A Modified Fast Marching Method
In most, if not all fast marching methods published hitherto, the input cost function and the output arrival time are sampled on exactly the same grid. But since the input data samples are differences of the output samples we found it natural to separate the input and output grid half a sampling unit in all coordinates (two or three).We also employ 8-neighborhood (26-neighborhood in the 3D-case) in the basic updating step of the algorithm. Some simple numerical experiments verify that the modified method improves the accuracy considerably. However, we also feel the modified method leads itself more naturally to image processing applications like tracking and segmentation.
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