In this paper we present a selective segmentation model using a dual level set variational formulation.Our variational model aims to segment all objects with one level set function(global)and the selected object,which...In this paper we present a selective segmentation model using a dual level set variational formulation.Our variational model aims to segment all objects with one level set function(global)and the selected object,which is the closest to the geometric constraints(markers),with another level set(local).It is a combination of edge detection,markers distance function and active contour without edges.Experimental results show that our model is more robust than previous work.展开更多
Some basic problems on the level set methods were discussed, such as the method used to preserve the distance junction , the existence and uniqueness of solution for the level set equations. The main contribution is t...Some basic problems on the level set methods were discussed, such as the method used to preserve the distance junction , the existence and uniqueness of solution for the level set equations. The main contribution is to prove that in a neighborhood of the initial zero level set, the level set equations with the restriction of the distance function have a unique solution, which must be the signed distance function with respect to the evolving surface. Some skillful approaches were used: Noticing that any solution for the original equation was a distance function, the original level set equations were transformed into a simpler alternative form. Moreover, since the new system was not a classical one, the system was transformed into an ordinary one, for which the implicit function method was adopted.展开更多
The electric inversion technique reconstructs the subsurface medium distribution from acquired data.On the basis of electric inversion,objects buried under the earth or seabed,such as pipelines and unexploded ordnance...The electric inversion technique reconstructs the subsurface medium distribution from acquired data.On the basis of electric inversion,objects buried under the earth or seabed,such as pipelines and unexploded ordnance,are detected and located in a contactless manner.However,the process of accurately reconstructing the shape of the target object is challenging because electric inversion is a nonlinear and ill-posed problem.In this work,we present an inverse multiquadric(IMQ)regularization method based on the level set function for reconstructing buried pipelines.In the case of locating underwater objects,the unknown inversion area is split into two parts,the background and the pipeline with known conductivity.The geometry of the pipeline is represented based on the level set function for achieving a noiseless inversion image.To obtain a binary image,the IMQ is used as the regularization term,which‘pushes’the level set function away from 0.We also provide an appropriate method to select the bandwidth and regularization parameters for the IMQ regularization term,resulting in reconstructed images with sharp edges.The simulation results and analysis show that the proposed method performs better than classical inversion methods.展开更多
Objective To present a novel modified level set algorithm for medical image segmentation. Methods The algorithm is developed by substituting the speed function of level set algorithm with the region and gradient infor...Objective To present a novel modified level set algorithm for medical image segmentation. Methods The algorithm is developed by substituting the speed function of level set algorithm with the region and gradient information of the image instead of the conventional gradient information. This new algorithm has been tested by a series of different modality medical images. Results We present various examples and also evaluate and compare the performance of our method with the classical level set method on weak boundaries and noisy images. Conclusion Experimental results show the proposed algorithm is effective and robust.展开更多
In the paper, we consider Moran-type sets E;given by sequences {a;};and{n;};. we prove that E;may be decompose into the disjoint union of level sets. Moreover,we define three type of equivalence between two dimension ...In the paper, we consider Moran-type sets E;given by sequences {a;};and{n;};. we prove that E;may be decompose into the disjoint union of level sets. Moreover,we define three type of equivalence between two dimension functions associated to two Morantype sets, respectively, and we classify Moran-type sets by these equivalent relations.展开更多
As a new method, the Level Set method had been developed to compute the interface of two-phase flow. The basic mathematical theory and the detailed method to solve the free surface hydrodynamic problem had been invest...As a new method, the Level Set method had been developed to compute the interface of two-phase flow. The basic mathematical theory and the detailed method to solve the free surface hydrodynamic problem had been investigated. By using the Level Set method, the transformation of a solitary wave over a front step was simulated. The results were in good agreement with laboratory experiments.展开更多
Short time existence and uniqueness for the classical motion are studied by the function of the principal curvatures of a smooth surface and the Evans and Spruck's results are generalized.
