scholarly journals Adaptive Regularized Level Set Method for Weak Boundary Object Segmentation

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Meng Li ◽  
Chuanjiang He ◽  
Yi Zhan
Keyword(s):  
Level Set Method ◽  
Level Set ◽  
Active Contours ◽  
Boundary Object ◽  
Level Curve ◽  
External Energy ◽  
Zero Level ◽  
Level Set Function ◽  
Wide Range ◽  
Level Set Evolution

An adaptive regularized level set method for image segmentation is proposed. A weightedp(x)-Dirichlet integral is presented as a geometric regularization on zero level curve, which is used to diminish the influence of image noise on level set evolution while ensuring the active contours not to pass through weak object boundaries. The idea behind the new energy integral is that the amount of regularization on the zero level curve can be adjusted automatically by the variable exponentp(x)to fit the image data. This energy is then incorporated into a level set formulation with an external energy term that drives the motion of the zero level set toward the desired objects boundaries, and a level set function regularization term that is necessary for maintaining stable level set evolution. The proposed model has been applied to a wide range of both real and synthetic images with promising results.

Kantorovich-Rubinstein misfit for inverting gravity-gradient data by the level-set method

Geophysics ◽  
2019 ◽  
Vol 84 (5) ◽  
pp. G55-G73
Author(s):  
Guanghui Huang ◽  
Xinming Zhang ◽  
Jianliang Qian
Keyword(s):  
Level Set Method ◽  
Level Set ◽  
Random Noise ◽  
Magnetic Data ◽  
Gravity Gradient ◽  
Local Minima ◽  
Target Model ◽  
Level Set Function ◽  
Level Set Evolution ◽  
Set Function

We have developed a novel Kantorovich-Rubinstein (KR) norm-based misfit function to measure the mismatch between gravity-gradient data for the inverse gradiometry problem. Under the assumption that an anomalous mass body has an unknown compact support with a prescribed constant value of density contrast, we implicitly parameterize the unknown mass body by a level-set function. Because the geometry of an underlying anomalous mass body may experience various changes during inversion in terms of level-set evolution, the classic least-squares ([Formula: see text]-norm-based) and the [Formula: see text]-norm-based misfit functions for governing the level-set evolution may potentially induce local minima if an initial guess of the level-set function is far from that of the target model. The KR norm from the optimal transport theory computes the data misfit by comparing the modeled data and the measured data in a global manner, leading to better resolution of the differences between the inverted model and the target model. Combining the KR norm with the level-set method yields a new effective methodology that is not only able to mitigate local minima but is also robust against random noise for the inverse gradiometry problem. Numerical experiments further demonstrate that the new KR norm-based misfit function is able to recover deep dipping flanks of SEG/EAGE salt models even at extremely low signal-to-noise ratios. The new methodology can be readily applied to gravity and magnetic data as well.

An Improved Integrated Active Contour Model without Re-Initialization for Vector-Valued Images Segmentation

2012 ◽  
Vol 429 ◽  
pp. 271-276 ◽  
Author(s):  
Ji Zhao ◽  
Fu Qun Shao ◽  
Ji Zhao ◽  
Xue Dong Zhang ◽  
Chuang Feng
Keyword(s):  
Level Set ◽  
Active Contour ◽  
Active Contours ◽  
Active Contour Model ◽  
Nonlinear Heat Equation ◽  
Level Set Function ◽  
Implementation Scheme ◽  
Level Set Evolution ◽  
Set Function ◽  
Vector Images

In this paper, an improved variational formulation for active contours model is introduced to force level set function to become fast and stably close to signed distance function, which can completely eliminate the need of the costly re-initialization procedure. A restriction item that is a nonlinear heat equation with balanced diffusion rate is attached to variational Integrated Active Contour (IAC) model on the basis of analysis on regions and edges information from all channels of the valued-vector images, so that the level set evolution segmentation process becomes fast and stable. In addition, more efficient discretization method with spatial rotation-invariance gradient and divergence operator is proposed as numerical implementation scheme. Finally, the experiments on some images have demonstrated the efficiency, accuracy and robustness of the proposed method.

