Abstract
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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References
D. Adalsteinsson and J. A. Sethian. A fast level set method for propagating interfaces. Journal of Computational Physics, 118:269–277, 1995.
E. W. Dijkstra. A note on two problems in connection with graphs. Numerische Mathematik, 1:269–271, 1959.
Seongjai Kim. An O(N) level set method for eikonal equations. SIAM J. Sci. Comput., 22(6):2178–2193, 2001.
Qingfen Lin. Enhancement, extraction, and visualization of 3D volume data. PhD thesis, Linköping University, 2003.
Ingemar Ragnemalm. Neighborhoods for distance transformation using ordered propagation. CVGIP-Image Understanding, 56:161–166, 1992.
J. A. Sethian. Level Set Methods and Fast Marching Methods. Cambridge University Press, 1999.
John N. Tsitsiklis. Efficient algorithm for globally optimal trajectories. IEEE Transactions on Automatic Control, 40(9):1528–1538, 1995.
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Danielsson, PE., Lin, Q. (2003). A Modified Fast Marching Method. In: Bigun, J., Gustavsson, T. (eds) Image Analysis. SCIA 2003. Lecture Notes in Computer Science, vol 2749. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45103-X_151
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DOI: https://doi.org/10.1007/3-540-45103-X_151
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