Fast marching method

J. A. Sethian, in Level set methods and fast marching methods, Cambridge University Press, Cambridge, 1999. 

J. A. Sethian. Evolution, implementation, and application of level set and fast marching methods for advancing fronts. J. Comput Phys., 169[2] 503-555,2001. 

The related fast marching methods (Sethian 1999) have also been applied to image segmentation. These methods are faster, but are designed for problems in which the speed function never changes sign, so that the front is always moving forward or backward. 

Popovici, A.M. and Sethian, ).A. (1998) Three-dimensional travel-time computation using the fast marching method. Proc. SPIE, 3453, 82-93. 

Sethian, A.J., 1999, Level Set Methods and Fast Marching Methods Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science. Cambridge University Press. 

J.A. Sethian (1996) Level Set Methods and Fast Marching Methods. Cambridge University Press. 

Sethian, J.A. (1996) A fast marching level set method for monotonically advancing fronts. Proc. Natl. Acad. Sci. 

Skillman, H. L, James P. MacDonald, Jr., and Henry A. Stiff, Jr. "A Simple, Accurate, Fast Method for Calculating Calcium Sulfate Solubility in Oil Field Brines, " Spring Meeting of the Southwest District, Division of Production, American Petroleum Institute, March, 1969, Lubbock, Texas. 

The marching algorithm mainly takes care of two tasks. Firstly, it updates the index matrix whether a node is outside ( 0 ), at the front ( 1 ), or inside 2 ) the object. The other task is to update the travel-time value for the current node and its neighboring nodes. In addition, we want the algorithm to do this fast as well. Two important reasons for why a group marching-based method works fast are ... 

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