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Level Set Methods in Segmentation of SDOCT Retinal Images
Published in Ayman El-Baz, Jasjit S. Suri, Level Set Method in Medical Imaging Segmentation, 2019
N Padmasini, R Umamaheswari, Yacin Sikkandar Mohamed, Manavi D Sindal
Level set methods provide a non-parametric way to describe the interface. In contrast to parametric methods—such as snakes that provide an explicit parameterization of the interface—level sets embed the interface implicitly, which has some computational advantages (i.e., regarding propagation and topology of the interface). The level set function φ is defined in the same space as the input data (which is three-dimensional for volumetric OCT data) and maps an input coordinate x to a scalar. The interface is then defined as the curve C for which the level set is zero: C={x|φ(x)=0}. The level set is evolved according to the general level set equation φt=−F|∇φ|
EEMS2015 organizing committee
Published in Yeping Wang, Jianhua Zhao, Advances in Energy, Environment and Materials Science, 2018
The level set method is a numerical technique of track the motion of interfaces. It describes the Interface shape by zero level set function, and gets to chang- ing the interface shape though analyzing the level set function, especially avoiding re-meshing at the time when the level set upgrades, which just conforms to the extended finite element method (Ventura G., 2006). So, in the calculation on the motion of the interface, the fixed mesh can be applied. As is showed in Figure 1, the position needed in calculation can be described by two level set functions ϕ and ϕ, which are perpendicular to each other. The whole field is divided into three parts: general elements, penetrated elements and crack tip elements. And those kinds of elements can be expressed by the level set functions (Stolarska, 2001). In detailed, general elements can be described as:
Scanning Techniques and Image Processing
Published in Yongjie Jessica Zhang, Geometric Modeling and Mesh Generation from Scanned Images, 2018
The level set method [86, 229, 290, 378, 402] is typically a partial differential equation-based variational method, which utilizes a signed function to represent the evolving contour. We can derive a similar flow for the implicit surface based on the motion equation of the contour. Level-set models are topologically flexible, but they are quite expensive in both computational time and memory. A surface in the input image ϕ is represented by an isosurface implicitly, and we have () S={x→|ϕ(x→)=c}
Large-eddy simulation of supercritical free-surface flow in an open-channel contraction
Published in Journal of Hydraulic Research, 2022
Filipa Adzic, Thorsten Stoesser, Yan Liu, Zhihua Xie
The level-set method (LSM) was first presented by Osher and Sethian (1988). It also employs a scalar transport equation to calculate the movement of a signed distance function (the level set), making it computationally cheaper than for instance the MAC method. The free-surface location is defined by a continuous function, more precisely where the signed distance function is equal to zero. The level-set method deals with complex surface topologies well and it can be applied to three dimensional cases with ease (Chang et al., 1996). Jeon et al. (2018) presented an experimental study investigating three-dimensional turbulent flow mechanisms around a non-submerged spur dike that can be used for validation of free-surface computational studies in the future. Several authors used the LSM with LES to simulate turbulent open-channel flows (Chua et al., 2019; S. Kara, Kara, et al., 2015; S. Kang & Sotiropoulos, 2015; S. Kara, Stoesser, et al., 2015; Khosronejad et al., 2019, 2020; R. McSherry & Mulahasan, 2018; Suh et al., 2011; Yue et al., 2005) achieving good agreement with experiments.
Interface Tracking Investigation of Geometric Effects on the Bubbly Flow in PWR Subchannels
Published in Nuclear Science and Engineering, 2019
Jun Fang, Joseph J. Cambareri, Michel Rasquin, Andre Gouws, Ramesh Balakrishnan, Kenneth E. Jansen, Igor A. Bolotnov
Introduced by Osher and Sethian29 and further developed by Sussman et al.,18 the level-set method has been widely used as one of the major interface tracking approaches in multiphase flow simulations. PHASTA incorporates this level-set method to extend the simulation capability from single-phase to two-phase flows.23 The bubble interface is modeled as the zero level set of a smooth function , where is called the first scalar and is represented as the signed distance from the zero level set. That is, at , the level set defines the interface. The scalar is advected with the fluid according to the advection Eq. (4):
Turbulent drag reduction over liquid-infused textured surfaces: effect of the interface dynamics
Published in Journal of Turbulence, 2021
M. Bernardini, E. J. García Cartagena, A. Mohammadi, A. J. Smits, S. Leonardi
The level set method [43] is used to track the motion of the interface between the two fluids, which takes advantage of the previously mentioned signed-distance function , also called the level set function. The interface is implicitly defined by the zero level set of this function . The unit normal and the local curvature can be easily expressed in terms of ϕ, being Since the interface is a material surface, its tracking can be carried out by evolving in time the level set function according to the equation which is written in conservative form due to flow incompressibility.