A study of numerical methods for the level set approach

Authors:
Pierre A. Gremaud;Christopher M. Kuster;Zhilin Li
Affiliations:
Department of Mathematics and Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC 27695-8205, USA;Department of Mathematics and Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC 27695-8205, USA;Department of Mathematics and Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC 27695-8205, USA and Nanjing Normal University, Nanjing, China
Venue:
Applied Numerical Mathematics
Year:
2007

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Abstract

The computation of moving curves by the level set method typically requires reinitializations of the underlying level set function. Two types of reinitialization methods are studied: a high order ''PDE'' approach and a second order Fast Marching method. Issues related to the efficiency and implementation of both types of methods are discussed, with emphasis on the tube/narrow band implementation and accuracy considerations. The methods are also tested and compared. Fast Marching reinitialization schemes are faster but limited to second order, PDE based reinitialization schemes can easily be made more accurate but are slower, even with a tube/narrow band implementation.