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.

scholarly journals Real-Time Runway Detection for Infrared Aerial Image Using Synthetic Vision and an ROI Based Level Set Method

2018 ◽  
Vol 10 (10) ◽  
pp. 1544 ◽  
Author(s):  
Changjiang Liu ◽  
Irene Cheng ◽  
Anup Basu
Keyword(s):  
Real Time ◽  
Level Set Method ◽  
Level Set ◽  
Infrared Image ◽  
Region Of Interest ◽  
Aerial Image ◽  
Real Time Processing ◽  
Synthetic Vision ◽  
Level Set Function ◽  
Rough Region

We present a new method for real-time runway detection embedded in synthetic vision and an ROI (Region of Interest) based level set method. A virtual runway from synthetic vision provides a rough region of an infrared runway. A three-thresholding segmentation is proposed following Otsu’s binarization method to extract a runway subset from this region, which is used to construct an initial level set function. The virtual runway also gives a reference area of the actual runway in an infrared image, which helps us design a stopping criterion for the level set method. In order to meet the needs of real-time processing, the ROI based level set evolution framework is implemented in this paper. Experimental results show that the proposed algorithm is efficient and accurate.

NUMERICAL SIMULATION OF RAYLEIGH–TAYLOR INSTABILITY BASED ON AN IMPROVED PARTICLE LEVEL SET METHOD

2014 ◽  
Vol 11 (04) ◽  
pp. 1350094 ◽  
Author(s):  
HUI TIAN ◽  
GUOJUN LI ◽  
XIONGWEN ZHANG
Keyword(s):  
Level Set Method ◽  
Level Set ◽  
Stokes Equations ◽  
Density Ratio ◽  
Immiscible Fluids ◽  
Taylor Instability ◽  
Wide Range ◽  
Particle Level ◽  
Rayleigh Taylor Instability ◽  
Particle Level Set Method

An improved particle correction procedure for particle level set method is proposed and applied to the simulation of Rayleigh–Taylor instability (RTI) of the incompressible two-phase immiscible fluids. In the proposed method, an improved particle correction method is developed to deal with all the relative positions between escaped particles and cell corners, which can reduce the disturbance arising in the distance function correction process due to the non-normal direction movement of escaped particles. The improved method is validated through accurately capturing the moving interface of the Zalesak's disk. Furthermore, coupled with the projection method for solving the Navier–Stokes equations, the time-dependent evolution of the RTI interface over a wide range of Reynolds numbers, Atwood numbers and Weber numbers are numerically investigated. A good agreement between the present results and the existing analytical solutions is obtained and the accuracy of the proposed method is further verified. Moreover, the effects of control parameters including viscosity, density ratio, and surface tension coefficient on the evolution of RTI are analyzed in detail, and a critical Weber number for the development of RTI is found.

Numerical Simulation of Breaking Waves Using a Level Set Method

2002 ◽  
Author(s):  
Pablo Go´mez ◽  
Julio Herna´ndez ◽  
Joaqui´n Lo´pez ◽  
Fe´lix Faura
Keyword(s):  
Free Surface ◽  
Level Set Method ◽  
Level Set ◽  
Stokes Equations ◽  
Numerical Study ◽  
Operating Conditions ◽  
Breaking Wave ◽  
Level Set Function ◽  
Set Function ◽  
The Impact

A numerical study of the initial stages of wave breaking processes in shallow water is presented. The waves considered are assumed to be generated by moving a piston in a two-dimensional channel, and may appear, for example, in the injection chamber of a high-pressure die casting machine under operating conditions far from the optimal. A numerical model based on a finite-difference discretization of the Navier-Stokes equations in a Cartesian grid and a second-order approximate projection method has been developed and used to carry out the simulations. The evolution of the free surface is described using a level set method, with a reinitialization procedure of the level set function which uses a local grid refinement near the free surface. The ability of different algorithms to improve mass conservation in the reinitialization step of the level set function has been tested in a time-reversed single vortex flow. The results for the breaking wave profiles show the flow characteristics after the impact of the first plunging jet onto the wave’s forward face and during the subsequent splash-up.

scholarly journals A local solution approach for level-set based structural topology optimization in isogeometric analysis

2020 ◽  
Vol 7 (4) ◽  
pp. 514-526
Author(s):  
Zijun Wu ◽  
Shuting Wang ◽  
Renbin Xiao ◽  
Lianqing Yu
Keyword(s):  
Topology Optimization ◽  
Level Set ◽  
Isogeometric Analysis ◽  
Iteration Process ◽  
Solid Material ◽  
Optimization Approach ◽  
Structural Topology ◽  
Zero Level ◽  
Solution Approach ◽  
Level Set Function

Abstract This paper develops a new topology optimization approach for minimal compliance problems based on the parameterized level set method in isogeometric analysis. Here, we choose the basis functions as level set functions. The design variables are obtained with Greville abscissae based on the corresponding collocation points. The zero-level set boundaries are derived from the level set function values of the interpolation points in all knot spans. In the optimization iteration process, the whole design domain is discretized into two types of subdomains around the zero-level set boundaries, undesign area with void materials and redesign domain with solid materials. To decrease the size of equations and the computational consumptions, only the solid material area is recalculated and the void material area is discarded according to the high accuracy of isogeometric analysis. Numerical examples demonstrate the validity of the proposed optimization method.

