Document Detail


Symmetric fast marching schemes for better numerical isotropy.
MedLine Citation:
PMID:  23868786     Owner:  NLM     Status:  In-Data-Review    
Abstract/OtherAbstract:
Existing fast marching methods solve the Eikonal equation using a continuous (first-order) model to estimate the accumulated cost, but a discontinuous (zero-order) model for the traveling cost at each grid point. As a result the estimate of the accumulated cost (calculated numerically) at a given point will vary based on the direction of the arriving front, introducing an anisotropy into the discrete algorithm even though the continuous partial differential equation (PDE) is itself isotropic. To remove this anisotropy, we propose two very different schemes. In the first model, we utilize a continuous interpolation of the traveling cost, which is not biased by the direction of the propagating front. In the second model, we upsample the traveling cost on a higher resolution grid to overcome the directional bias. We show the significance of removing the directional bias in the computation of the cost in some applications of the fast marching method, demonstrating that both methods make the discrete implementation more isotropic, in accordance with the underlying continuous PDE.
Authors:
Vikram Appia; Anthony Yezzi
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Publication Detail:
Type:  Journal Article    
Journal Detail:
Title:  IEEE transactions on pattern analysis and machine intelligence     Volume:  35     ISSN:  1939-3539     ISO Abbreviation:  IEEE Trans Pattern Anal Mach Intell     Publication Date:  2013 Sep 
Date Detail:
Created Date:  2013-07-22     Completed Date:  -     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  9885960     Medline TA:  IEEE Trans Pattern Anal Mach Intell     Country:  United States    
Other Details:
Languages:  eng     Pagination:  2298-304     Citation Subset:  IM    
Affiliation:
Texas Instruments, Dallas.
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