scholarly journals An Improved Joint Optimization of Multiple Level Set Functions for the Segmentation of Overlapping Cervical Cells

2015 ◽  
Vol 24 (4) ◽  
pp. 1261-1272 ◽  
Author(s):  
Zhi Lu ◽  
Gustavo Carneiro ◽  
Andrew P. Bradley
Keyword(s):  
Level Set ◽  
Joint Optimization ◽  
Multiple Level ◽  
Set Functions ◽  
Cervical Cells ◽  
Level Set Functions

scholarly journals Identifying arbitrary parameter zonation using multiple level set functions

2018 ◽  
Vol 364 ◽  
pp. 257-273
Author(s):  
Zhiming Lu ◽  
Velimir V. Vesselinov ◽  
Hongzhuan Lei
Keyword(s):  
Level Set ◽  
Arbitrary Parameter ◽  
Multiple Level ◽  
Set Functions ◽  
Level Set Functions

A multiple level-set method for 3D inversion of magnetic data

Geophysics ◽  
2017 ◽  
Vol 82 (5) ◽  
pp. J61-J81 ◽  
Author(s):  
Wenbin Li ◽  
Wangtao Lu ◽  
Jianliang Qian ◽  
Yaoguo Li
Keyword(s):  
Inverse Problem ◽  
Magnetic Susceptibility ◽  
Level Set Method ◽  
Level Set ◽  
A Priori ◽  
Magnetic Data ◽  
Specific Class ◽  
Multiple Level ◽  
Set Functions ◽  
Level Set Functions

We have developed a multiple level-set method for inverting magnetic data produced by weak induced magnetization only. The method is designed to deal with a specific class of 3D magnetic inverse problems in which the magnetic susceptibility is known and the objective of the inversion is to find the boundary or geometric shape of the causative bodies. We adopt the conceptual representation of the subsurface geologic structure by a set of magnetic bodies, each having a uniform magnetic susceptibility embedded in a nonmagnetic background. This representation enables us to reformulate the magnetic inverse problem into a domain inverse problem for those unknown domains defining the supports of the magnetic causative bodies. Because each body may take on a variety of shapes, and we may not know the number of bodies a priori either, we use multiple level-set functions to parameterize these domains so that the domain inverse problem can be further reduced to an optimization problem of multiple level-set functions. To efficiently compute gradients of the nonlinear functional arising from the multiple level-set formulation, we take advantage of the rapid decay of the magnetic kernels with distance to significantly speed up the matrix-vector multiplications in the minimization process. We apply the new method to the synthetic and field data sets and determine its effectiveness.

High-order time-marching reinitialization for regional level-set functions

2018 ◽  
Vol 354 ◽  
pp. 311-319 ◽  
Author(s):  
Shucheng Pan ◽  
Xiuxiu Lyu ◽  
Xiangyu Y. Hu ◽  
Nikolaus A. Adams
Keyword(s):  
Level Set ◽  
High Order ◽  
Regional Level ◽  
Set Functions ◽  
Time Marching ◽  
High Order Time ◽  
Level Set Functions
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