NEIGHBOR SUPPORT BASED SPEED FUNCTION FOR LEVEL SET METHOD

2010 ◽  
Vol 18 (spec01) ◽  
pp. 149-158 ◽  
Author(s):  
XUESHU LIU ◽  
YUTAKA OHTAKE ◽  
HIROMASA SUZUKI
Keyword(s):  
Level Set Method ◽  
Level Set ◽  
Normal Direction ◽  
Mesh Segmentation ◽  
Zero Level ◽  
Sharp Feature ◽  
Normal Diffusion ◽  
Speed Function ◽  
Made In

With a different speed function, Level Set Method has been widely applied to many applications. Generally speaking, speed function may depend on many factors, such as curvature, normal direction. In this paper, we discuss a novel speed function which is only determined by neighbors' support. With enough support, zero level set can move or stop. Otherwise, it must wait for a moment before a decision to move or stop is made. In addition, an algorithm based on normal diffusion is proposed to smooth the zero level set, which can preserve the sharp feature and round corner at the same time. Experimentally, the proposed method has been successfully used for interested objection segmentation and mesh segmentation.

An Improved Three-Dimensional Level Set Method for Gas-Liquid Two-Phase Flows

2004 ◽  
Vol 126 (4) ◽  
pp. 578-585 ◽  
Author(s):  
Hiroyuki Takahira ◽  
Tomonori Horiuchi ◽  
Sanjoy Banerjee
Keyword(s):  
Level Set Method ◽  
Level Set ◽  
Stokes Equations ◽  
Interpolation Method ◽  
Density Ratio ◽  
Three Dimensional ◽  
Mass Conservation ◽  
Staggered Grid ◽  
Two Phase ◽  
Level Set Function

For the present study, we developed a three-dimensional numerical method based on the level set method that is applicable to two-phase systems with high-density ratio. The present solver for the Navier-Stokes equations was based on the projection method with a non-staggered grid. We improved the treatment of the convection terms and the interpolation method that was used to obtain the intermediate volume flux defined on the cell faces. We also improved the solver for the pressure Poisson equations and the reinitialization procedure of the level set function. It was shown that the present solver worked very well even for a density ratio of the two fluids of 1:1000. We simulated the coalescence of two rising bubbles under gravity, and a gas bubble bursting at a free surface to evaluate mass conservation for the present method. It was also shown that the volume conservation (i.e., mass conservation) of bubbles was very good even after bubble coalescence.

Parametric Shape and Topology Optimization: A New Level Set Approach Based on Cardinal Kernel Functions

2017 ◽  
Author(s):  
Long Jiang ◽  
Shikui Chen ◽  
Xiangmin Jiao
Keyword(s):  
Topology Optimization ◽  
Level Set Method ◽  
Level Set ◽  
Material Property ◽  
Kernel Function ◽  
Level Set Methods ◽  
Level Set Function ◽  
Set Function ◽  
Distance Regularization ◽  
Parametric Level Set Method

The parametric level set method is an extension of the conventional level set methods for topology optimization. By parameterizing the level set function, conventional levels let methods can be easily coupled with mathematical programming to achieve better numerical robustness and computational efficiency. Furthermore, the parametric level set scheme not only can inherit the original advantages of the conventional level set methods, such as clear boundary representation and high topological changes handling flexibility but also can alleviate some un-preferred features from the conventional level set methods, such as needing re-initialization. However, in the RBF-based parametric level set method, it was difficult to determine the range of the design variables. Moreover, with the mathematically driven optimization process, the level set function often results in significant fluctuations during the optimization process. This brings difficulties in both numerical stability control and material property interpolation. In this paper, an RBF partition of unity collocation method is implemented to create a new type of kernel function termed as the Cardinal Basis Function (CBF), which employed as the kernel function to parameterize the level set function. The advantage of using the CBF is that the range of the design variable, which was the weight factor in conventional RBF, can be explicitly specified. Additionally, a distance regularization energy functional is introduced to maintain a desired distance regularized level set function evolution. With this desired distance regularization feature, the level set evolution is stabilized against significant fluctuations. Besides, the material property interpolation from the level set function to the finite element model can be more accurate.

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