Level set (data structures): Difference between revisions

Revision as of 06:44, 11 October 2014

Revision as of 23:20, 1 June 2016

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===Narrow band===

The narrow band level set method, introduced in 1995 by Adalsteinsson and Sethian,<ref name="Adalsteinsson">Adalsteinsson, D. & Sethian, J. A. 1995. "A fast level set method for propagating interfaces." ''[[Journal of Computational Physics]]''. 118(2)269–277.</ref> restricted most computations to a thin band of active [[voxel]]s immediately surrounding the interface, thus reducing the time complexity in three dimensions to <math>O(n^2)</math> for most operations. Periodic updates of the narrowband structure, to rebuild the list of active voxels, were required which entailed an <math>O(n^3)</math> operation in which voxels over the entire volume were accessed. The storage complexity for this narrowband scheme was still <math>O(n^3).</math> Differential constructions over the narrow band ___domain edge require careful interpolation and ___domain alteration schemes to stabilise the solution.<ref>{{cite journal|title=A fast level set Method for Propagating Interfaces|authorauthor1=Adalsteinsson, D and |author2=Sethian, J|year=1994|url=http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.46.1716&rep=rep1&type=ps}}</ref>

===Sparse field===