Numerical Simulation of Interface Time Evolution by Oriented Lagrangian Particles and Level-Set Method

2009 ◽  
Author(s):  
Sandro Ianniello ◽  
Andrea Di Mascio
Keyword(s):  
Level Set ◽  
Eikonal Equation ◽  
Evolution Equations ◽  
Normal Vector ◽  
Geometrical Properties ◽  
Level Set Function ◽  
Standard Level ◽  
Fundamental Vector ◽  
Set Function ◽  
Level Set Approach

A new computational approach for tracking evolving interfaces is proposed. The procedure is based on the copuling of lagrangian massless particles and the standard Level-Set methodology, and the use of evolution equations for fundamental vector and tensor quantities related to the geometrical properties of the interface Γ. In particular, the normal vector n and the second fundamental tensor ∇n are linked to the particles and advected with them; in this way, the particles can be located upon Γ and enable a step–by–step calculation of the Level–Set function φ through a direct solution of the eikonal equation. No transport equation and reinitialization procedure for φ have to be taken into account and the usual numerical diffusion affecting the Level–Set approach is removed. The method is easy to code and carries out an accurate reconstruction of the front, limited only by the spatial resolution of the mesh.

FCMLSM Segmentation of Micro-Vessels in Slight Defocused Microscopic Images

2019 ◽  
Vol 23 (6) ◽  
pp. 1073-1079
Author(s):  
Zhongming Luo ◽  
Yu Zhang ◽  
Zixuan Zhou ◽  
Xuan Bi ◽  
Haibin Wu ◽  
...  
Keyword(s):  
Image Segmentation ◽  
Level Set ◽  
Clustering Algorithm ◽  
Evolution Equations ◽  
High Efficiency ◽  
Level Set Function ◽  
Level Set Segmentation ◽  
Segmentation Algorithms ◽  
Fcm Clustering ◽  
Set Function

To address problems relating to microscopic micro-vessel images of living bodies, including poor vessel continuity, blurry boundaries between vessel edges and tissue and uneven field illuminance, and this paper put forward a fuzzy-clustering level-set segmentation algorithm. By this method, pre-treated micro-vessel images were segmented by the fuzzy c-means (FCM) clustering algorithm to obtain original contours of interesting areas in images. By the evolution equations of the improved level set function, accurate segmentation of microscopic micro-vessel images was realized. This method can effectively solve the problem of manual initialization of contours, avoid the sensitivity to initialization and improve the accuracy of level-set segmentation. The experiment results indicate that compared with traditional micro-vessel image segmentation algorithms, this algorithm is of high efficiency, good noise immunity and accurate image segmentation.

scholarly journals Automatic Global Level Set Approach for Lumbar Vertebrae CT Image Segmentation

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Yang Li ◽  
Wei Liang ◽  
Yinlong Zhang ◽  
Jindong Tan
Keyword(s):  
Image Segmentation ◽  
Level Set ◽  
Lumbar Vertebrae ◽  
Ct Image ◽  
Global Level ◽  
Level Set Function ◽  
Weak Boundary ◽  
Irregular Boundaries ◽  
Set Function ◽  
Level Set Approach

Vertebrae computed tomography (CT) image automatic segmentation is an essential step for Image-guided minimally invasive spine surgery. However, most of state-of-the-art methods still require human intervention due to the inherent limitations of vertebrae CT image, such as topological variation, irregular boundaries (double boundary, weak boundary), and image noise. Therefore, this paper intentionally designed an automatic global level set approach (AGLSA), which is capable of dealing with these issues for lumbar vertebrae CT image segmentation. Unlike the traditional level set methods, we firstly propose an automatically initialized level set function (AILSF) that comprises hybrid morphological filter (HMF) and Gaussian mixture model (GMM) to automatically generate a smooth initial contour which is precisely adjacent to the object boundary. Secondly, a regularized level set formulation is introduced to overcome the weak boundary leaking problem, which utilizes the region correlation of histograms inside and outside the level set contour as a global term. Ultimately, a gradient vector flow (GVF) based edge-stopping function is employed to guarantee a fast convergence rate of the level set evolution and to avoid level set function oversegmentation at the same time. Our proposed approach has been tested on 115 vertebrae CT volumes of various patients. Quantitative comparisons validate that our proposed AGLSA is more accurate in segmenting lumbar vertebrae CT images with irregular boundaries and more robust to various levels of salt-and-pepper noise.

scholarly journals Evaluation of Level Set reinitialization algorithms for phase change simulation on unstructured grids