A novel flotation froth image segmentation based on threshold level set method is put forward in view of the problem of over-segmentation and under-segmentation which occurs when the existing method segmented the flot...A novel flotation froth image segmentation based on threshold level set method is put forward in view of the problem of over-segmentation and under-segmentation which occurs when the existing method segmented the flotation froth images. Firstly, the proposed method adopts histogram equalization to improve the contrast of the image, and then chooses the upper threshold and lower threshold from grey value of histogram of the image equalization, and complete image segmentation using the level set method. In this paper, the model which integrates edge with region level set model is utilized, and the speed energy term is introduced to segment the target. Experimental results show that the proposed method has better segmentation results and higher segmentation efficiency on the images with under-segmentation and incorrect segmentation, and it is meaningful for ore dressing industrial.展开更多
This article is an addendum to the 2001 paper [1] which investigated an approach to hierarchical clustering based on the level sets of a density function induced on data points in a d-dimensional feature space. We ref...This article is an addendum to the 2001 paper [1] which investigated an approach to hierarchical clustering based on the level sets of a density function induced on data points in a d-dimensional feature space. We refer to this as the “level-sets approach” to hierarchical clustering. The density functions considered in [1] were those formed as the sum of identical radial basis functions centered at the data points, each radial basis function assumed to be continuous, monotone decreasing, convex on every ray, and rising to positive infinity at its center point. Such a framework can be investigated with respect to both the Euclidean (L2) and Manhattan (L1) metrics. The addendum here puts forth some observations and questions about the level-sets approach that go beyond those in [1]. In particular, we detail and ask the following questions. How does the level-sets approach compare with other related approaches? How is the resulting hierarchical clustering affected by the choice of radial basis function? What are the structural properties of a function formed as the sum of radial basis functions? Can the levels-sets approach be theoretically validated? Is there an efficient algorithm to implement the level-sets approach?展开更多
There are many uncertain factors,such as stochastic,fuzzy and gray information in the risk analysis on natural hazard.The set pair analysis(SPA)deals effectively with the various uncertain factors contributing to eval...There are many uncertain factors,such as stochastic,fuzzy and gray information in the risk analysis on natural hazard.The set pair analysis(SPA)deals effectively with the various uncertain factors contributing to evaluation of the risk level of natural disasters.The evaluation indicators and standards of natural disasters risk are analyzed by identity-discrepancycontrary(IDC).The result,the connection numbers,still has uncertainty information.Thus,yielding the risk evaluation model of natural disasters based on connection function,which construct a set pair relation between the indicators of connection numbers and comprehensive evaluation standards,and describe uncertainty of the connection numbers by using connection function.The study showed that the proposed model takes into account only the uncertainty of risk evaluation indicator identification on natural disasters,also the uncertainty of result connection numbers.This approach gives full consideration to the uncertainty of systematic evaluation process along with the actual meaning of comprehensive evaluation functions.Therefore,this means it is able to reduce the uncertainty of final evaluation results and improve the accuracy and reasonability of evaluation results.This model is capable of reflecting actual situation of the risk evaluation on natural disaster affected by various uncertain factors and has a promotional value in the natural disaster risk assessment.展开更多
文摘In this paper we present a selective segmentation model using a dual level set variational formulation.Our variational model aims to segment all objects with one level set function(global)and the selected object,which is the closest to the geometric constraints(markers),with another level set(local).It is a combination of edge detection,markers distance function and active contour without edges.Experimental results show that our model is more robust than previous work.
基金the National Natural Science Foundation of China (6001161942, 60203003)
文摘Some basic problems on the level set methods were discussed, such as the method used to preserve the distance junction , the existence and uniqueness of solution for the level set equations. The main contribution is to prove that in a neighborhood of the initial zero level set, the level set equations with the restriction of the distance function have a unique solution, which must be the signed distance function with respect to the evolving surface. Some skillful approaches were used: Noticing that any solution for the original equation was a distance function, the original level set equations were transformed into a simpler alternative form. Moreover, since the new system was not a classical one, the system was transformed into an ordinary one, for which the implicit function method was adopted.
基金supported by the National Natural Sci-ence Foundation of China(No.52101383)the Fundamen-tal Research Funds for the Central Universities(No.3072021CF0802)+3 种基金the Key Laboratory of Advanced Marine Communication and Information Technology,Ministry of Industry and Information Technology(No.AMCIT2101-02)the Sino-Russian Cooperation Fund of Harbin Engi-neering University(No.2021HEUCRF006)the Ministry of Science and Higher Education of the Russian Federation(No.075-15-2020-934)the International Science&Technology Cooperation Program of China(No.2014DF R10240).
文摘The electric inversion technique reconstructs the subsurface medium distribution from acquired data.On the basis of electric inversion,objects buried under the earth or seabed,such as pipelines and unexploded ordnance,are detected and located in a contactless manner.However,the process of accurately reconstructing the shape of the target object is challenging because electric inversion is a nonlinear and ill-posed problem.In this work,we present an inverse multiquadric(IMQ)regularization method based on the level set function for reconstructing buried pipelines.In the case of locating underwater objects,the unknown inversion area is split into two parts,the background and the pipeline with known conductivity.The geometry of the pipeline is represented based on the level set function for achieving a noiseless inversion image.To obtain a binary image,the IMQ is used as the regularization term,which‘pushes’the level set function away from 0.We also provide an appropriate method to select the bandwidth and regularization parameters for the IMQ regularization term,resulting in reconstructed images with sharp edges.The simulation results and analysis show that the proposed method performs better than classical inversion methods.
