Biomedical Engineering Reference
In-Depth Information
4.4 Conclusion
The level set method has been used for a wide variety of applications and con-
tinues to be a very popular tool. Since 2001, the method has been applied to
multiphase flow [7-9, 11, 16, 26, 34, 48, 49, 58, 61, 64, 72, 92, 94, 108-113, 135-138],
combustion [98], granular flow [36], surfactants [1], solid mechanics [90, 119],
crack propagation [53, 116, 117, 127], welding [65, 66], superconductor man-
ufacturing [91], sintering [77], crystal growth [70, 71], Ostwald ripening and
epitaxial growth [18, 37, 51, 89, 95], etching and deposition [59, 62, 63, 73, 96,
97, 130, 132], inverse scattering and shape reconstruction [15, 31, 43-45], im-
age processing [10, 13, 27, 54, 79, 93, 99, 125, 126, 128, 134], medical imaging
[30, 87, 122], shape optimization and tomography [5, 60, 86, 131], grid genera-
tion [57], bacterial biofilms [33], tissue engineering [83], and string theory [56].
The breadth of the applications is a tribute to the level set method and its
creators.
In addition, the fast marching method on its own has made a contribution to a
number of areas including crack propagation [24,120], shape reconstruction [35],
image processing [4, 28, 47, 52, 67, 114], medical imaging [6, 12, 32, 133], computer
graphics and visualization [139], and robotic navigation [68, 69].
Despite its tremendous popularity, the level set method is not suitable for
every interface propagation problem. The implicit representation of the interface
can be cumbersome at times, and if the more powerful features of the level set
method are not required for a given problem, then simpler methods may be
more appropriate. This is especially true if the alternative methods are also
faster, which can often be the case. For this reason, it is important to remember
the following key distinguishing features of the level set method:
1. topological changes are handled smoothly with no user intervention re-
quired,
2. corners and cusps in the interface are handled properly by using methods
borrowed from hyperbolic conservation laws,
3. the method is easily extended to higher dimensions.
Any one of these reasons may be sufficient to employ the level set method, but
not every problem requires these advantages. In that case, it would serve the
