• 한국전산유체공학회:학술대회논문집
• /
• 2009.04a
• /
• pp.283-289
• /
• 2009

In level set method, material properties are made to change smoothly across an interface of two materials with different properties by introducing an interpolation or smoothing scheme. So far, the weighted arithmetic mean (WAM) method has been exclusively adopted in level set method, without complete assessment for its validity. We showed here that the weighted harmonic mean (WHM) method for rate constants of various rate processes, including viscosity, thermal conductivity, electrical conductivity, and permittivity, gives much more accurate results than the WAM method. The selection of interpolation scheme is particularly important in multi-phase electrohydrodynamic problems in which driving force for fluid flow is electrical force exerted on the phase interface. Our analysis also showed that WHM method for both electrical conductivity and permittivity gives not only more accurate, but also more physically realistic distribution of electrical force at the interface. Our arguments are confirmed by numerical simulations of drop deformation under DC electric field.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2001.12a
• /
• pp.353-356
• /
• 2001

In this paper, we study the existence of fuzzy solution for the following differential system with fuzzy coefficient using the different two methods: (equation omitted), where a, b is the fuzzy natural number generated by fuzzy number l . The a-level set of the fuzzy number (equation omitted). The -level set of a is (equation omitted) and -level set of b is (equation omitted).

• KOGO NEWS
• /
• v.6 no.1
• /
• pp.29-33
• /
• 2006

Gene set analysis is a new concept and method. to analyze and interpret microarray gene expression data and tries to extract biological meaning from gene expression data at gene set level rather than at gene level. Compared with methods which select a few tens or hundreds of genes before gene ontology and pathway analysis, gene set analysis identifies important gene ontology terms and pathways more consistently and performs well even in gene expression data sets with minimal or moderate gene expression changes. Moreover, gene set analysis is useful for comparing multiple gene expression data sets dealing with similar biological questions. This review briefly summarizes the rationale behind the gene set analysis and introduces several algorithms and tools now available for gene set analysis.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.18 no.3
• /
• pp.225-244
• /
• 2014

In this work, we discuss segmentation algorithms based on the level set method that incorporates shape prior knowledge. Fundamental segmentation models fail to segment desirable objects from a background when the objects are occluded by others or missing parts of their whole. To overcome these difficulties, we incorporate shape prior knowledge into a new segmentation energy that, uses global and local image information to construct the energy functional. This method improves upon other methods found in the literature and segments images with intensity inhomogeneity, even when images have missing or misleading information due to occlusions, noise, or low-contrast. We consider the case when the shape prior is placed exactly at the locations of the desired objects and the case when the shape prior is placed at arbitrary locations. We test our methods on various images and compare them to other existing methods. Experimental results show that our methods are not only accurate and computationally efficient, but faster than existing methods as well.

• Proceedings of the IEEK Conference
• /
• 1998.06a
• /
• pp.765-768
• /
• 1998

Level set method is used for extracting a shape within an image. This method is based on the ideas developed by osher and sethian to model propagating solid/liquid interfaces moving with curvature-dependent speeds. In this paper, we propose the new generalized formulation and stopping function of evolution for more accurate extraction of shape. Our method shows good results in some cases compared with the conventional ones.

• Communications of the Korean Mathematical Society
• /
• v.13 no.3
• /
• pp.655-681
• /
• 1998

Discontinuous solutions or interfaces are common in nature, for examples, shock waves or material interfaces. However, their numerical computation is difficult by the feature of discontinuities. In this paper, we summarize the numerical approaches for discontinuities and interfaces appearing mostly in the system of hyperbolic conservation laws, and explain various numerical methods for them. We explain two numerical approaches to handle discontinuities in the solution: shock capturing and shock tracking, and illustrate their underlying algorithms and mathematical problems. The front tracking method is explained in details and the level set method is outlined briefly. The several applications of front tracking are illustrated, and the research issues in this field are discussed.