2020 ◽  
pp. 43-48
Author(s):  
Guillaume Sahut ◽  
Giovanni Ghigliotti ◽  
Guillaume Balarac ◽  
Philippe Marty
Keyword(s):  
Phase Change ◽  
Level Set ◽  
Unstructured Grids ◽  
Bubble Radius ◽  
Mass Transfer Rate ◽  
Normal Vector ◽  
Pressure Jump ◽  
Level Set Function ◽  
Set Function ◽  
Liquid Vapor

In this study, we present different numerical methods for the simulation of liquid-vapor phase change (boiling). We use a Level Set formalism to capture the liquid-vapor interface. Such a formalism requires a reinitialization (aka redistancing) step of the Level Set function after advection. This step is critical for phase change simulation as it must neither move the interface nor induce perturbations in the Level Set function profile, otherwise the normal vector to the interface and its curvature, two quantities that are crucial to define respectively the interface velocity due to phase change and the pressure jump at the interface due to surface tension, would be in turn affected by too large numerical errors. Here we present a comparison of different reinitialization algorithms of the Level Set function for boiling simulations, on structured and unstructured grids. These methods are then validated against the analytical case of a static growing bubble with a fixed mass transfer rate. In particular, we observe that at the time corresponding to a doubled bubble radius, the error on the bubble radius decreases with the grid cell size for all presented methods.

Generative Design of Origami-Inspired Mechanisms With a Variational Level Set Approach

2020 ◽  
Author(s):  
Qian Ye ◽  
Xianfeng David Gu ◽  
Shikui Chen
Keyword(s):  
Level Set ◽  
3D Structure ◽  
Level Set Function ◽  
Shell Models ◽  
Proposed Model ◽  
Out Of Plane ◽  
Variational Level Set ◽  
Systematic Solution ◽  
Set Function ◽  
Level Set Approach

Abstract Origami has inspired the engineering design of self-assemble and re-configurable devices. Under particular crease patterns, a 2D flatten object can be transformed into a complex 3D structure. This work intends to find out a systematic solution for topology optimization of origami structures. The origami mechanism is simulated using shell models where the in-plane membrane, out of plane bending, and shear deformation can be well captured. Moreover, the pattern of the folds is represented implicitly by the boundaries of the level set function. The topology of the folds is optimized by minimizing a new multiobjective function, aiming to balance the kinematic performance with the structural stiffness as well as the geometric requirements. Besides regular straight folds, our proposed model can mimic crease patterns with curved folds. With the folding curves implicitly represented, the curvature flow are utilized to control the complexity of the generated folds. The effectiveness of the proposed method is demonstrated through the computational generation and physical validation of a thin-shell origami gripper.

scholarly journals An Image Segmentation Method Based on Improved Regularized Level Set Model

2018 ◽  
Vol 8 (12) ◽  
pp. 2393 ◽  
Author(s):  
Lin Sun ◽  
Xinchao Meng ◽  
Jiucheng Xu ◽  
Shiguang Zhang
Keyword(s):  
Image Segmentation ◽  
Level Set ◽  
Energy Functional ◽  
External Energy ◽  
Regularization Term ◽  
Level Set Function ◽  
New Energy ◽  
Segmentation Approach ◽  
Set Function ◽  
Distance Regularization

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.

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

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.

Low-Dimensional Components of Flows With Large Free/Moving-Surface Motion

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Yi Zhang ◽  
Solomon C. Yim
Keyword(s):  
Flow Field ◽  
Level Set ◽  
Wave Impact ◽  
Moving Surface ◽  
Surface Motion ◽  
Level Set Function ◽  
Highly Nonlinear ◽  
Flow Systems ◽  
Low Dimensional ◽  
Set Function

Flow systems with highly nonlinear free/moving surface motion are common in engineering applications, such as wave impact and fluid-structure interaction (FSI) problems. In order to reveal the dynamics of such flows, as well as provide a reduced-order modeling (ROM) for large-scale applications, we propose a proper orthogonal decomposition (POD) technique that couples the velocity flow field and the level-set function field, as well as a proper normalization for the snapshots data so that the low-dimensional components of the flow can be retrieved with a priori knowledge of equal distribution of the total variance between velocity and level-set function data. Through numerical examples of a sloshing problem and a water entry problem, we show that the low-dimensional components obtained provide an efficient and accurate approximation of the flow field. Moreover, we show that the velocity contour and orbits projected on the space of the reduced basis greatly facilitate understanding of the intrinsic dynamics of the flow systems.

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