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

TitleA Second Order Multi-Stencil Fast Marching Method With a Non-Constant Local Cost Model
Publication TypeJournal Article
Year of Publication2019
AuthorsMerino-Caviedes, S., L. Cordero-Grande, M. T. Pérez, P. Casaseca-de-la-Higuera, M. Martín-Fernández, R. Deriche, and C. Alberola-López
JournalIEEE Transactions on Image Processing
Date Published04/2019
KeywordsApproximation algorithms, Differential equations, Eikonal equation, Frequency modulation, MSFM, Mathematical model, Silicon, Three-dimensional displays, Unmanned aerial vehicles, Vectors, axis swapping, difference equations, fast marching methods, finite difference methods, finite differences, image processing, iterative methods, least squares approximations, multi-stencil schemes, multistencil version, nonconstant local cost model, permutation-invariant stencil sets, second order multistencil fast marching method, stencil orthogonality, stencil set

The fast marching method is widely employed in several fields of image processing. Some years ago a multi-stencil version (MSFM) was introduced to improve its accuracy by solving the equation for a set of stencils and choosing the best solution at each considered node. The following work proposes a modified numerical scheme for MSFM to take into account the variation of the local cost, which has proven to be second order. The influence of the stencil set choice on the algorithm outcome with respect to stencil orthogonality and axis swapping is also explored, where stencils are taken from neighborhoods of varying radius. The experimental results show that the proposed schemes improve the accuracy of their original counterparts, and that the use of permutation-invariant stencil sets provides robustness against shifted vector coordinates in the stencil set.