文摘Objective To present a novel modified level set algorithm for medical image segmentation. Methods The algorithm is developed by substituting the speed function of level set algorithm with the region and gradient information of the image instead of the conventional gradient information. This new algorithm has been tested by a series of different modality medical images. Results We present various examples and also evaluate and compare the performance of our method with the classical level set method on weak boundaries and noisy images. Conclusion Experimental results show the proposed algorithm is effective and robust.
基金supported by NSFC (11201152)supported by NSFC(11371148)+4 种基金STCSM(13dz2260400)FDPHEC(20120076120001)Fundamental Research Funds for the central Universities,scut(2012zz0073)Fundamental Research Funds for the Central Universities SCUT(D2154240)Guangdong Natural Science Foundation(2014A030313230)
文摘In the paper, we consider Moran-type sets E;given by sequences {a;};and{n;};. we prove that E;may be decompose into the disjoint union of level sets. Moreover,we define three type of equivalence between two dimension functions associated to two Morantype sets, respectively, and we classify Moran-type sets by these equivalent relations.
文摘As a new method, the Level Set method had been developed to compute the interface of two-phase flow. The basic mathematical theory and the detailed method to solve the free surface hydrodynamic problem had been investigated. By using the Level Set method, the transformation of a solitary wave over a front step was simulated. The results were in good agreement with laboratory experiments.
文摘Short time existence and uniqueness for the classical motion are studied by the function of the principal curvatures of a smooth surface and the Evans and Spruck's results are generalized.
文摘A novel flotation froth image segmentation based on threshold level set method is put forward in view of the problem of over-segmentation and under-segmentation which occurs when the existing method segmented the flotation froth images. Firstly, the proposed method adopts histogram equalization to improve the contrast of the image, and then chooses the upper threshold and lower threshold from grey value of histogram of the image equalization, and complete image segmentation using the level set method. In this paper, the model which integrates edge with region level set model is utilized, and the speed energy term is introduced to segment the target. Experimental results show that the proposed method has better segmentation results and higher segmentation efficiency on the images with under-segmentation and incorrect segmentation, and it is meaningful for ore dressing industrial.
文摘This article is an addendum to the 2001 paper [1] which investigated an approach to hierarchical clustering based on the level sets of a density function induced on data points in a d-dimensional feature space. We refer to this as the “level-sets approach” to hierarchical clustering. The density functions considered in [1] were those formed as the sum of identical radial basis functions centered at the data points, each radial basis function assumed to be continuous, monotone decreasing, convex on every ray, and rising to positive infinity at its center point. Such a framework can be investigated with respect to both the Euclidean (L2) and Manhattan (L1) metrics. The addendum here puts forth some observations and questions about the level-sets approach that go beyond those in [1]. In particular, we detail and ask the following questions. How does the level-sets approach compare with other related approaches? How is the resulting hierarchical clustering affected by the choice of radial basis function? What are the structural properties of a function formed as the sum of radial basis functions? Can the levels-sets approach be theoretically validated? Is there an efficient algorithm to implement the level-sets approach?
基金supported by the auspices of National Natural Science Foundation of China(No.51079037)Opening Foundation of Chengdu Institute of Plateau Meteorology,China Meteorological Administration(LPM2011002)Natural Science Foundation of Anhui Province(No.1208085ME75)
文摘There are many uncertain factors,such as stochastic,fuzzy and gray information in the risk analysis on natural hazard.The set pair analysis(SPA)deals effectively with the various uncertain factors contributing to evaluation of the risk level of natural disasters.The evaluation indicators and standards of natural disasters risk are analyzed by identity-discrepancycontrary(IDC).The result,the connection numbers,still has uncertainty information.Thus,yielding the risk evaluation model of natural disasters based on connection function,which construct a set pair relation between the indicators of connection numbers and comprehensive evaluation standards,and describe uncertainty of the connection numbers by using connection function.The study showed that the proposed model takes into account only the uncertainty of risk evaluation indicator identification on natural disasters,also the uncertainty of result connection numbers.This approach gives full consideration to the uncertainty of systematic evaluation process along with the actual meaning of comprehensive evaluation functions.Therefore,this means it is able to reduce the uncertainty of final evaluation results and improve the accuracy and reasonability of evaluation results.This model is capable of reflecting actual situation of the risk evaluation on natural disaster affected by various uncertain factors and has a promotional value in the natural disaster risk assessment.
