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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 (http://www.shawnlankton.com/2009/04/sfm-and-active-contours/)</ref> for implementation details.
===Sparse block grid===
The sparse block grid method, introduced by Bridson in 2003 <ref name=Bridson>Bridson, R. 2003. "Computational aspects of dynamic surfaces (dissertation)." [[Stanford University]], Stanford, California.</ref>, divides the entire bounding volume of size <math>n^3</math> into small cubic blocks of <math>m^3</math> voxels each. A coarse grid of size <math>(n/m
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