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The powerful [[level set method]] is due to [[Stanley Osher|Osher]] and [[James Sethian|Sethian]] 1988 <ref name=Osher>Osher, S. & Sethian, J. A. 1988. "Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi
formulations". ''Journal of Computation Physics'' 79:12–49.</ref>. However, the straightforward implementation via a dense d-dimensional [[array data structure|array]] of values, results in both time and storage complexity of <math>O(n^d)</math>, where <math>n</math> is the cross sectional resolution of the spatial extents of the ___domain and <math>d</math> is the number of spatial dimensions of the ___domain.
===Narrow band===
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===Sparse field===
This <math>O(n^3)</math> time complexity was eliminated in the approximate "sparse field" level set method introduced by Whitaker in 1998 <ref name=Whitaker>Whitaker, R. T. 1998. "A level-set approach to 3d reconstruction from range data." ''[[International Journal of Computer Vision]].'' 29(3)203–231.</ref>. The sparse field level set method employs a set of linked lists to track the active voxels around the interface. This allows incremental extension of the active region as needed without incurring any significant overhead. While consistently <math>O(n^2)</math> efficient in time, <math>O(n^3)</math> storage space is still required by the sparse field level set method. See <ref name=Lankton>S. Lankton. "Sparse Field Method - Technical Report." April 21, 2009
===Sparse block grid===
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