The Set Function $${\mathcal {T}}$$

When the level set algorithm is used to segment an image, the level set function must be initialized periodically to ensure that it remains a signed distance function (SDF). To avoid this defect, an improved regularized level set method-based image segmentation approach is presented. First, a new potential function is defined and introduced to reconstruct a new distance regularization term to solve this issue of periodically initializing the level set function. Second, by combining the distance regularization term with the internal and external energy terms, a new energy functional is developed. Then, the process of the new energy functional evolution is derived by using the calculus of variations and the steepest descent approach, and a partial differential equation is designed. Finally, an improved regularized level set-based image segmentation (IRLS-IS) method is proposed. Numerical experimental results demonstrate that the IRLS-IS method is not only effective and robust to segment noise and intensity-inhomogeneous images but can also analyze complex medical images well.

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On a Fuzzy Integral as the Product-Sum Calculation Between a Set Function and a Fuzzy Measure

Information Processing and Management of Uncertainty in Knowledge-Based Systems - Communications in Computer and Information Science ◽

10.1007/978-3-319-40596-4_9 ◽

2016 ◽

pp. 91-100 ◽

Cited By ~ 1

Author(s):

Eiichiro Takahagi

Keyword(s):

Fuzzy Measure ◽

Fuzzy Integral ◽

Set Function

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A Method for Tracking a Solid Body in a Fluid Field in Immersed Boundary Methods

Volume 1: Flow Manipulation and Active Control; Bio-Inspired Fluid Mechanics; Boundary Layer and High-Speed Flows; Fluids Engineering Education; Transport Phenomena in Energy Conversion and Mixing; Turbulent Flows; Vortex Dynamics; DNS/LES and Hybrid RANS/LES Methods; Fluid Structure Interaction; Fluid Dynamics of Wind Energy; Bubble, Droplet, and Aerosol Dynamics ◽

10.1115/fedsm2018-83012 ◽

2018 ◽

Author(s):

Guangfa Yao

Keyword(s):

Level Set ◽

Solid Body ◽

Volume Fraction ◽

Transformation Matrix ◽

The Body ◽

New Method ◽

Immersed Boundary ◽

Body Interaction ◽

Level Set Function ◽

Set Function

Immersed boundary method has got increasing attention in modeling fluid-solid body interaction using computational fluid dynamics due to its robustness and simplicity. It usually simulates fluid-solid body interaction by adding a body force in the momentum equation. This eliminates the body conforming mesh generation that frequently requires a very labor-intensive and challenging task. But accurately tracking an arbitrary solid body is required to simulate most real world problems. In this paper, a few methods that are used to track a rigid solid body in a fluid domain are briefly reviewed. A new method is presented to track an arbitrary rigid solid body by solving a transformation matrix and identifying it using a level set function. Knowing level set function, the solid volume fraction can be derived if needed. A three-dimensional example is used to study a few methods used to represent and solve the transformation matrix, and demonstrate the presented new method.

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NUMERICAL SIMULATION OF 2D LIQUID SLOSHING

International Journal of Applied Mechanics ◽

10.1142/s1758825112500147 ◽

2012 ◽

Vol 04 (02) ◽

pp. 1250014 ◽

Cited By ~ 1

Author(s):

LI CAI ◽

JUN ZHOU ◽

FENGQI ZHOU ◽

WENXIAN XIE ◽

YUFENG NIE

Keyword(s):

Kinematic Viscosity ◽

Numerical Experiments ◽

Viscous Fluids ◽

Liquid Sloshing ◽

Ghost Fluid Method ◽

Weighted Essentially Nonoscillatory ◽

Level Set Function ◽

Real Fluid ◽

Set Function

In this paper, we present an extended ghost fluid method (GFM) for computations of liquid sloshing in incompressible multifluids consisting of inviscid and viscous regions. That is, the sloshing interface between inviscid and viscous fluids is tracked by the zero contour of a level set function and the appropriate sloshing interface conditions are captured by defining ghost fluids that have the velocities and pressure of the real fluid at each point while fixing the density and the kinematic viscosity of the other fluid. Meanwhile, a second order single-fluid solver, the central-weighted-essentially-nonoscillatory(CWENO)-type central-upwind scheme, is developed from our previous works. The high resolution and the nonoscillatory quality of the scheme can be verified by solving several numerical experiments. Nonlinear sloshing inside a pitching partially filled rectangular tank with/without baffles has been investigated.

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