qi, Yingyu

doi:10.1016/j.amc.2021.126776

Cited by 4 publications

(8 citation statements)

References 79 publications

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“…The fast marching algorithm fills the highlight area with pixels in its neighborhood [25]. To ensure natural filling, the weight function is adopted to distinguish the importance of different pixels in the neighborhood.…”

Section: Type II Detection Parallel Multi-decision Algorithmmentioning

confidence: 99%

Automatic State Recognition of Multi-type Protection Platens based on YOLOv5 and Parallel Multi-Decision Algorithm

Zhang¹,

Zhang²,

Wu³

et al. 2022

IJACSA

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A protection platen is a vital component in relay protection systems. The manual inspection of protection platen states is long-term repetitive work with low efficiency and imposes a heavy burden on workers. In this work, we propose a new system to automatically detect the states of multi-type protection platens in images. This system can classify two protection platen categories and further recognize the states of protection platens. For the classification of protection platen types, we propose a new algorithm that automatically detects two protection platen types based on HSV (Hue, Saturation, Value) color space weighting operators. The proposed operators quantify the color variation in the protection platen and reduce the influence of environmental factors. With respect to the state recognition of protection platens, the Type-I protection platen states are automatically classified by the YOLOv5 (You only look once version 5) network. Since the Type-II protection platen has three primary states and more complicated structures, we investigate a new parallel multi-decision algorithm to recognize the states of Type-II protection platens based on the newly proposed watershed-color space difference-shape feature (W-CD-SF) method and the YOLOv5 network. The W-CD-SF technique can segment the protection platens and extract their shape features automatically. This multi-decision mechanism improves the robustness and generalization of state recognition. Experiments were conducted on the collected protection platen images containing 8,969 protection platens. The recognition accuracies of protection platen states exceed 95%. This system can provide auxiliary detection and long-term monitoring of protection platen states.

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Section: Type II Detection Parallel Multi-decision Algorithmmentioning

confidence: 99%

Automatic State Recognition of Multi-type Protection Platens based on YOLOv5 and Parallel Multi-Decision Algorithm

Zhang¹,

Zhang²,

Wu³

et al. 2022

IJACSA

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show abstract

“…In this section, we introduce a quadratic approximation of the eikonal equations [97] with respect to orthorhombic anisotropy and its tilted case (ORT and TOR), vertical and tilted transverse isotropy (VTI and TTI), azimuthal anisotropy and radial anisotropy (AZI and RAD). The Christoffel equation (3.3) applied to track the wavefront has 21 independent stiffness tensor coefficients [11].…”

Section: Anisotropic Eikonal Equationsmentioning

confidence: 99%

“…Algorithm 4.7. Multi-stencils fast marching algorithm for factored eikonal equations with quadratic anisotropy [97] During every iteration, one of the following tags p(•) ∈ X is assigned to each grid point s.…”

Section: The New Algorithmmentioning

confidence: 99%

“…Remark 4.4. For the convergency of the algorithm, please refer to the proof by Treister and Haber [128], Luo and Qian [98] and Qi [97] and the reference therein.…”

Section: 3 (See Remark 43)mentioning

confidence: 99%

“…As suggested in Hassouna and Farag (2007) we choose four stencils for fast marching method which are the F-stencil and three E-stencils. Details of the choice of stencils are explained in Qi [97].…”

Section: Accuracy Convergency and Stabilitymentioning

confidence: 99%

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Improved fast marching methods with application in traveltime tomography

Qi¹

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Time‐average stochastic control based on a singular local Lévy model for environmental project planning under habit formation

Yoshioka

Tsujimura

Hamagami

et al. 2023

Math Methods in App Sciences

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This study applies the theory of stochastic control to an environmental project planning to counteract against the sediment starvation problem in river environments. This can be considered as a time-average inventory problem to time-discretely control a continuous-time system driven by a non-smooth jump process under habit formation disturbing project implementation. The system is modeled such that the sediment storage dynamics are physically consistent with certain experimental results. Further, the habit formation is modeled as simple linear dynamics and serves as a constraint related to the replenishment amount of the sediment. We show that the time-average control problem is not necessarily ergodic. Consequently, the effective Hamiltonian may become a non-constant. Thereafter, ratcheting cases as extreme cases of the irreversible habit formation are considered, owing to them being unique exactly solvable non-ergodic control problems. The optimality equation associated with a regularized and hence well-defined control problem is verified. Furthermore, a finite difference scheme is examined against the exactly solvable case and then applied to more complicated cases.

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Multi-stencils fast marching method for factored eikonal equations with quadratic anisotropy

Cited by 4 publications

References 79 publications

Automatic State Recognition of Multi-type Protection Platens based on YOLOv5 and Parallel Multi-Decision Algorithm

Automatic State Recognition of Multi-type Protection Platens based on YOLOv5 and Parallel Multi-Decision Algorithm

Improved fast marching methods with application in traveltime tomography

Time‐average stochastic control based on a singular local Lévy model for environmental project planning under habit formation

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