• 한국전산유체공학회:학술대회논문집
• /
• 2009.11a
• /
• pp.193-200
• /
• 2009

Recently, there have been efforts to construct hybrids among the existing methodologies for multiphase flow such as VOF, Level Set, and Front Tracking with the intention of facilitating simulations of general three-dimensional problems. As one of the hybrid method, we have developed the Level Contour Reconstruction Method (LCRM) for general three-dimensional multiphase flows including phase change. The main idea was focused on simplicity and a robust algorithm especially for the three-dimensional case. It combines characteristics of both Front Tracking and Level Set methods. While retaining an explicitly tracked interface using interfacial elements, the calculation of a vector distance function plays a crucial role in the periodic reconstruction of the interface elements in the LCRM method to maintain excellent mass conservation and interface fidelity. In addition, compact curvature formulation is incorporated for the calculation of the surface tension force thereby reducing parasitic currents to a negligible level.

• Proceedings of the Korea Information Processing Society Conference
• /
• 2010.11a
• /
• pp.668-671
• /
• 2010

In this paper, we present a novel automatic algorithm for scalp and skull segmentation in T1-weighted head MR images. First, the scalp and skull part are constructed by using intensity threshold. Second, the scalp outer surface is extracted based on an active level set method. Third, the skull inner surface is extracted using a canny edge detection algorithm. Finally, the fast sweeping, tagging and level set methods are applied to reconstruct surfaces from the detected points in three-dimensional space. The results of the new segmentation algorithm on MRI data acquired from eight persons were compared with manual segmented data. The average similarity indices for the scalp and skull segmented regions were equal to 84.42% for the test data.

• Proceedings of the KSRS Conference
• /
• v.1
• /
• pp.126-129
• /
• 2006

The marine environment is under considerable threat from intentional or accidental oil spills, ballast water discharged, dredging and infilling for coastal development, and uncontrolled sewage and industrial wastewater discharges. Monitoring spills and illegal oil discharges is an important component in ensuring compliance with marine protection legislation and general protection of the coastal environments. For the monitoring task an image processing system is needed that can efficiently perform the detection and the tracking of oil spills and in this direction a significant amount of research work has taken place mainly with the use of radar (SAR) remote sensing data. In this paper the level set image segmentation technique was tested for the detection of oil spills. Level set allow the evolving curve to change topology (break and merge) and therefore boundaries of particularly intricate shapes can be extracted. Experimental results demonstrated that the level set segmentation can be used for the efficient detection and monitoring of oil spills, since the method coped with abrupt shape’s deformations and splits.

• Steel and Composite Structures
• /
• v.47 no.5
• /
• pp.569-585
• /
• 2023

This paper proposes an efficient approach for the structural topology optimization of bi-directional functionally graded structures by incorporating popular radial basis functions (RBFs) into an implicit level set (ILS) method. Compared to traditional element density-based methods, a level set (LS) description of material boundaries produces a smoother boundary description of the design. The paper develops RBF implicit modeling with multiquadric (MQ) splines, thin-plate spline (TPS), exponential spline (ES), and Gaussians (GS) to define the ILS function with high accuracy and smoothness. The optimization problem is formulated by considering RBF-based nodal densities as design variables and minimizing the compliance objective function. A LS-RBF optimization method is proposed to transform a Hamilton-Jacobi partial differential equation (PDE) into a system of coupled non-linear ordinary differential equations (ODEs) over the entire design domain using a collocation formulation of the method of lines design variables. The paper presents detailed mathematical expressions for BiDFG beams topology optimization with two different material models: continuum functionally graded (CFG) and mechanical functionally graded (MFG). Several numerical examples are presented to verify the method's efficiency, reliability, and success in accuracy, convergence speed, and insensitivity to initial designs in the topology optimization of two-dimensional (2D) structures. Overall, the paper presents a novel and efficient approach to topology optimization that can handle bi-directional functionally graded structures with complex geometries.