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2015•Unpublished venueRequires access

A Wavefront Marching Method for Solving the Eikonal Equation on Cartesian Grids

Brais Cancela, Marcos Ortega, Manuel G. Penedo

Open publisher page 5 citations

Abstract

This paper presents a new wavefront propagation method for dealing with the classic Eikonal equation. While classic Dijkstra-like graph-based techniques achieve the solution in O(M log M), they do not approximate the unique physically relevant solution very well. Fast Marching Methods (FMM) were created to efficiently solve the continuous problem. The proposed approximation tries to maintain the complexity, in order to make the algorithm useful in a wide range of contexts. The key idea behind our method is the creation of 'mini wave-fronts', which are combined to propagate the solution. Experimental results show the improvement in the accuracy with respect to the state of the art, while the average computational speed is maintained in O(M log M), similar to the FMM techniques.

About this research paper

What this paper is about

This paper presents a new wavefront propagation method for dealing with the classic Eikonal equation. While classic Dijkstra-like graph-based techniques achieve the solution in O(M log M), they do not approximate the unique physically relevant solution very well. Fast Marching Methods (FMM) were created to efficiently solve the continuous problem. The proposed approximation tries to maintain the complexity, in order to make the algorithm useful in a wide range of contexts. The key idea behind our method is the creation of 'mini wave-fronts', which are combined to propagate the solution. Experimental results show the improvement in the accuracy with respect to the state of the art, while the average computational speed is maintained in O(M log M), similar to the FMM techniques.

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OpenAlex reports 5 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

This paper presents a new wavefront propagation method for dealing with the classic Eikonal equation. While classic Dijkstra-like graph-based techniques achieve the solution in O(M log M), they do not approximate the unique physically relevant solution very well. Fast Marching Methods (FMM) were created to efficiently solve the continuous problem. The proposed approximation tries to maintain the complexity, in order to make the algorithm useful in a wide range of contexts. The key idea behind our method is the creation of 'mini wave-fronts', which are combined to propagate the solution. Experimental results show the improvement in the accuracy with respect to the state of the art, while the average computational speed is maintained in O(M log M), similar to the FMM techniques.

Key concepts: Eikonal equation, Fast marching method, Wavefront, Dijkstra's algorithm, Computer science, Cartesian coordinate system, Eikonal approximation, Range (aeronautics)

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