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Multistencils Fast Marching Methods: A Highly Accurate Solution to the Eikonal Equation on Cartesian Domains

10 years 6 months ago
Multistencils Fast Marching Methods: A Highly Accurate Solution to the Eikonal Equation on Cartesian Domains
A wide range of computer vision applications require an accurate solution of a particular Hamilton-Jacobi (HJ) equation known as the Eikonal equation. In this paper, we propose an improved version of the fast marching method (FMM) that is highly accurate for both 2D and 3D Cartesian domains. The new method is called multistencils fast marching (MSFM), which computes the solution at each grid point by solving the Eikonal equation along several stencils and then picks the solution that satisfies the upwind condition. The stencils are centered at each grid point and cover its entire nearest neighbors. In 2D space, two stencils cover 8-neighbors of the point, whereas in 3D space, six stencils cover its 26-neighbors. For those stencils that are not aligned with the natural coordinate system, the Eikonal equation is derived using directional derivatives and then solved using higher order finite difference schemes. The accuracy of the proposed method over the state-of-the-art FMM-based techni...
M. Sabry Hassouna, Aly A. Farag
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Hassouna_Farag_TPAMI_2007.pdf3.85 MB
Added 07 Nov 2008
Updated 25 Nov 2008
Type Journal
Year 2007
Where PAMI (IEEE Transaction on Pattern Analysis and Machine Intelligence)
Authors M. Sabry Hassouna, Aly A. Farag
Attachments 1 file(s)
Related Work

M. Sabry Hassouna and Aly A. Farag, "Accurate Tracking of Monotonically Advancing Fronts," Proc. of IEEE Conference on Computer Vision and Pattern Recognition CVPR, New York, NY, USAJune 17-22, 2006, vol I, pp. 355 - 362.
Acceptance rate is 23.5%.
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